# Chapter 5 - The Integral - 5.7 Substitution Method - Exercises - Page 275: 38

$\frac{1}{117} (3x+8)^{13}-\frac{2}{27} (3x+8)^{12}+C$

#### Work Step by Step

Given $$\int x(3x+8)^{11}d x$$ Let $$u=3x+8 \ \ \ \Rightarrow \ \ du=3dx$$ then \begin{align*} \int x(3 x+8)^{11} d x &=\frac{1}{3} \int \frac{1}{3}(u-8) u^{11} d u \\ &=\frac{1}{9}\left(u^{12}-8 u^{11}\right) d u \\ &=\frac{1}{9}\left(\frac{1}{13} u^{13}-\frac{8}{12} u^{12}+C\right) \\ &=\frac{1}{117} u^{13}-\frac{2}{27} u^{12}+C \\ & =\frac{1}{117} (3x+8)^{13}-\frac{2}{27} (3x+8)^{12}+C \end{align*}

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.