Question

$\int \frac{1}{{\left(7x-5\right)}^3}+\frac{1}{\sqrt{5x-4}}dx$

Answer 1

$$\begin{gathered} \int \left[\frac{1}{{\left(7x-5\right)}^3}+\frac{1}{\sqrt{5x-4}}\right]dx \\ =\int \left[{\left(7x-5\right)}^{-3}+{\left(5x-4\right)}^{-\frac{1}{2}}\right]dx \\ =\frac{{\left(7x-5\right)}^{-3+1}}{7\left(-3+1\right)}+\frac{{\left(5x-4\right)}^{{\displaystyle -\frac{1}{2}}+1}}{5\left(-{\displaystyle \frac{1}{2}}+1\right)}+\mathrm{C} \\ =\frac{{\left(7x-5\right)}^{-2}}{-14}+\frac{2}{5}{\left(5x-4\right)}^{\frac{1}{2}}+\mathrm{C} \end{gathered}$$