Question #de65e

1 Answer
Raknos
Oct 1, 2017

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

Explanation:

I=9intsecx*sec^2xdx
Using integration by parts
=9secx intsec^2xdx-9int(d/dx secx*intsec^2xdx)dx
=9secx*tanx-9int(secx*tanx*tanx)dx
=9secx*tanx-9int(secx*tan^2x)dx
=9secx*tanx-9int(secx*(sec^2x-1)dx
I=9secx*tanx-9intsec^3xdx+9intsecxdx
I=9secx*tanx-9I+9intsecxdx
10I=9secx*tanx+9ln|secx+tanx|+C
I=9/10 secx*tanx+9/10 ln|secx+tanx|+C

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