Calculus (3rd Edition)

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

Chapter 7 - Exponential Functions - Chapter Review Exercises - Page 387: 82


$$\frac{10^x e^x}{1+\ln 10}+c$$

Work Step by Step

We do the integration by parts; we choose $u=10^x$ and $dv=e^xdx$. Then, $du=10^x\ln 10$, $v=e^x$ $$I=\int e^x 10^x dx=\int udv=uv-\int vdu\\ =10^x e^x- (\ln 10)\int e^x 10^x dx\\ =10^x e^x-I \ln 10 $$ Hence $$\int e^x 10^x dx=\frac{10^x e^x}{1+\ln 10}+c$$
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