求不定积分∫xtanx(sec^2)xdx!

题目

求不定积分∫xtanx(sec^2)xdx!

答案

原式=∫xsinx/cos^3(x)*dx
=-∫x/cos^3(x)*d(cosx)
=1/2∫xd(1/cos^2(x))
=x/(2cos^2(x))-1/2∫dx/cos^2(x)
=x/(2cos^2(x))-tanx/2+C