Question

∫xarctanxdx

能不能全写下来。。。。。。。

Answer 1

∫xarctanxdx
=∫arctanxd(0.5*x^2)
=0.5*x^2 *arctanx-∫0.5*x^2d(arctanx)
=0.5*x^2 *arctanx-∫0.5*x^2/(1+x^2)dx
=0.5*x^2 *arctanx-0.5*∫(1-(1/(1+x^2))dx
=0.5*x^2 *arctanx-0.5*∫dx+0.5*∫(1/(1+x^2))dx
=0.5*x^2 *arctanx-0.5x+0.5*arctanx+C

主要就是灵活运用凑微分和部分积分法
就是dontknow 说的极是:疏忽疏忽

Answer 2

第二步中间是减号!!!!!!!!!!