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Math Help - Integral of exponential function

  1. #1
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    Integral of exponential function

    Ok, so maybe I'm just missing something simple here, but I'm trying to take the integral of x^2 e^x^3 so I'm doing it with the tabular method, so I'm trying to integrate e^x^3dx for dv and for some reason I just can't get it to match up. I'm using a u sub for x^3 and then du is 3xdx but the original integral, e^x^3dx has no x next to e, so I don't see how I can modify du to match up. Even if you divide by 3 to factor that out, you still have xdx instead of dx.
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  2. #2
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    Quote Originally Posted by emttim84 View Post
    Ok, so maybe I'm just missing something simple here, but I'm trying to take the integral of x^2 e^x^3
    This is just Chain Rule. (We can even tackle many integrals without applyin' substitution.)

    (x^3)'=3x^2. Look at your integrand, you have an x^2.

    Now

    \int {x^2 e^{x^3 } \,dx}  = \frac{1}<br />
{3}\int {\left( {x^3 } \right)'e^{x^3 } \,dx}  = \frac{1}<br />
{3}\int {\left( {e^{x^3 } } \right)'\,dx}  = \frac{1}<br />
{3}e^{x^3 }  + k.

    Differentiate to check.
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