Calculus (3rd Edition)

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

Chapter 7 - Exponential Functions - 7.3 Logarithms and Their Derivatives - Exercises - Page 343: 103


$\frac{3^{{x^2}}}{2\ln 3} +c $

Work Step by Step

Let $ u=3^{x^2}$, then $ du= 2x3^x \ln 3 dx $ and hence $$\int x3^{x^2}dx = \frac{1}{2\ln 3}\int du +c=\frac{1}{2\ln 3}u +c\\ =\frac{1}{2\ln 3}3^{x^2} +c =\frac{3^{{x^2}}}{2\ln 3} +c. $$
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