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.

Answer and Explanation: 1

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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}...

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Indefinite Integrals as Anti Derivatives

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Chapter 12 / Lesson 11
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Indefinite integrals, an integral of the integrand which does not have upper or lower limits, can be used to identify individual points at specific times. Learn more about the fundamental theorem, use of antiderivatives, and indefinite integrals through examples in this lesson.


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