## Step 1: See if your integral is the correct function for this technique

For this example, we will use the following integral which has been chosen because it requires this technique. ðŸ™‚

You can check it against the formats for which this technique applies on the page with the general explanation of this technique.

Note: If you are reading this on a phone, it will work better in landscape than in portrait.

## Step 2: Find u and du to substitute into your integral

## Step 3: Make the substitution & simplify

At this point, we will need to use the trig identities to simplify it into an easy-to-integrate form. First, we will multiple by a “fancy one” (^{4}/_{4}) inside the square root to force it into the x^{2} âˆ’ a^{2} format so you can identify “a” easily.

Generalizing this, **you can always find “a” by dividing the constant by the coefficient of the x ^{2} term**. You can skip all of the above work as long as you remember this. I included the long way in this example so you could see where “a” comes from rather than just memorizing it without knowing why.

This means that our **x** and **dx** will be:

**Step 4: Integrate**

**Step 5: Convert back to the original variable**

Substitute back to get the answer in terms of the variable that you started with.

**x =**, we need to solve for

^{3}/_{2}sec(u)**u**.

I hope this example helped. Keep practicing and it will get easier with experience.

If you have questions or thoughts about this or think of anything you would like to see covered, please leave a comment below!