$\displaystyle \int(2x+7)\sqrt{4x-5}$

$\displaystyle \frac{1}{4}\int(2x+7)\sqrt{4x-5}du$

$\displaystyle \frac{1}{4}\int\frac{2u+12}{4}u^{1/2}du$

$\displaystyle \frac{1}{16}[2(\frac{2}{5})u^{5/2}+12(\frac{2}{3})u^{3/2}]du$

$\displaystyle \frac{1}{16}[\frac{4}{5}(4x-5)u^{5/2}+8(4x-5)^{3/2}]+c$