IntegralsDefinite_1.gif

Table of Integrals

A. Dieckmann, Physikalisches Institut der Uni Bonn

IntegralsDefinite_2.gif

IntegralsDefinite_3.gif

This integral table contains hundreds of expressions: indefinite and definite integrals of elliptic integrals, of square roots, arcustangents and a few more exotic functions. Most of them are not found in Gradsteyn-Ryzhik.

IntegralsDefinite_4.gif

Sometimes m, n, k denote real parameters and are restricted mostly to 0<{m, n, k}<1, at times they represent natural numbers.

Results may be valid outside of the given region of parameters, but should always be checked numerically!

Definite Integrals:

Substitute   IntegralsDefinite_5.gif   and the Feynman-Hibbs Integral can be calculated with Mathematica:

IntegralsDefinite_6.gif

IntegralsDefinite_7.gif

IntegralsDefinite_8.gif

IntegralsDefinite_9.gif

IntegralsDefinite_10.gif

IntegralsDefinite_11.gif

IntegralsDefinite_12.gif

IntegralsDefinite_13.gif

IntegralsDefinite_14.gif

IntegralsDefinite_15.gif

IntegralsDefinite_16.gif

IntegralsDefinite_17.gif

IntegralsDefinite_18.gif

IntegralsDefinite_19.gif

IntegralsDefinite_20.gif

IntegralsDefinite_21.gif

IntegralsDefinite_22.gif

IntegralsDefinite_23.gif

IntegralsDefinite_24.gif

IntegralsDefinite_25.gif

IntegralsDefinite_26.gif

IntegralsDefinite_27.gif

IntegralsDefinite_28.gif

IntegralsDefinite_29.gif

IntegralsDefinite_30.gif

IntegralsDefinite_31.gif

IntegralsDefinite_32.gif

IntegralsDefinite_33.gif

IntegralsDefinite_34.gif

IntegralsDefinite_35.gif

IntegralsDefinite_36.gif

IntegralsDefinite_37.gif

IntegralsDefinite_38.gif

IntegralsDefinite_39.gif

IntegralsDefinite_40.gif

IntegralsDefinite_41.gif

IntegralsDefinite_42.gif

IntegralsDefinite_43.gif

IntegralsDefinite_44.gif

IntegralsDefinite_45.gif

IntegralsDefinite_46.gif

IntegralsDefinite_47.gif

IntegralsDefinite_48.gif

IntegralsDefinite_49.gif

IntegralsDefinite_50.gif

IntegralsDefinite_51.gif

IntegralsDefinite_52.gif

IntegralsDefinite_53.gif

IntegralsDefinite_54.gif

IntegralsDefinite_55.gif

IntegralsDefinite_56.gif

IntegralsDefinite_57.gif

IntegralsDefinite_58.gif

IntegralsDefinite_59.gif

IntegralsDefinite_60.gif

IntegralsDefinite_61.gif

IntegralsDefinite_62.gif

IntegralsDefinite_63.gif

IntegralsDefinite_64.gif

IntegralsDefinite_65.gif

IntegralsDefinite_66.gif

IntegralsDefinite_67.gif

IntegralsDefinite_68.gif

IntegralsDefinite_69.gif

IntegralsDefinite_70.gif

IntegralsDefinite_71.gif

IntegralsDefinite_72.gif

IntegralsDefinite_73.gif

IntegralsDefinite_74.gif

IntegralsDefinite_75.gif

IntegralsDefinite_76.gif

IntegralsDefinite_77.gif

IntegralsDefinite_78.gif

IntegralsDefinite_79.gif

IntegralsDefinite_80.gif

IntegralsDefinite_81.gif

IntegralsDefinite_82.gif

IntegralsDefinite_83.gif

IntegralsDefinite_84.gif

IntegralsDefinite_85.gif

IntegralsDefinite_86.gif

IntegralsDefinite_87.gif

IntegralsDefinite_88.gif

IntegralsDefinite_89.gif

IntegralsDefinite_90.gif

IntegralsDefinite_91.gif

To see a nice cancellation of singularities at work plot the next expression around c = negative Integer:

IntegralsDefinite_92.gif

IntegralsDefinite_93.gif

IntegralsDefinite_94.gif

IntegralsDefinite_95.gif

IntegralsDefinite_96.gif

IntegralsDefinite_97.gif

IntegralsDefinite_98.gif

IntegralsDefinite_99.gif

IntegralsDefinite_100.gif

IntegralsDefinite_101.gif

IntegralsDefinite_102.gif

IntegralsDefinite_103.gif

IntegralsDefinite_104.gif

this is a special case of the next integral below (m = -1 / 2).

