求arctanx/(x2(1+x2))的不定积分?
问题描述:
求arctanx/(x2(1+x2))的不定积分?
答
∫arctanxdx/[x^2(1+x^2)]=∫arctanxdx/x^2 -∫arctanxdx/(1+x^2)=∫arctanxd(-1/x)-∫arctanxdarctanx=-(arctanx)/x +∫(1/x)darctanx-(arctanx)^2/2=-(arctanx)/x-(arctanx)^2/2+∫dx/[x(1+x^2)]其中 ∫dx/[x(1+x^...