# Evaluate the following integrals. int_1^{e^2}frac{(ln x)^5}{x}dx

Evaluate the following integrals.
${\int }_{1}^{{e}^{2}}\frac{\left(\mathrm{ln}x{\right)}^{5}}{x}dx$
You can still ask an expert for help

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

unessodopunsep
$\text{Given:}$
${\int }_{1}^{{e}^{2}}\frac{\left(\mathrm{ln}x{\right)}^{5}}{x}dx$
$\text{Use substitution to solve}$
$\text{Let}$
$\mathrm{ln}x=t$
$\frac{1}{x}dx=dt$
$\text{when}$

$={\int }_{0}^{2}{t}^{5}dt$
$=\left[\frac{{t}^{6}}{6}{\right]}_{0}^{2}$
$=\frac{1}{6}\left({2}^{6}-0\right)$
$=\frac{64}{6}\approx 10.66$