How do you find the antiderivative of #(cosx+secx)^2#?
1 Answer
Mar 9, 2018
# int \ (cosx+secx)^2 \ dx = sin(2x)/4 + 5/2x + tanx + C #
Explanation:
We seek:
# I = int \ (cosx+secx)^2 \ dx #
Which we can write:
# I = int \ cos^2x + 2cosxsecx + sec^2x \ dx #
# \ \ = int \ cos^2x + 2 + sec^2x \ dx #
# \ \ = int \ (cos(2x)+1)/2 + 2 + sec^2x \ dx #
# \ \ = int \ cos(2x)/2 + 5/2 + sec^2x \ dx #
All integrand functions are standard results, so we can now readily integrate to get:
# I = sin(2x)/4 + 5/2x + tanx + C #
