Question

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

Answer 1

`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`