Science

Math

Humanities

... and beyond

Socratic Meta
Featured Answers

Topics

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#

Related questions

See all questions in Integrals of Trigonometric Functions

Impact of this question

3711 views around the world

You can reuse this answer
Creative Commons License