Calculus 8th Edition

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

Chapter 6 - Inverse Functions - 6.4* General Logarithmic and Exponential Functions - 6.4* Exercise: 48

Answer

$\int x2^{x^{2}}dx=\frac{1}{2}\frac {2^{x^{2}}}{ln2}+constant$

Work Step by Step

Evaluate the integral $\int x2^{x^{2}}dx$ Consider $x^{2}=t$ and $xdx=\frac{dt}{2}$ Thus, $\int x2^{x^{2}}dx=\int 2^{t}\frac{dt}{2}$ $=\frac{1}{2}\frac{2^{t}}{ln2}+constant$ Hence, $\int x2^{x^{2}}dx=\frac{1}{2}\frac {2^{x^{2}}}{ln2}+constant$
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