Exercise
$ln\left(\sqrt{\frac{\left(8x-8\right)}{\left(7x+2\right)}}\right)$
Derivative of this function
$\frac{d}{dx}\left(\ln\left(\sqrt{\frac{8x-8}{7x+2}}\right)\right)=\frac{8\left(7x+2\right)+7\left(-8x+8\right)}{2\sqrt{\frac{8x-8}{7x+2}}\left(7x+2\right)^2}\sqrt{\frac{7x+2}{8x-8}}$
See step-by-step solution
Integral of this function
$\int\ln\left(\sqrt{\frac{8x-8}{7x+2}}\right)dx=\frac{1}{2}\left(\left(8x-8\right)\ln\left(8x-8\right)-8x+8\right)-\frac{1}{2}\left(\left(7x+2\right)\ln\left(7x+2\right)-7x-2\right)+C_0$
See step-by-step solution