求∫x*tan^2x dx
问题描述：
求∫x*tan^2x dx
答
原式=∫x(sec²x-1)dx
=∫xsec²xdx-∫xdx
=∫xdtanx-x²/2
=xtanx--∫tanxdx-x²/2
=xtanx--∫sinx/cosx dx-x²/2
=xtanx+∫dcosx/cosx-x²/2
=xtanx+ln|cosx|-x²/2+C