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Math Help - Difficult integration

  1. #1
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    Difficult integration

    I'm having some trouble with a more complicated problem.

    \int \frac {x^{3x}} {\sqrt {4 - e^{6x}}}

    So far I have:

    u = e ^{3x} so \frac {1}{3}du = e^{3x}dx

    That gives me:

    \frac {1}{3}\int \frac {x^{3x}}{\sqrt{4-u^2}}dx

    I need help getting rid of that x on top and turn that 4 into a 1. I'm sure that I'm missing something obvious.
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  2. #2
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    Quote Originally Posted by Chicken Enchilada View Post
    I'm having some trouble with a more complicated problem.

    \int \frac {x^{3x}} {\sqrt {4 - e^{6x}}}

    So far I have:

    u = e ^{3x} so \frac {1}{3}du = e^{3x}dx

    That gives me:

    \frac {1}{3}\int \frac {x^{3x}}{\sqrt{4-u^2}}dx

    I need help getting rid of that x on top and turn that 4 into a 1. I'm sure that I'm missing something obvious.
    I suspect the question is meant to be \int \frac {{\color{red}e}^{3x}} {\sqrt {4 - e^{6x}}} \, {\color{red}dx}
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  3. #3
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    Quote Originally Posted by mr fantastic View Post
    I suspect the question is meant to be \int \frac {{\color{red}e}^{3x}} {\sqrt {4 - e^{6x}}} \, {\color{red}dx}
    Good point. I will take it for a typo then. I got all the other problems done, so I think I'm set. Thank You.
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