IntegralsDefinite_105.gif

IntegralsDefinite_106.gif

IntegralsDefinite_107.gif

IntegralsDefinite_108.gif

IntegralsDefinite_109.gif

IntegralsDefinite_110.gif

IntegralsDefinite_111.gif

IntegralsDefinite_112.gif

IntegralsDefinite_113.gif

IntegralsDefinite_114.gif

IntegralsDefinite_115.gif

IntegralsDefinite_116.gif

IntegralsDefinite_117.gif

IntegralsDefinite_118.gif

IntegralsDefinite_119.gif

IntegralsDefinite_120.gif

IntegralsDefinite_121.gif

IntegralsDefinite_122.gif

IntegralsDefinite_123.gif

IntegralsDefinite_124.gif

IntegralsDefinite_125.gif

IntegralsDefinite_126.gif

IntegralsDefinite_127.gif

IntegralsDefinite_128.gif

IntegralsDefinite_129.gif

IntegralsDefinite_130.gif

IntegralsDefinite_131.gif

IntegralsDefinite_132.gif

IntegralsDefinite_133.gif

IntegralsDefinite_134.gif

IntegralsDefinite_135.gif

IntegralsDefinite_136.gif

IntegralsDefinite_137.gif

IntegralsDefinite_138.gif

IntegralsDefinite_139.gif

IntegralsDefinite_140.gif

IntegralsDefinite_141.gif

IntegralsDefinite_142.gif

IntegralsDefinite_143.gif

IntegralsDefinite_144.gif

IntegralsDefinite_145.gif

IntegralsDefinite_146.gif

IntegralsDefinite_147.gif

IntegralsDefinite_148.gif

IntegralsDefinite_149.gif

IntegralsDefinite_150.gif

IntegralsDefinite_151.gif

IntegralsDefinite_152.gif

IntegralsDefinite_153.gif

IntegralsDefinite_154.gif

IntegralsDefinite_155.gif

IntegralsDefinite_156.gif

IntegralsDefinite_157.gif

IntegralsDefinite_158.gif

IntegralsDefinite_159.gif

IntegralsDefinite_160.gif

IntegralsDefinite_161.gif

IntegralsDefinite_162.gif

IntegralsDefinite_163.gif

IntegralsDefinite_164.gif

IntegralsDefinite_165.gif

IntegralsDefinite_166.gif

IntegralsDefinite_167.gif

IntegralsDefinite_168.gif

IntegralsDefinite_169.gif

IntegralsDefinite_170.gif

IntegralsDefinite_171.gif

IntegralsDefinite_172.gif

IntegralsDefinite_173.gif

IntegralsDefinite_174.gif

IntegralsDefinite_175.gif

IntegralsDefinite_176.gif

IntegralsDefinite_177.gif

IntegralsDefinite_178.gif

IntegralsDefinite_179.gif

IntegralsDefinite_180.gif

IntegralsDefinite_181.gif

IntegralsDefinite_182.gif

IntegralsDefinite_183.gif

IntegralsDefinite_184.gif

IntegralsDefinite_185.gif

IntegralsDefinite_186.gif

IntegralsDefinite_187.gif

IntegralsDefinite_188.gif

IntegralsDefinite_189.gif

IntegralsDefinite_190.gif

IntegralsDefinite_191.gif

IntegralsDefinite_192.gif

IntegralsDefinite_193.gif

IntegralsDefinite_194.gif

IntegralsDefinite_195.gif

IntegralsDefinite_196.gif

IntegralsDefinite_197.gif

IntegralsDefinite_198.gif

IntegralsDefinite_199.gif

IntegralsDefinite_200.gif

IntegralsDefinite_201.gif

IntegralsDefinite_202.gif

IntegralsDefinite_203.gif

IntegralsDefinite_204.gif

IntegralsDefinite_205.gif

IntegralsDefinite_206.gif

IntegralsDefinite_207.gif

IntegralsDefinite_208.gif

IntegralsDefinite_209.gif

IntegralsDefinite_210.gif

IntegralsDefinite_211.gif

IntegralsDefinite_212.gif

IntegralsDefinite_213.gif

IntegralsDefinite_214.gif

IntegralsDefinite_215.gif

