求不定积分:(x*arctanx)/[(1+x^2)^3]希望有过程.

问题描述:

求不定积分:(x*arctanx)/[(1+x^2)^3]
希望有过程.

-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.

∫(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)...