Results 1 to 4 of 4

Math Help - nice integral

  1. #1
    Newbie
    Joined
    May 2009
    Posts
    9

    nice integral

    find :
    Attached Thumbnails Attached Thumbnails nice integral-nice-integral.jpg  
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Amer's Avatar
    Joined
    May 2009
    From
    Jordan
    Posts
    1,093
    Quote Originally Posted by a.h.m.a.d View Post
    find :
    \int_{1}^{e}(x+1)e^x lnx dx

    \int_{1}^{e}(xe^x ln(x)+e^x (lnx )dx

    the second integral let
    du=dx,,u=x....v=e^x lnx...dv=e^x lnx + \frac{e^x}{x}

    \int_{1}^{e}(xe^x ln(x))dx+\int_{1}^{e}e^x (lnx )dx

    \int_{1}^{e}(xe^x ln(x))dx+xe^x ln(x)-\int_{1}^{e} x(e^x lnx +\frac{e^x}{x})dx

    \int_{1}^{e}(xe^x ln(x))dx+xe^x ln(x)-\int_{1}^{e} xe^x ln(x) dx+\int_{1}^{e} e^x dx

    xe^x ln(x)+\int_{1}^{e} e^x dx

    xe^x ln(x) +e^x

    now just substitute
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    May 2009
    Posts
    9
    Amer
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,809
    Thanks
    700
    Hello, a.h.m.a.d!

    Find: . \int^e_1(x+1)\,e^x\ln x\,dx
    Integration by parts . . .

    . . \begin{array}{ccccccc}u &=& \ln x & & dv &=& (x+1)e^x\,dx \\ du &=& \frac{dx}{x} & & v &=& xe^x\;\;{\color{red}*} \end{array}

    We have: . xe^x\ln x - \int e^x\,dx \;=\;xe^x\ln x - e^x\,\bigg]^e_1 \quad\hdots\;\text{ etc.}


    ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

    * . To integrate: . \int(x+1)e^x\,dx

    . . . By parts: . \begin{array}{ccccccc} u &=& x+1 & & dv &=& e^x\,dx \\ du &=& dx & & v &=& e^x \end{array}

    . . . And we have: . (x+1)e^x - \int e^x\,dx \;\;=\;\;(x+1)e^x - e^x

    . . . . . . =\;\;xe^x + e^x - e^x \;\;=\;\;xe^x

    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. nice integral :D
    Posted in the Calculus Forum
    Replies: 7
    Last Post: March 20th 2010, 11:46 AM
  2. A nice integral
    Posted in the Math Challenge Problems Forum
    Replies: 1
    Last Post: August 12th 2009, 12:12 AM
  3. nice integral
    Posted in the Calculus Forum
    Replies: 2
    Last Post: November 21st 2008, 05:09 PM
  4. A nice integral
    Posted in the Calculus Forum
    Replies: 1
    Last Post: May 20th 2008, 07:28 PM
  5. integral with nice result
    Posted in the Math Challenge Problems Forum
    Replies: 6
    Last Post: July 10th 2007, 03:14 PM

Search Tags


/mathhelpforum @mathhelpforum