=∫xsex^3xdsecx
=(1/4)∫xdsec^4x
=(1/4)xsec^4x-(1/4)∫sec^4xdx
=(1/4)xsec^4x-(1/4)∫sec^2xdtanx
=(1/4)xsec^4x-(1/4)∫(tan^2x+1)dxtanx
=(1/4)xsec^4x-(1/12)tan^3x-(1/4)tanx+C
=∫xsex^3xdsecx
=(1/4)∫xdsec^4x
=(1/4)xsec^4x-(1/4)∫sec^4xdx
=(1/4)xsec^4x-(1/4)∫sec^2xdtanx
=(1/4)xsec^4x-(1/4)∫(tan^2x+1)dxtanx
=(1/4)xsec^4x-(1/12)tan^3x-(1/4)tanx+C