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Thread: Integration

  1. #1
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    Integration

    I have the following integral.

    $\displaystyle
    \int cos(x) - 2e^x + 3x^-1
    $

    So far I can work out the first and last terms to be, I did this by simplying splitting this up into 3 terms.

    $\displaystyle
    \int sin(x) - 2e^x + 3ln(x) + C
    $

    What I am unsure about is how to integrate the $\displaystyle -2e^x$
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by gk99 View Post
    I have the following integral.

    $\displaystyle
    \int cos(x) - 2e^x + 3x^-1
    $

    So far I can work out the first and last terms to be, I did this by simplying splitting this up into 3 terms.

    $\displaystyle
    \int sin(x) - 2e^x + 3ln(x) + C
    $

    What I am unsure about is how to integrate the $\displaystyle -2e^x$
    1. You don't need the integration symbol once you have integrated.

    2. You're correct in your solution. Recall the property $\displaystyle \int c f(x)dx=c\int f(x)dx$ where $\displaystyle c\in\mathbb{R}$ and since $\displaystyle \frac{d}{dx}\left[e^x\right]=e^x$, it would make sense that $\displaystyle \int e^xdx=e^x+C$.

    Does this clarify things?
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  3. #3
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    Quote Originally Posted by gk99 View Post
    I have the following integral.

    $\displaystyle
    \int cos(x) - 2e^x + 3x^-1
    $

    So far I can work out the first and last terms to be, I did this by simplying splitting this up into 3 terms.

    $\displaystyle
    \int sin(x) - 2e^x + 3ln(x) + C
    $

    What I am unsure about is how to integrate the $\displaystyle -2e^x$
    $\displaystyle \int{a\,e^{b\,x}\,dx} = \frac{a}{b}\,e^{b\,x} + C$.
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