Part $1.$

Using the substitution: $u=5x-9x^2-7.$ Re$-$write the indefinite integral then evaluate in terms of $u.$

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}(-\frac{18}{7}x+\frac{5}{7})e^{5x-9x^2-7}dx={\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}=$

$$

Note: answer should be in terms of $u$ only

Part $2.$

Back substituting in the antiderivative you found in Part $1.$ above we have

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}(-\frac{18}{7}x+\frac{5}{7})e^{5x-9x^2-7}dx=$

Note: answer should be in terms of $x$ only