Math Help - Improper Integral Problem

1. Improper Integral Problem

if $k>0$,show that $\int_e^\infty\frac{k}{x(lnx)^{k+1}} dx = 1$

2. Re: Improper Integral Problem

Originally Posted by mastermin346
if $k>0$,show that $\int_e^\infty\frac{k}{x(lnx)^{k+1}} dx = 1$

What is the derivative of $\frac{-1}{(\ln(x))^k}~?$

3. Re: Improper Integral Problem

$\frac{{}k (ln (x))^{-k-1}}{x}$?

4. Re: Improper Integral Problem

Originally Posted by mastermin346
$\frac{{}k (ln (x))^{-k-1}}{x}$?

OR $\frac{k (ln (x))^{-k-1}}{x}=\frac{k}{x(ln (x))^{k+1}}$

So now you know the anti-derivative. Use it to find the integral.

5. Re: Improper Integral Problem

thanks Plato! i got it !