IntegralsDefinite_216.gif

IntegralsDefinite_217.gif

IntegralsDefinite_218.gif

IntegralsDefinite_219.gif

IntegralsDefinite_220.gif

IntegralsDefinite_221.gif

IntegralsDefinite_222.gif

IntegralsDefinite_223.gif

IntegralsDefinite_224.gif

IntegralsDefinite_225.gif

IntegralsDefinite_226.gif

IntegralsDefinite_227.gif

IntegralsDefinite_228.gif

IntegralsDefinite_229.gif

IntegralsDefinite_230.gif

IntegralsDefinite_231.gif

IntegralsDefinite_232.gif

IntegralsDefinite_233.gif

IntegralsDefinite_234.gif

IntegralsDefinite_235.gif

IntegralsDefinite_236.gif

IntegralsDefinite_237.gif

IntegralsDefinite_238.gif

IntegralsDefinite_239.gif

IntegralsDefinite_240.gif

IntegralsDefinite_241.gif

IntegralsDefinite_242.gif

IntegralsDefinite_243.gif

IntegralsDefinite_244.gif

IntegralsDefinite_245.gif

IntegralsDefinite_246.gif

IntegralsDefinite_247.gif

IntegralsDefinite_248.gif

IntegralsDefinite_249.gif

IntegralsDefinite_250.gif

IntegralsDefinite_251.gif

IntegralsDefinite_252.gif

IntegralsDefinite_253.gif

IntegralsDefinite_254.gif

IntegralsDefinite_255.gif

IntegralsDefinite_256.gif

IntegralsDefinite_257.gif

IntegralsDefinite_258.gif

IntegralsDefinite_259.gif

IntegralsDefinite_260.gif

IntegralsDefinite_261.gif

IntegralsDefinite_262.gif

IntegralsDefinite_263.gif

IntegralsDefinite_264.gif

IntegralsDefinite_265.gif

IntegralsDefinite_266.gif

IntegralsDefinite_267.gif

IntegralsDefinite_268.gif

IntegralsDefinite_269.gif

IntegralsDefinite_270.gif

IntegralsDefinite_271.gif

IntegralsDefinite_272.gif

IntegralsDefinite_273.gif

IntegralsDefinite_274.gif

IntegralsDefinite_275.gif

IntegralsDefinite_276.gif

IntegralsDefinite_277.gif

IntegralsDefinite_278.gif

IntegralsDefinite_279.gif

IntegralsDefinite_280.gif

IntegralsDefinite_281.gif

IntegralsDefinite_282.gif

IntegralsDefinite_283.gif

IntegralsDefinite_284.gif

IntegralsDefinite_285.gif

IntegralsDefinite_286.gif

IntegralsDefinite_287.gif

IntegralsDefinite_288.gif

IntegralsDefinite_289.gif

IntegralsDefinite_290.gif

IntegralsDefinite_291.gif

IntegralsDefinite_292.gif

IntegralsDefinite_293.gif

IntegralsDefinite_294.gif

IntegralsDefinite_295.gif

IntegralsDefinite_296.gif

IntegralsDefinite_297.gif

IntegralsDefinite_298.gif

IntegralsDefinite_299.gif

IntegralsDefinite_300.gif

IntegralsDefinite_301.gif

IntegralsDefinite_302.gif

IntegralsDefinite_303.gif

IntegralsDefinite_304.gif

IntegralsDefinite_305.gif

IntegralsDefinite_306.gif

IntegralsDefinite_307.gif

IntegralsDefinite_308.gif

IntegralsDefinite_309.gif

IntegralsDefinite_310.gif

IntegralsDefinite_311.gif

IntegralsDefinite_312.gif

IntegralsDefinite_313.gif

IntegralsDefinite_314.gif

IntegralsDefinite_315.gif

IntegralsDefinite_316.gif

IntegralsDefinite_317.gif

IntegralsDefinite_318.gif

IntegralsDefinite_319.gif

IntegralsDefinite_320.gif

IntegralsDefinite_321.gif

IntegralsDefinite_322.gif

IntegralsDefinite_323.gif

IntegralsDefinite_324.gif

IntegralsDefinite_325.gif

