Question

求不定积分：(x*arctanx)/[(1+x^2)^3]

希望有过程。

Answer 1

∫(x*arctanx)/[(1+x^2)^3]dx
=∫(1/2)(arctanx)/[(1+x^2)^3]d(x^2+1)
=∫(1/2)(arctanx)(-1/2)d[(x^2+1)^(-2)]
=(-1/4)arctanx/(x^2+1)^2+(1/4)∫(x^2+1)^(-2)d(arctanx)
=(-1/4)arctanx/(x^2+1)^2+(1/4)∫(x^2+1)^(-2)(x^2+1)^2dx
=(-1/4)arctanx/(x^2+1)^2+(1/4)∫dx
=-arctanx/[4(x^2+1)^2]+x/4+C
C是积分任意常数。

Answer 2

-1/4*1/(1+x^2)^2*arctan(x)+1/16/(1+x^2)^2*x+3/32*x/(1+x^2)+3/32*arctan(x)

赏点分的话给你过程.