How do I evaluate the indefinite integral int(1+cos(x))^2dx ?

1 Answer
Sep 8, 2014

int(1+cosx)^2dx=3/2x+2sinx+1/4sin2x+C

Let us look at some details.
By multiplying out the integrand,
int(1+cosx)^2dx=int(1+2cosx+cos^2x) dx
by cos^2x={1+cos2x}/2,
=int(1+2cosx+{1+cos2x}/2)dx
by cleaning us the integrand,
=int(3/2+2cosx+1/2cos2x)dx
by finding antiderivatives,
=3/2x+2sinx+1/4sin2x+C