# Evaluate the integral. {eq}\displaystyle \int x^3 \sin 3 x\ dx {/eq}

## Question:

Evaluate the integral.

{eq}\displaystyle \int x^3 \sin 3 x\ dx {/eq}

## Indefinite Integrals:

An indefinite integral is an integral where the limits of integration are not specified. In looking for the solution of the indefinite integral, we include in writing the arbitrary constant C at the end of the expression. One method in evaluating an integral is through the use of integration by parts.

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The given integral is:

{eq}\int x^3\sin{3x}dx {/eq}

To solve this, we use integration by parts where

{eq}u = x^3 \\ du = 3x^2dx {/eq}

and

{eq}...