不定积分[x(tanx)^2]dx用分部积分法如何求?

问题描述:

不定积分[x(tanx)^2]dx用分部积分法如何求?

解;
∫x(tanx)^2dx
=∫x[(secx)^2-1]dx
=∫x (secx)^2 dx-∫x dx
=∫x d(tanx) -x^2/2(下面用分步积分法)
=xtanx-∫tanxdx -x^2/2
=xtanx+ln|cosx|-x^2/2+C
(C是常数)