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Math Help - Integration of exponential

  1. #1
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    Integration of exponential

    \int x e^{7x^2+1}
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  2. #2
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    Hello,

    7x^2+1 is a polynomial of degree 2.
    x is a polynomial of degree 2-1.

    So you have to think : substitution !

    -> substitute t=7x^2+1
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  3. #3
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    So what happens after I substitute?

    It becomes \int x e^t?

    or

    \int \sqrt{\frac{t-1}{7}} e^t?
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    Quote Originally Posted by nerdzor View Post
    So what happens after I substitute?

    It becomes \int x e^t?

    or

    \int \sqrt{\frac{t-1}{7}} e^t?
    The problem is that you didn't put the dx in the first integral.
    It's \int xe^{7x^2+1} ~{\color{red}dx}

    So you can't think of the dx/dt...

    t=7x^2+1 \Rightarrow \frac{dt}{dx}=14x \Rightarrow dx=dt\cdot\frac{1}{14x}
    So you have to substitute dx by dt\cdot\frac{1}{14x}

    and the x will simplify : \int xe^{7x^2+1} ~dx=\int x e^t \cdot \frac{1}{14x} ~dt=\frac{1}{14} \int e^t ~dt

    After that, don't forget to back substitute (you will have a formula with t, but t=7x^2+1, so you have to change it)
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