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What is the antiderivative of #1/cosx(2+sinx)#?

1 Answer

Mar 5, 2017

#int frac{sinx+2}{cosx}dx#
#=ln|secx|+2ln|secx+tanx|+C#

Explanation:

#int frac{sinx+2}{cosx}dx#

#int frac{sinx}{cosx}+frac{2}{cosx}dx#

#=int (tanx)dx + 2int(secx)dx#

#=ln|secx|+2ln|secx+tanx|+C#

Use logarithm rules:
#=ln|secx|+ln(secx+tanx)^2+C#

#=ln|(secx)(secx + tanx)^2|+C#

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