Integral involving a power of the Arctan: Find .

Since a power of the Arctan is present in the integrand, we may be able to apply the Power Rule for Integration. To check this, substitute w for the Arctan:

Let .

Using the Derivative of the Arctan, we get

, or .

Now we substitute these results into the original equation:

.

Next apply the Power Rule of Integration:

.

Finally, we convert back to a function of x by replacing w: