求不定积分∫(1/x^2)arctanxdx

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求不定积分∫(1/x^2)arctanxdx求不定积分∫(1/x^2)arctanxdx求不定积分∫(1/x^2)arctanxdx∫1/(1+x^2)*arctanxdx=∫arctanx[dx/(

求不定积分∫(1/x^2)arctanxdx
求不定积分∫(1/x^2)arctanxdx

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

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

ans =

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