1. ## simple integration problem

$\int_4^9 \frac{1}{(2x)(1+ \sqrt x)}$

2. ## Re: simple integration problem

Originally Posted by earthboy
$\int_4^9 \frac{1}{(2x)(1+ \sqrt x)}$
Assuming you mean \displaystyle \begin{align*} \int_4^9{\frac{1}{2x\left(1 + \sqrt{x}\right)}\,dx} &= \int_4^9{\frac{1}{2\sqrt{x}\sqrt{x}\left(1 + \sqrt{x}\right)}\,dx} \end{align*}
Now make the substitution \displaystyle \begin{align*} u = \sqrt{x} \implies du = \frac{1}{2\sqrt{x}}\,dx \end{align*} and also note that this means \displaystyle \begin{align*} 1 + \sqrt{x} = 1 + u \end{align*} and the limits will change to 2 and 3, and the integral becomes
\displaystyle \begin{align*} \int_4^9{\frac{1}{2\sqrt{x}\sqrt{x}\left(1 + \sqrt{x}\right)}\,dx} = \int_2^3{\frac{1}{u\left(1 + u\right)}\,du} \end{align*}