Results 1 to 3 of 3

Math Help - Integration by parts sqrt(x)*e^sqrt(x)

  1. #1
    Junior Member
    Joined
    Sep 2008
    Posts
    28

    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
    Follow Math Help Forum on Facebook and Google+

  2. #2
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by bnay View Post
    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
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Sep 2008
    Posts
    28
    thank you very much. That worked wonderfully
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: September 22nd 2010, 03:48 PM
  2. Prove Q(\sqrt{2}+\sqrt{3})=Q(\sqrt{2},\sqrt{3})
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: April 11th 2010, 05:52 PM
  3. Limit of sqrt(2*sqrt(2)) sequence
    Posted in the Calculus Forum
    Replies: 3
    Last Post: April 4th 2010, 05:06 AM
  4. Replies: 11
    Last Post: January 6th 2008, 10:33 AM
  5. prove sqrt(3) + sqrt (5) is an irrational number
    Posted in the Number Theory Forum
    Replies: 2
    Last Post: October 6th 2006, 07:48 PM

Search Tags


/mathhelpforum @mathhelpforum