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

• Jan 22nd 2009, 08:04 PM
bnay
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
• Jan 22nd 2009, 08:13 PM
Jhevon
Quote:

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
• Jan 22nd 2009, 09:42 PM
bnay
thank you very much. That worked wonderfully
• May 13th 2016, 09:39 PM
Shay2016
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