Question #89694

1 Answer
Apr 14, 2017

cosx1+cos2xdx=x+sinxcosx2+C

Explanation:

Use the trigonometric identity:

cos2x=1+cos2x2

so:

cosx1+cos2x=cosx2cos2x=2cos2x=1+cos2x2

and:

cosx1+cos2xdx=1+cos2x2dx

cosx1+cos2xdx=12dx+122cos2xd(2x)

cosx1+cos2xdx=x2+sin2x22+C

cosx1+cos2xdx=x+sinxcosx2+C