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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