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Thread: u-substitution with e?!

  1. #1
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    u-substitution with e?!

    The question is:

    u-substitution with e?!-codecogseqn-1.gif

    and we have to use u-substitution to solve. I've tried using u = e^2 and du=e^2, however, this doesn't work out easily. Any suggestions?
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  2. #2
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    Re: u-substitution with e?!

    That's not do-able, check the spelling. And it needs a dx, yes?
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    Re: u-substitution with e?!

    u-substitution with e?!-codecogseqn-2.gif

    Ah, yes! Sorry about that. Here it is fixed.
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    Re: u-substitution with e?!

    You surely do not mean " u= e^2" then? That is a constant. If you mean " u= e^{2x}" then du= 2e^{2x}dx. But you don't have " e^{2x} in the numerator to use with the "dx".

    Instead, write the integral as \int_0^{ln(3)}\frac{e^x}{e^{2x}}dx- \int_0^{ln(3)}\frac{1}{e^{2x}}dx= \int_0^{ln(3)} e^{-x}dx- \int_0^{ln(3)} e^{-2x}dx and do the two integrals separately. If you need to, let u= -x in the first integral and let u= -2x in the second integral.
    Thanks from topsquark
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    Re: u-substitution with e?!

    Quote Originally Posted by HallsofIvy View Post
    You surely do not mean " u= e^2" then? That is a constant. If you mean " u= e^{2x}" then du= 2e^{2x}dx. But you don't have " e^{2x} in the numerator to use with the "dx".

    Instead, write the integral as \int_0^{ln(3)}\frac{e^x}{e^{2x}}dx- \int_0^{ln(3)}\frac{1}{e^{2x}}dx= \int_0^{ln(3)} e^{-x}dx- \int_0^{ln(3)} e^{-2x}dx and do the two integrals separately. If you need to, let u= -x in the first integral and let u= -2x in the second integral.
    Okay, I'll try that. Thanks!
    Last edited by scorks; Oct 6th 2013 at 11:46 AM.
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  6. #6
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    Re: u-substitution with e?!

    Possibly a sub of u = e^x was intended. Just in case a picture helps...



    ... where (key in spoiler) ...

    Spoiler:


    ... is the chain rule. Straight continuous lines differentiate downwards (integrate up) with respect to the main variable (in this case x), and the straight dashed line similarly but with respect to the dashed balloon expression (the inner function of the composite which is subject to the chain rule).



    Full size


    __________________________________________________ __________

    Don't integrate - balloontegrate!

    Balloon Calculus; standard integrals, derivatives and methods

    Balloon Calculus Drawing with LaTeX and Asymptote!
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