Question

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

Answer 1

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