Answer
$\frac{(7x-1)^{3/2}}{3/2}+c$
Work Step by Step
$u=7x-1$, therefore $du=7dx$. Let's rewrite the integral! $\int (7\sqrt {7x-1})dx=\int (\sqrt {7x-1})7dx$
We do the substitution! $\int (\sqrt {7x-1})7dx=\int u^{1/2}du=\frac{u^{3/2}}{3/2}+c$ We re-do the substitution! $\frac{u^{3/2}}{3/2}+c=\frac{(7x-1)^{3/2}}{3/2}+c$