1.∫sin2x/cos3xdx=∫tan2xsecxdx=∫tanxdsecx=tanxsecx-∫secxdtanx
=tanxsecx-∫sec3xdx=tanxsecx-∫(sin2x+cos2x)/cos3xdx
=tanxsecx-∫secxdx-∫sin2x/cos3xdx
2∫sin2x/cos3xdx=tanxsecx-∫secxdx
∫sin2x/cos3xdx=(tanxsecx-ln|secx+tanx|)/2+C
2.∫dx/(3+sin2x)=∫dx/(4-cos2x)=∫dx/(2-cox)(2+cosx)
=1/4∫[1/(2-cox)+1/(2+cox)]dx
用万能代换t=tanx/2,原式=1/2[∫（1/（1+3t^2)dt+∫1/(3+t^2)dt]
=√3/6(arctan√3t+arctan√3/3t)+C
=√3/6(arctan√3tanx/2+arctan√3/3tanx/2)+C
3.∫xtan2xdx=∫x(sec2x-1)dx=∫xsec2xdx-∫xdx=∫xdtanx-∫xdx
=xtanx-∫tanxdx-∫xdx=xtanx+ln|cosx|-x^2/2+C