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Math Help - integration by substitution

  1. #1
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    integration by substitution

    I am unsure if I am doing the next to the last step correctly.

    integral e^5x dx
    g(u) = 1/6*u^6
    u = 5x
    du = 5

    1/6 * 1/du * u^6
    1/30 (5x)^6
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  2. #2
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    Quote Originally Posted by startingover View Post
    I am unsure if I am doing the next to the last step correctly.

    integral e^5x dx
    g(u) = 1/6*u^6
    u = 5x
    du = 5

    1/6 * 1/du * u^6
    1/30 (5x)^6
    Your result is wrong. You have used the wrong formula.
    Notice that e^(5x) is NOT a power function. It is an exponential function.
    The correct answer is e^(5x)/5+C.
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  3. #3
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by startingover View Post
    I am unsure if I am doing the next to the last step correctly.

    integral e^5x dx
    g(u) = 1/6*u^6
    u = 5x
    du = 5

    1/6 * 1/du * u^6
    1/30 (5x)^6
    Yes, curvature is right. The standard way to do this is by substitution, which seems to be what you attempted.

    However, it is probably best to just remember that:

    \int e^{kx} dx = \frac {1}{k} e^{kx} + C for k \neq 0
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