Results 1 to 5 of 5

Math Help - Integration, general power formula

  1. #1
    Member
    Joined
    Sep 2011
    Posts
    75

    Integration, general power formula

    Question - integrate the following:

    (int) (4- (e^x))^3 e^x dx

    attempt:
    u = (4 + e^x)
    n = 3
    du = e^x

    therefore answer is:
    ((4 + (e^x))^4) / 4 + c

    which is incorrect, and should be:
    4 / (e^(x^1/2)) + c

    Stared at it for a while and can't figure it out. Any help, thanks?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,607
    Thanks
    1574
    Awards
    1

    Re: Integration, general power formula

    Quote Originally Posted by togo View Post
    Question - integrate the following:

    (int) (4- (e^x))^3 e^x dx

    attempt:
    u = (4 + e^x)
    n = 3
    du = e^x

    therefore answer is:
    ((4 + (e^x))^4) / 4 + c

    which is incorrect, and should be:
    4 / (e^(x^1/2)) + c, NO indeed!

    \int {{{\left( {4 - {e^x}} \right)}^3}{e^x}dx =  - \tfrac{1}{4}} {\left( {4 - {e^x}} \right)^4} + c
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Apr 2013
    From
    Green Bay
    Posts
    68
    Thanks
    16

    Re: Integration, general power formula

    Need to find  \int (4 - e^x)^3 e^x dx .

    Set  u = 4 - e^x . Then  du = -e^x dx . Then  -du = e^x dx

     \int (4 - e^x)^3 e^x dx = \int -u^3 du = -\frac{u^4}{4} + C = -\frac{(4 - e^x)^4}{4} + C
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member
    Joined
    Sep 2011
    Posts
    75

    Re: Integration, general power formula

    you guys are telling me the book is wrong
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Super Member
    Joined
    Oct 2012
    From
    Ireland
    Posts
    586
    Thanks
    155

    Re: Integration, general power formula

    Try differentiating the book's answer to check that it is correct
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Integration: General Power Formula
    Posted in the Calculus Forum
    Replies: 4
    Last Post: April 30th 2013, 08:31 PM
  2. general power rule
    Posted in the Calculus Forum
    Replies: 2
    Last Post: May 28th 2011, 05:23 PM
  3. Replies: 4
    Last Post: May 4th 2010, 07:15 PM
  4. Power series - general solution
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: December 4th 2008, 11:36 AM
  5. general integration formula
    Posted in the Calculus Forum
    Replies: 7
    Last Post: April 20th 2008, 08:26 AM

Search Tags


/mathhelpforum @mathhelpforum