I=9∫secx⋅sec2xdx
Using integration by parts =9secx∫sec2xdx−9∫(ddxsecx⋅∫sec2xdx)dx =9secx⋅tanx−9∫(secx⋅tanx⋅tanx)dx =9secx⋅tanx−9∫(secx⋅tan2x)dx =9secx⋅tanx−9∫(secx⋅(sec2x−1)dx I=9secx⋅tanx−9∫sec3xdx+9∫secxdx I=9secx⋅tanx−9I+9∫secxdx 10I=9secx⋅tanx+9ln|secx+tanx|+C I=910secx⋅tanx+910ln|secx+tanx|+C