Question #de65e

1 Answer
Oct 1, 2017

9/10 secx*tanx+9/10ln|secx+tanx|+C910secxtanx+910ln|secx+tanx|+C

Explanation:

I=9intsecx*sec^2xdxI=9secxsec2xdx
Using integration by parts
=9secx intsec^2xdx-9int(d/dx secx*intsec^2xdx)dx=9secxsec2xdx9(ddxsecxsec2xdx)dx
=9secx*tanx-9int(secx*tanx*tanx)dx=9secxtanx9(secxtanxtanx)dx
=9secx*tanx-9int(secx*tan^2x)dx=9secxtanx9(secxtan2x)dx
=9secx*tanx-9int(secx*(sec^2x-1)dx=9secxtanx9(secx(sec2x1)dx
I=9secx*tanx-9intsec^3xdx+9intsecxdxI=9secxtanx9sec3xdx+9secxdx
I=9secx*tanx-9I+9intsecxdxI=9secxtanx9I+9secxdx
10I=9secx*tanx+9ln|secx+tanx|+C10I=9secxtanx+9ln|secx+tanx|+C
I=9/10 secx*tanx+9/10 ln|secx+tanx|+CI=910secxtanx+910ln|secx+tanx|+C