∫xtanxdtanx
=x(tanx)^2 - ∫tanx ( tanx + x(secx)^2 dx
=x(tanx)^2 - ∫ [(secx)^2 -1 + (1/2)x.sin2x ] dx
=x(tanx)^2 - tanx + x -(1/2)∫x.sin2x dx
=x(tanx)^2 - tanx + x +(1/4)∫x dcos2x
=x(tanx)^2 - tanx + x +(1/4)x.cos2x -(1/4) ∫cos2x dx
=x(tanx)^2 - tanx + x +(1/4)x.cos2x -(1/8) sin2x + C
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