# Chapter 4 - Integrals - 4.5 The Substitution Rule - 4.5 Exercises - Page 346: 9

$-\frac{(1-2x)^{10}}{20} +C$

#### Work Step by Step

Evaluate the Integral using substitution: $\int (1-2x)^9dx$ Substitution Rule: $\int f(g(x))g’(x)dx = \int f(u)du$ $u= 1-2x$ $du = -2$ Determine if $du$ is modified by a constant. In this expression $du$ is multipled by $-\frac{1}{2}$ to equal $1$ Solve the integral in terms of $u$: $\int (u)^9(-\frac{1}{2}du)$ $-\frac{1}{2}\int (u)^9du$ $-\frac{1}{2} \frac{u^{10}}{10} +C$ $-\frac{(u)^{10}}{20} +C$ Substitute for $u$: $-\frac{(1-2x)^{10}}{20} +C$

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