# Integral of (cos(x))^2 in the hard way

#### Yankel

##### Active member
Hello guys

I am trying to solve the integral of cos(x) squared, i.e. (cos(x))^2, but not using the trigonometric identity of this function, but using integration by parts.

I tried turning it into 1*(cos(x))^2, but I didn't go too far, maybe did something wrong.

Am I on the right direction ?

cheers

#### Opalg

##### MHB Oldtimer
Staff member
Hello guys

I am trying to solve the integral of cos(x) squared, i.e. (cos(x))^2, but not using the trigonometric identity of this function, but using integration by parts.

I tried turning it into 1*(cos(x))^2, but I didn't go too far, maybe did something wrong.

Am I on the right direction ?
You would do better to write it as cos(x)*cos(x). After integrating by parts, use the fact that sin^2 = 1 – cos^2.

#### MarkFL

$$\displaystyle u=\cos(x)\,\therefore\,du=-\sin(x)\,dx$$
$$\displaystyle dv=\cos(x)\,dx\,\therefore\,v=\sin(x)$$