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Help with integral

  1. Jun 12, 2009 #1
    Hello, I need help witht he following integral which has come up while trying to solve a differential equation.


    \int \frac{e^t}{cos^2(5t)}sin(6t)dt


    I'm not sure it can be integrated analytically, I 've tried to think of possible trigonometric manipulations and integrating by parts ... but not leading anywhere, any help would be appreciated.
  2. jcsd
  3. Jun 12, 2009 #2


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    I am pretty sure a primitive of this function does not exist in closed form/elementary functions.
  4. Jun 12, 2009 #3


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    Gradshteyn & Rhyzik states that indefinite integrals of the forms exp[ax] divided by sin(bx), cos(bx), sin^2(bx) or cos^2(bx) aren't expressible as a finite combination of elementary functions, so your integral is similarly hopeless, as it's a linear combination of such integrals (for complex a).

    You might be able to get an infinite series for it, though.

    Or, if you had constant limits it might be a doable integral.
  5. Jun 12, 2009 #4
    Thank you, I've been breaking my head trying to find a closed form in terms of elementary functions, but wasn't able to come up with anything. I guess the only way then is to use Taylor expansions or the like and then integrate the terms of the resulting series.

    No, I don't have constant limits: the integral came up in the process of trying to find the solution function of an ordinary differential equation.

    Thank you for your help :)
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