Question #c7592

1 Answer
Feb 26, 2018

#int cos^2x dx =(x+sinxcosx)/2+C#

Explanation:

Using the trigonometric identity:

#cos^2 alpha =(1+cos 2 alpha)/2#

we have:

#int cos^2x dx = int (1+cos 2x )/2 dx#

based on the linearity of the integral

#int cos^2x dx =1/2 int dx +1/2 int cos 2x dx#

#int cos^2x dx =x/2 +1/4 int cos 2x d (2x)#

#int cos^2x dx =x/2 +1/4 sin 2x + C#

and as #sin 2 alpha = sin alpha cos alpha#, finally:

#int cos^2x dx =(x+sinxcosx)/2+C#