# Integration by Trig Substitution: Example 2

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

For this example, we will use the following integral:

So in this case, our **“x” is really “x + 5”** and our **a is 1**.

Notice the sneaky trick to force it into the x^{2} + a^{2} format:

we separated 26 into 25 + 1.

Think of math as a puzzle; you need to move pieces around in order to solve it.

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

## Step 3: Make the substitution & simplify

Now we substitute into our original equation:

**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.

Because we started with **x + 5 = tan (u)**, we can substitute **(x + 5)** for **tan(u)**.

From a trig identity, we know that sec^{2}(u) = tan^{2}(u) + 1,

so for sec(u), we can substitute the square root of tan^{2}(u) + 1,

but remember that tan(u) is x + 5, so putting all of this together, we get:

I hope this example helped. Practice with some problems that have answers so you can check your work 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!