Answer
$$\int x(7x+5)^{3/2}dx=\frac{(7x+5)^{5/2}}{49}\Big[\frac{14x-4}{7}\Big]+C$$
Work Step by Step
$$A=\int x(7x+5)^{3/2}dx$$
Using Formula 22, which states that
$$\int x(ax+b)^ndx=\frac{(ax+b)^{n+1}}{a^2}\Big[\frac{ax+b}{n+2}-\frac{b}{n+1}\Big]+C$$
with $a=7$, $b=5$ and $n=3/2$ here, we have
$$A=\frac{(7x+5)^{5/2}}{7^2}\Big[\frac{7x+5}{\frac{7}{2}}-\frac{5}{\frac{5}{2}}\Big]+C$$ $$A=\frac{(7x+5)^{5/2}}{49}\Big[\frac{14x+10}{7}-2\Big]+C$$ $$A=\frac{(7x+5)^{5/2}}{49}\Big[\frac{14x-4}{7}\Big]+C$$
