Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 5 - The Integral - 5.7 Substitution Method - Exercises - Page 275: 15


$$ \int x(x+1)^9 dx= \frac{1}{11}(x+1)^{11}-\frac{1}{10}(x+1)^{10} +c $$

Work Step by Step

Since $ u=x+1$, then $ du=dx $ and hence, $$ \int x(x+1)^9 dx=\int (u-1)u^9 d u=\int u^{10}-u^9 d u\\ =\frac{1}{11}u^{11}-\frac{1}{10}u^{10} +c=\frac{1}{11}(x+1)^{11}-\frac{1}{10}(x+1)^{10} +c $$
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