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}
Answer and Explanation: 1
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View this answerBefore integrating by parts lets have:
- {eq}\displaystyle u = x {/eq}
- {eq}\displaystyle du = \, dx {/eq}
- {eq}\displaystyle dv = \sin (3x) \,...
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Chapter 13 / Lesson 7Learn how to use and define integration by parts. Discover the integration by parts rule and formula. Learn when and how to use integration by parts with examples.