Question

这道不定积分题怎么求

这道不定积分怎么求

Answer 1

∫arctanx dx = xarctanx -∫xdarctanx =xarctanx -∫x/(1+x^2)dx
=xarctanx -0.5∫1/(1+x^2)d(1+x^2)
=xarctanx -0.5ln(1+x^2)+C