# How do you integrate int (3-x)7^((3-x) ^2)dx?

$\int \left(3 - x\right) {7}^{{\left(3 - x\right)}^{2}} \mathrm{dx} = - \frac{{7}^{{\left(3 - x\right)}^{2}}}{2 \ln 7} + C$
Substitute $t = {\left(3 - x\right)}^{2}$, $\mathrm{dt} = - 2 \left(3 - x\right) \mathrm{dx}$, and consider that ${7}^{\alpha} = {e}^{\alpha \ln 7}$:
$\int \left(3 - x\right) {7}^{{\left(3 - x\right)}^{2}} \mathrm{dx} = - \frac{1}{2} \int {e}^{\ln 7 t} \mathrm{dt} = - \frac{1}{2} \ln 7 {e}^{\ln 7 t} + C = - \frac{{7}^{{\left(3 - x\right)}^{2}}}{2 \ln 7} + C$