IntegralsDefinite_326.gif

IntegralsDefinite_327.gif

IntegralsDefinite_328.gif

IntegralsDefinite_329.gif

IntegralsDefinite_330.gif

IntegralsDefinite_331.gif

IntegralsDefinite_332.gif

IntegralsDefinite_333.gif

IntegralsDefinite_334.gif

IntegralsDefinite_335.gif

IntegralsDefinite_336.gif

IntegralsDefinite_337.gif

IntegralsDefinite_338.gif

IntegralsDefinite_339.gif

IntegralsDefinite_340.gif

IntegralsDefinite_341.gif

IntegralsDefinite_342.gif

IntegralsDefinite_343.gif

IntegralsDefinite_344.gif

IntegralsDefinite_345.gif

IntegralsDefinite_346.gif

IntegralsDefinite_347.gif

IntegralsDefinite_348.gif

IntegralsDefinite_349.gif

IntegralsDefinite_350.gif

IntegralsDefinite_351.gif

IntegralsDefinite_352.gif

IntegralsDefinite_353.gif

IntegralsDefinite_354.gif

IntegralsDefinite_355.gif

IntegralsDefinite_356.gif

IntegralsDefinite_357.gif

IntegralsDefinite_358.gif

IntegralsDefinite_359.gif

IntegralsDefinite_360.gif

IntegralsDefinite_361.gif

IntegralsDefinite_362.gif

IntegralsDefinite_363.gif

IntegralsDefinite_364.gif

IntegralsDefinite_365.gif

IntegralsDefinite_366.gif

IntegralsDefinite_367.gif

IntegralsDefinite_368.gif

IntegralsDefinite_369.gif

IntegralsDefinite_370.gif

IntegralsDefinite_371.gif

IntegralsDefinite_372.gif

IntegralsDefinite_373.gif

IntegralsDefinite_374.gif

IntegralsDefinite_375.gif

IntegralsDefinite_376.gif

IntegralsDefinite_377.gif

IntegralsDefinite_378.gif

IntegralsDefinite_379.gif

IntegralsDefinite_380.gif

IntegralsDefinite_381.gif

IntegralsDefinite_382.gif

IntegralsDefinite_383.gif

IntegralsDefinite_384.gif

IntegralsDefinite_385.gif

IntegralsDefinite_386.gif

IntegralsDefinite_387.gif

IntegralsDefinite_388.gif

IntegralsDefinite_389.gif

IntegralsDefinite_390.gif

IntegralsDefinite_391.gif

IntegralsDefinite_392.gif

IntegralsDefinite_393.gif

IntegralsDefinite_394.gif

IntegralsDefinite_395.gif

IntegralsDefinite_396.gif

IntegralsDefinite_397.gif

IntegralsDefinite_398.gif

IntegralsDefinite_399.gif

IntegralsDefinite_400.gif

IntegralsDefinite_401.gif

IntegralsDefinite_402.gif

IntegralsDefinite_403.gif

IntegralsDefinite_404.gif

IntegralsDefinite_405.gif

IntegralsDefinite_406.gif

IntegralsDefinite_407.gif

IntegralsDefinite_408.gif

IntegralsDefinite_409.gif

IntegralsDefinite_410.gif

IntegralsDefinite_411.gif

IntegralsDefinite_412.gif

IntegralsDefinite_413.gif

IntegralsDefinite_414.gif

IntegralsDefinite_415.gif

IntegralsDefinite_416.gif

IntegralsDefinite_417.gif

IntegralsDefinite_418.gif

IntegralsDefinite_419.gif

IntegralsDefinite_420.gif

IntegralsDefinite_421.gif

IntegralsDefinite_422.gif

IntegralsDefinite_423.gif

IntegralsDefinite_424.gif

IntegralsDefinite_425.gif

in the following expressions (∫ f(x)/(a x^2 + b x + c ) dx)   we abbreviate s = IntegralsDefinite_426.gif:

IntegralsDefinite_427.gif

IntegralsDefinite_428.gif

IntegralsDefinite_429.gif

the values at integer n can be found approximately by setting n near to an integer IntegralsDefinite_430.gif.

