## Calculus (3rd Edition)

Published by W. H. Freeman

# Chapter 7 - Exponential Functions - 7.1 Derivative of f(x)=bx and the Number e - Exercises - Page 328: 86

#### Answer

$3e^{x^{1/3}}+c$

#### Work Step by Step

Recall that $(e^x)'=e^x$ Let $u= x^{1/3}$, then $du=\frac{1}{3} x^{-2/3}dx$ and hence we have $$\int x^{-2/3}e^{x^{1/3}} dx=3\int e^{u} du\\ =3e^u+c=3e^{x^{1/3}}+c .$$

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