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    Could anyone help me with these two?
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    (Original post by TimGB)
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    Could anyone help me with these two?
    For the first one think about using the exponential definition of sinhx, and for the other perhaps just write it as cosec4x and see if you can do anything with integrating it my recognition etc.
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    (Original post by TimGB)
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    Could anyone help me with these two?
    First one notes sinh2x=2sinhxcoshx



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    (Original post by physicsmaths)
    First one notes sinh2x=2sinhxcoshx



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    It's cos not cosh though. There's both a hyperbolic and trig function in the integral.
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    (Original post by TimGB)
    It's cos not cosh though. There's both a hyperbolic and trig function in the integral.
    Oh ok.
    Do what Jordon suggested.
    Notes something about doing parts a few times on two integrals.


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    (Original post by Jordan\)
    For the first one think about using the exponential definition of sinhx, and for the other perhaps just write it as cosec4x and see if you can do anything with integrating it my recognition etc.
    I'm not sure if parts will help - it looks like it will go on in a continuous cycle.

    For the second on I did what you suggested, rearranged to csc²(x) + csc²(x)cot²(x) - not sure how to integrate the second part though. My mind is kind of dead after doing these for 4 hours, so I might be making an easy mistake.
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    (Original post by TimGB)
    I'm not sure if parts will help - it looks like it will go on in a continuous cycle. For the second on I did that, rearranged to csc²(x) + csc²(x)cot²(x) - not sure how to integrate the second part though. My mind is kind of dead after doing these for 4 hours, so I might be making an easy mistake.
    It is a cycle that is the point' consider rearranging when you have the same integral on the right!


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    (Original post by TimGB)
    It's cos not cosh though. There's both a hyperbolic and trig function in the integral.
    Would you mind terribly making a new thread and asking for help, you're cluttering this thread up integrals you need help on. This thread has a slightly different purpose.

    Thanks.
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    (Original post by Zacken)
    Would you mind terribly making a new thread and asking for help, you're cluttering this thread up integrals you need help on. This thread has a slightly different purpose.

    Thanks.
    I will do that. I was going to do that originally but then I found this thread which I thought would be a better place for it, but never mind.
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    (Original post by TimGB)


    Could anyone help me with these two?
    Separating into

     2I = \displaystyle\int \Big( e^x \cos{x} - e^{-x} \cos{x} \Big) \mathrm{d}x

    Both parts of that integral can be solved independently by using integration by parts twice. Basically the idea is that you let

     I_a = \displaystyle\int u \dfrac{\mathrm{d}v}{\mathrm{d}x} \mathrm{d} x

    and do parts until the original integral forms again, you can then solve for  I_a .

    Note that I'm just using sub a as notation so you don't get mixed up with two integrals.
 
 
 
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