Originally Posted by

**Alex01tib** Hi guys, i have an exam tomarrow in calc II and i have been having the same problem with integrals of ln in quotients

for example, i know through the answer key and my TI89 that

$\displaystyle \int

\frac{\ln(n)}{(n^2)}=\frac{-\ln(x)-1}{x}

$

integration by parts ... $\displaystyle \textcolor{red}{u = \ln{n} \, , \, dv = \frac{1}{n^2}}$

and

$\displaystyle \int{\frac{\ln{(x+1)}}{x+1}}=\frac{(ln(x+1))^2}{2}$

straight substitution ... $\displaystyle \textcolor{red}{u = \ln(x+1) \, , \, du = \frac{1}{x+1}}$

and

$\displaystyle \int{\frac{1}{\sqrt{x}*(\sqrt{x}+1)}}=\ln{\sqrt{n} }+1$

straight substitution again ... $\displaystyle \textcolor{red}{u = \sqrt{x} + 1 \, , \, du = \frac{1}{2\sqrt{x}}}$