Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 4 - Integrals - 4.5 The Substitution Rule - 4.5 Exercises - Page 346: 25


$-\frac{2(cot(x))^{3/2}}{3} +C$

Work Step by Step

Evaluate the Integral using substitution: $\int \sqrt{cot(x)}csc^2(x)dx$ Substitution Rule: $\int f(g(x))gā€™(x)dx = \int f(u)du$ $u= cot(x)$ $du =-csc^2(x)$ Since $du$ in the expression is equal to $(csc^2(x))$ it must be multiplied by $-1$ Solve the integral in terms of $u$: $\int \sqrt{u}(-1)du$ $-1\int \sqrt{u}du $ $-\frac{2(u)^{3/2}}{3}+C$ Substitute for $u$: $-\frac{2(cot(x))^{3/2}}{3} +C$
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