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Math Help - finding an integral

  1. #1
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    finding an integral

    Find the integral of:

    [e^[3ln(x)] + e^(3x)] dx
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  2. #2
    GAMMA Mathematics
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    Quote Originally Posted by DINOCALC09 View Post
    Find the integral of:

    [e^[3ln(x)] + e^(3x)] dx
    First, let's simplify the integrand:

    e^{3ln(x)} + e^{3x} = x^3+e^{3x}

    The integral of that is:

    \frac{x^4}{4} + \frac{e^{3x}}{3}
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  3. #3
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    for the integral of e and its power dont u multiply it by the coefficient of x (chain rule) instead of dividing?
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    ignore what i said above- woops, my bad. you did it right
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  5. #5
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    Say we have: e^{ln(x^a)}

    Obviously, it equals x^a

    Also, e^{ln(x^a)} = e^{aln(x)}

    Let a = 3

    e^{3ln(x)} = e^{ln(x)+ln(x)+ln(x)} \Rightarrow e^{ln(x)}e^{ln(x)}e^{ln(x)} = x*x*x
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