∫(secx)^3 dx
=∫ dx/(cosx)^3
=∫d(sinx)/(cosx)^4, 令t=sinx
=∫dt*/(1-t^4)
=0.5∫dt*[1/(1-t^2)+1/(1+t^2)]
=0.5∫dt*[ 0.5/(1-t)+0.5/(1+t)+1/(1+t^2)]
=0.5[0.5ln|(1+t)/(1-t)|+arctant]+C
=1/4*ln|(1+sinx)/(1-sinx)|+1/2*arctan(sinx)+C
追问有没有分步积分法的啊
追答分部积分法:
∫secx^3 dx
=∫secxdtanx
=secx*tanx-∫tanx dsecx
=secx*tanx-∫tanx^2secx dsecx
=secx*tanx-∫secx^3dx+∫secx dx
∫(secx)^3dx=(secx*tanx+∫secxdx)/2=(secx*tanx+ln|secx+tanx|)/2+C