Compute the following integral.

First, we want to make the substitution

Therefore, we have

Now, we use integration by parts, letting

Therefore, we have

Moving the back to the left side we have

Plugging this back in above we have,

Then we note that

(If you don’t remember your trigonometry, which I usually don’t, you can figure things like this out by drawing the triangle. Since means you have a right triangle with legs of length and . That means the hypotenuse has length . So, which then gives the above result for .)

Plugging this back in we then have

(Where we absorbed into the constant in the final line, since it is just a constant.)