IntegralsDefinite_431.gif

IntegralsDefinite_432.gif

IntegralsDefinite_433.gif

IntegralsDefinite_434.gif

IntegralsDefinite_435.gif

IntegralsDefinite_436.gif

IntegralsDefinite_437.gif

IntegralsDefinite_438.gif

IntegralsDefinite_439.gif

IntegralsDefinite_440.gif

IntegralsDefinite_441.gif

IntegralsDefinite_442.gif

IntegralsDefinite_443.gif

IntegralsDefinite_444.gif

IntegralsDefinite_445.gif

IntegralsDefinite_446.gif

IntegralsDefinite_447.gif

IntegralsDefinite_448.gif

IntegralsDefinite_449.gif

IntegralsDefinite_450.gif

IntegralsDefinite_451.gif

IntegralsDefinite_452.gif

IntegralsDefinite_453.gif

IntegralsDefinite_454.gif

in the following expressions (∫ f(x)/(a x^4 + b x^2 + c ) dx)   we abbreviate s = IntegralsDefinite_455.gif:

IntegralsDefinite_456.gif

IntegralsDefinite_457.gif

IntegralsDefinite_458.gif

IntegralsDefinite_459.gif

IntegralsDefinite_460.gif

IntegralsDefinite_461.gif

IntegralsDefinite_462.gif

IntegralsDefinite_463.gif

IntegralsDefinite_464.gif

IntegralsDefinite_465.gif

IntegralsDefinite_466.gif

IntegralsDefinite_467.gif

IntegralsDefinite_468.gif

IntegralsDefinite_469.gif

IntegralsDefinite_470.gif

IntegralsDefinite_471.gif

IntegralsDefinite_472.gif

IntegralsDefinite_473.gif

IntegralsDefinite_474.gif

IntegralsDefinite_475.gif

IntegralsDefinite_476.gif

IntegralsDefinite_477.gif

IntegralsDefinite_478.gif

IntegralsDefinite_479.gif

IntegralsDefinite_480.gif

IntegralsDefinite_481.gif

IntegralsDefinite_482.gif

IntegralsDefinite_483.gif

IntegralsDefinite_484.gif

IntegralsDefinite_485.gif

IntegralsDefinite_486.gif

IntegralsDefinite_487.gif

IntegralsDefinite_488.gif

IntegralsDefinite_489.gif

IntegralsDefinite_490.gif

IntegralsDefinite_491.gif

IntegralsDefinite_492.gif

IntegralsDefinite_493.gif

IntegralsDefinite_494.gif

IntegralsDefinite_495.gif

IntegralsDefinite_496.gif

IntegralsDefinite_497.gif

IntegralsDefinite_498.gif

IntegralsDefinite_499.gif

IntegralsDefinite_500.gif

IntegralsDefinite_501.gif

IntegralsDefinite_502.gif

IntegralsDefinite_503.gif

IntegralsDefinite_504.gif

IntegralsDefinite_505.gif

IntegralsDefinite_506.gif

IntegralsDefinite_507.gif

IntegralsDefinite_508.gif

IntegralsDefinite_509.gif

IntegralsDefinite_510.gif

IntegralsDefinite_511.gif

IntegralsDefinite_512.gif

IntegralsDefinite_513.gif

IntegralsDefinite_514.gif

IntegralsDefinite_515.gif

IntegralsDefinite_516.gif

IntegralsDefinite_517.gif

IntegralsDefinite_518.gif

IntegralsDefinite_519.gif

IntegralsDefinite_520.gif

IntegralsDefinite_521.gif

IntegralsDefinite_522.gif

IntegralsDefinite_523.gif

IntegralsDefinite_524.gif

IntegralsDefinite_525.gif

IntegralsDefinite_526.gif

IntegralsDefinite_527.gif

IntegralsDefinite_528.gif

IntegralsDefinite_529.gif

IntegralsDefinite_530.gif

IntegralsDefinite_531.gif

IntegralsDefinite_532.gif

IntegralsDefinite_533.gif

IntegralsDefinite_534.gif

IntegralsDefinite_535.gif

IntegralsDefinite_536.gif

IntegralsDefinite_537.gif

IntegralsDefinite_538.gif

IntegralsDefinite_539.gif

IntegralsDefinite_540.gif

IntegralsDefinite_541.gif

IntegralsDefinite_542.gif

IntegralsDefinite_543.gif

IntegralsDefinite_544.gif

IntegralsDefinite_545.gif

IntegralsDefinite_546.gif

IntegralsDefinite_547.gif

IntegralsDefinite_548.gif

IntegralsDefinite_549.gif

IntegralsDefinite_550.gif

IntegralsDefinite_551.gif

IntegralsDefinite_552.gif

IntegralsDefinite_553.gif

