We have some choices for u in this example: sin^-14x, 1 − 16x², or √(1 − 16x²). Only one of these gives a result for du that we can use to integrate the given expression, and that's the first one.

So we let u = sin^-14x.

Then, using the derivative of the inverse sine, we have:

We divide both sides by 4 so we can substitue into our original expression:

Now to complete the required subsitution (u = sin^-14x and the du/4 expression we just found):

The expression on the right is a simple integral:

To complete the porblem, we substitute sin^-14x for u: