Write the polynomial as a function of .

The function can be found by finding the indefinite integral of the derivative .

Set up the integral to solve.

Let . Find .

Differentiate .

Differentiate using the Power Rule which states that is where .

Rewrite the problem using and .

Combine and .

Since is constant with respect to , move out of the integral.

The integral of with respect to is .

Simplify.

Combine and .

Replace all occurrences of with .

Reorder terms.

The answer is the antiderivative of the function .

Find the Antiderivative xsin(x^2)