# Thread: Integration by parts sqrt(x)*e^sqrt(x)

1. ## Integration by parts sqrt(x)*e^sqrt(x)

Hello, I've been trying to solve for the integral from 0 to 4 of sqrt(x)*e^sqrt(x)
(aka, the integral from 0 to 4 of the square root of x times e to the power of the square root of x, incase the above wasn't clear).

I've tried integration by parts, but each time I integrate the new integrand just aquires a higher power of x and this seems to go on indefinately. I've also tried a change of base to make the integral equal e^(sqrt(x) + ln(x)) but the same thing happens.

If anybody has any ideas on how to get around this, it would be wonderful.

Thank you

2. Originally Posted by bnay
Hello, I've been trying to solve for the integral from 0 to 4 of sqrt(x)*e^sqrt(x)
(aka, the integral from 0 to 4 of the square root of x times e to the power of the square root of x, incase the above wasn't clear).

I've tried integration by parts, but each time I integrate the new integrand just aquires a higher power of x and this seems to go on indefinately. I've also tried a change of base to make the integral equal e^(sqrt(x) + ln(x)) but the same thing happens.

If anybody has any ideas on how to get around this, it would be wonderful.

Thank you
here's a trick that will make it easier on you

do a substitution first

Let $u = \sqrt{x}$, then our integral becomes

$2 \int u^2 e^u~du$

which is a relatively easy integral to do by parts

3. thank you very much. That worked wonderfully

4. ## Re: Integration by parts sqrt(x)*e^sqrt(x)

Substitute 1st then do integration by parts x2 and the and should be 10e^(3) -4

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# integration of e to the power x Ã—square root x

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