Question

定积分问题(高数)

定积分. X2/(1-x6)dx 结果是什么？平方和六次方 可以发照片

Answer 1

Answer 2

原式=1/3∫ 1/(1-x^6)d(x^3)
=1/6∫ [1/(1-x^3)+1/(1+x^3)]d(x^3)
=1/6[ln(1+x^3)-ln(1-x^3)]+C

Answer 3

∫x^2/(1-x^6) dx

let
x^3 = siny
3x^2 dx = cosy dy

∫x^2/(1-x^6) dx
=(1/3)∫secy dy
=(1/3)ln|secy+tany| + C
=(1/3)ln|√(1-x^6)+x^3| + C

Answer 4

令t等于x的立方

Answer 5

？