# Find the Antiderivative xsin(x^2)

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 . Then , so . Rewrite using and .
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.
Simplify.
Combine and .
Replace all occurrences of with .
Reorder terms.
The answer is the antiderivative of the function .
Find the Antiderivative xsin(x^2)