Results 1 to 4 of 4

Math Help - Need fast help on an integration problem.

  1. #1
    Newbie
    Joined
    Nov 2007
    Posts
    4

    Need fast help on an integration problem.

    Hi, I need urgent help on this problem
    int((e^(8x))*cos(9x))dx

    I've tried integration by parts but you end up with a even more complicated integral. Tabular integration doesn't work since the e^8x never reduces to 0. I'm stumped , please help thanks!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Opalg's Avatar
    Joined
    Aug 2007
    From
    Leeds, UK
    Posts
    4,041
    Thanks
    7
    Quote Originally Posted by HclBr View Post
    Hi, I need urgent help on this problem
    int((e^(8x))*cos(9x))dx

    I've tried integration by parts but you end up with a even more complicated integral. Tabular integration doesn't work since the e^8x never reduces to 0. I'm stumped , please help thanks!
    Integrate by parts twice. It may look as though it's getting more complicated, but when you do it a second time it gets you back to a multiple of the integral that you started with. That gives you an equation for the integral. The answer should be of the form e^{8x}(A\cos(9x)+B\sin(9x)) (plus a constant of integration, of course).
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Math Engineering Student
    Krizalid's Avatar
    Joined
    Mar 2007
    From
    Santiago, Chile
    Posts
    3,654
    Thanks
    11
    I suggest (for this problems, 'cause they're well-known) take them more generally:

    \int e^{ax}\cos(bx)\,dx.

    As Opalg said, this requires a twice integration by parts.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Math Engineering Student
    Krizalid's Avatar
    Joined
    Mar 2007
    From
    Santiago, Chile
    Posts
    3,654
    Thanks
    11
    Or we can use the following method:

    \int {e^{ax} \cos (bx)\,dx} = \text{Re} \int {e^{(a + bi)x} \,dx} = \text{Re} \,\frac{{e^{ax} \cdot (\cos (bx) + i\sin (bx))}}<br />
{{a + bi}}.

    After some simple calculations we have

    \int {e^{ax} \cos (bx)\,dx} = \frac{{e^{ax} (a\cos (bx) + b\sin (bx))}}<br />
{{a^2 + b^2 }} + k.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Help Fast on Series/Sigma problem!!!
    Posted in the Calculus Forum
    Replies: 7
    Last Post: April 30th 2009, 10:41 PM
  2. Replies: 0
    Last Post: February 19th 2009, 06:10 PM
  3. Need help fast: Pre-Calculus Problem
    Posted in the Pre-Calculus Forum
    Replies: 7
    Last Post: April 18th 2008, 11:52 PM
  4. Movement Calc Problem, need help fast!!!!
    Posted in the Calculus Forum
    Replies: 2
    Last Post: April 6th 2008, 03:23 PM
  5. Calculus Problem-Need FAST!
    Posted in the Calculus Forum
    Replies: 4
    Last Post: December 15th 2007, 05:13 PM

Search Tags


/mathhelpforum @mathhelpforum