Answer
$\frac{2}{3}(7x-1)^{\frac{3}{2}}+C$
Work Step by Step
Derivative of 7x-1 is 7. Thus we use the substitution 7x-1= u so that du= 7dx.
Therefore, $\int 7\sqrt (7x-1)dx= \int \sqrt u du$
=$\frac{u^{\frac{1}{2}+1}}{\frac{1}{2}+1}$+C= $\frac{2}{3}u^{\frac{3}{2}}$+C=$\frac{2}{3}(7x-1)^{\frac{3}{2}}+C$
