求不定积分arctan(1/x)/(1+x2)dx
问题描述：
求不定积分arctan(1/x)/(1+x2)dx
答
令1/x = t
则原式=
∫arctant/(1 + 1/t²) * (-1/t²)dt
=∫-arctant/(1+t²) dt
=∫-arctant darctant
=-1/2 arctan²t + C
=-1/2 arctan(1/x²) + C