Question

How do you integrate `int(sinx+cosx)^2`?

Answer 1

The answer is: `x-1/2cos2x+c`.

`int(sinx+cosx)^2dx=int(sin^2x+2sinxcosx+cos^2x)dx=`

`=int(1+sin2x)dx=intdx+1/2int2sin2xdx=`

`=x-1/2cos2x+c`.