Question

Integrate the following with respect to x :

(a) (5x-3)^4

Answer 1

We can integrate the function $(5x-3)^4$ by substitution. Set $u=5x-3$, then $du=5dx,$ and $dx=\frac{du}{5}.$

Hence

$\int (5x-3)^4dx=\int u^4\frac{du}{5}=\frac{1}{5}\int u^4du=\frac{1}{5}\cdot \frac{u^5}{5}+C=\frac{u^5}{25}+C=$

$=\frac{(5x-3)^5}{25}+C.$