Question

求不定积分∫(1/x^2)arctanxdx

尽可能详细

Answer 1

∫1/(1+x^2)*arctanxdx
=∫arctanx[dx/(1+x^2)]
=∫arctanxd(arctanx)
=(arctanx)²/2+C

Answer 2

syms x
int(atan(x)/x^2)

ans =

-1/x*atan(x)-1/2*log(x^2+1)+log(x)