求∫arctanx/x^2dx

求∫arctanx/x^2dx
求∫arctanx/x^2dx

求∫arctanx/x^2dx
∫arctanx/x^2dx
=-∫arctanxd(1/x)
=-1/x*arctanx+∫1/x*1/(1+x²)dx
=-arctanx/x+∫(1/x-x/(1+x²))dx
=-arctanx/x+lnx-1/2∫1/(1+x²)d(1+x²)
=-arctanx/x+lnx-1/2*ln(1+x²)+c