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