# Chapter 6 - Inverse Functions - 6.2 Exponential Functions and Their Derivatives - 6.2 Exercises: 90

$\frac{(4+e^x)^6}{6}+C$

#### Work Step by Step

Let $u=4+e^x$. Then $du=e^xdx$. $\int e^x(4+e^x)^5 dx$ $=\int (4+e^x)^5e^x dx$ $=\int u^5 du$ $=\frac{u^6}{6}+C$ $=\frac{(4+e^x)^6}{6}+C$

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