Question

急急急 求大神解答 谢谢！！！

Answer 1

∫ arctanx /x^2 dx
=-∫ arctanx d(1/x)
=-arctanx/x + ∫ dx/[x(1+x^2)]

=-arctanx/x + ∫ [1/x - x/(1+x^2) ] dx
=-arctanx/x + ln|x| - (1/2)ln|1+x^2| +C
=-arctanx/x + ln|x/√(1+x^2) | +C
∫(1->∞) arctanx /x^2 dx
=[-arctanx/x + ln|x/√(1+x^2) |] | (1->∞)
=π/4 + (1/2)ln2 + lim(x->∞ ) { -arctanx/x + ln(x/√(1+x^2)) }
=π/4 + (1/2)ln2 + 0
=π/4 + (1/2)ln2