Answer
$-\frac{5^{-x^2}}{2\ log 5}+C$
Work Step by Step
$\int (x(5^{-x^2})dx$
let $-x^2=u$
$-2x$ $dx=du$
$\int (x(5^{-x^2})dx$
$=-\frac{1}{2} \int 5^u du$
$=\frac{1}{2}(\frac{5^u}{\log 5})+C$
$=-\frac{5^{-x^2}}{2\ log 5}+C$
Calculus 10th Edition
by Larson, Ron; Edwards, Bruce H.
Published by
Brooks Cole
ISBN 10:
1-28505-709-0
ISBN 13:
978-1-28505-709-5
Chapter 5 - Logarithmic, Exponential, and Other Transcendental Functions - 5.5 Exercises - Page 363: 75
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