Answer
$\frac{(4x-3)^{10}}{40}+C$
Work Step by Step
Use the substitution $u=4x-3$. This means $du=4dx$, so $dx=\frac{1}{4} du$.
$\int (4x-3)^9dx$
$=\int u^9*\frac{1}{4} du$
$=\int \frac{1}{4}u^9 du$
$=\frac{1}{4}*\frac{u^{10}}{10}+C$
$=\frac{u^{10}}{40}+C$
$=\frac{(4x-3)^{10}}{40}+C$