# Find the integral by integration by parts {eq}\displaystyle \int x \sin (3 x)\ dx {/eq}.

## Question:

Find the integral by integration by parts {eq}\displaystyle \int x \sin (3 x)\ dx {/eq}.

## Integration by Parts:

To use the method of integration by parts in determining the solution to the integral, we must first rewrite the integrand in the form {eq}\int u \, dv {/eq} where u and x are both integrable functions. After doing this, we can already the apply integration by parts which is given by

{eq}\displaystyle \int u \, dv=uv - \int v \, du {/eq}

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Before integrating by parts lets have:

• {eq}\displaystyle u = x {/eq}
• {eq}\displaystyle du = \, dx {/eq}
• {eq}\displaystyle dv = \sin (3x) \,...