simple integration problem

**earthboy** · June 30th 2012, 08:50 PM

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

**Prove It** · June 30th 2012, 09:39 PM

Originally Posted by earthboy

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

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

$\displaystyle \begin{align*} \int_4^9{\frac{1}{2\sqrt{x}\sqrt{x}\left(1 + \sqrt{x}\right)}\,dx} = \int_2^3{\frac{1}{u\left(1 + u\right)}\,du} \end{align*}$

which you can solve using partial fractions.

**biffboy** · June 30th 2012, 10:05 PM

Substitute u=x^1/2

Thread: simple integration problem

LinkBack

Thread Tools

Display

simple integration problem

Re: simple integration problem

Re: simple integration problem

Similar Math Help Forum Discussions

Simple Integration problem: Trigonometric Integration

Simple integration problem

simple integration problem

Simple integration problem.

Relatively simple integration problem

Search Tags