IntegralsDefinite_554.gif

IntegralsDefinite_555.gif

IntegralsDefinite_556.gif

IntegralsDefinite_557.gif

IntegralsDefinite_558.gif

IntegralsDefinite_559.gif

IntegralsDefinite_560.gif

IntegralsDefinite_561.gif

IntegralsDefinite_562.gif

IntegralsDefinite_563.gif

IntegralsDefinite_564.gif

IntegralsDefinite_565.gif

IntegralsDefinite_566.gif

IntegralsDefinite_567.gif

IntegralsDefinite_568.gif

IntegralsDefinite_569.gif

IntegralsDefinite_570.gif

IntegralsDefinite_571.gif

IntegralsDefinite_572.gif

IntegralsDefinite_573.gif

IntegralsDefinite_574.gif

IntegralsDefinite_575.gif

IntegralsDefinite_576.gif

IntegralsDefinite_577.gif

IntegralsDefinite_578.gif

IntegralsDefinite_579.gif

IntegralsDefinite_580.gif

IntegralsDefinite_581.gif

IntegralsDefinite_582.gif

IntegralsDefinite_583.gif

IntegralsDefinite_584.gif

IntegralsDefinite_585.gif

IntegralsDefinite_586.gif

IntegralsDefinite_587.gif

IntegralsDefinite_588.gif

IntegralsDefinite_589.gif

IntegralsDefinite_590.gif

IntegralsDefinite_591.gif

IntegralsDefinite_592.gif

IntegralsDefinite_593.gif

IntegralsDefinite_594.gif

IntegralsDefinite_595.gif

IntegralsDefinite_596.gif

IntegralsDefinite_597.gif

IntegralsDefinite_598.gif

IntegralsDefinite_599.gif

IntegralsDefinite_600.gif

IntegralsDefinite_601.gif

IntegralsDefinite_602.gif

IntegralsDefinite_603.gif

IntegralsDefinite_604.gif

IntegralsDefinite_605.gif

IntegralsDefinite_606.gif

IntegralsDefinite_607.gif

IntegralsDefinite_608.gif

IntegralsDefinite_609.gif

IntegralsDefinite_610.gif

IntegralsDefinite_611.gif

IntegralsDefinite_612.gif

IntegralsDefinite_613.gif

IntegralsDefinite_614.gif

IntegralsDefinite_615.gif

IntegralsDefinite_616.gif

IntegralsDefinite_617.gif

IntegralsDefinite_618.gif

IntegralsDefinite_619.gif

IntegralsDefinite_620.gif

IntegralsDefinite_621.gif

IntegralsDefinite_622.gif

IntegralsDefinite_623.gif

IntegralsDefinite_624.gif

IntegralsDefinite_625.gif

IntegralsDefinite_626.gif

IntegralsDefinite_627.gif

IntegralsDefinite_628.gif

IntegralsDefinite_629.gif

IntegralsDefinite_630.gif

IntegralsDefinite_631.gif

IntegralsDefinite_632.gif

IntegralsDefinite_633.gif

IntegralsDefinite_634.gif

IntegralsDefinite_635.gif

IntegralsDefinite_636.gif

IntegralsDefinite_637.gif

IntegralsDefinite_638.gif

IntegralsDefinite_639.gif

IntegralsDefinite_640.gif

IntegralsDefinite_641.gif

IntegralsDefinite_642.gif

IntegralsDefinite_643.gif

IntegralsDefinite_644.gif

IntegralsDefinite_645.gif

IntegralsDefinite_646.gif

IntegralsDefinite_647.gif

IntegralsDefinite_648.gif

IntegralsDefinite_649.gif

IntegralsDefinite_650.gif

IntegralsDefinite_651.gif

IntegralsDefinite_652.gif

IntegralsDefinite_653.gif

IntegralsDefinite_654.gif

IntegralsDefinite_655.gif

Master formula of Boros and Moll:

IntegralsDefinite_656.gif

IntegralsDefinite_657.gif

IntegralsDefinite_658.gif

IntegralsDefinite_659.gif

IntegralsDefinite_660.gif

IntegralsDefinite_661.gif

IntegralsDefinite_662.gif

Here the result is a threefold sum shown in Mathematica syntax:
KSubsets[aList, k] is in Package DiscreteMath`Combinatorica` and gives a list of all subsets with k elements of aList .
For n=3 the sum is IntegralsDefinite_663.gif.
<<DiscreteMath`Combinatorica`

IntegralsDefinite_664.gif

IntegralsDefinite_665.gif

IntegralsDefinite_666.gif

Created with the Wolfram Language      Download Page    Indefinite Integrals    Products and Series