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Math Help - Integrating different kinds of functions

  1. #1
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    Integrating different kinds of functions

    I have an assignment, which is to show the proofs for

    f(x)=x^{n}
    F(x)=\frac{x^{n+1}}{n+1}+k

    And also proofs for how you integrate logarithm functions:
    log(x), ln(x)

    And trigonometric functions:
    sin(x), cos(x), tan(x)

    I looked in my books, but they don't have any proofs for why you get what you get when integrating them.
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  2. #2
    Math Engineering Student
    Krizalid's Avatar
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    Quote Originally Posted by No Logic Sense View Post
    I have an assignment, which is to show the proofs for

    f(x)=x^{n}
    F(x)=\frac{x^{n+1}}{n+1}+k
    \int{x^{n}\,dx}=\int{e^{n\ln x}\,dx}. Now put u=\ln x and the integral becomes \int e^{(n+1)u}\,du=\frac{e^{(n+1)\ln x}}{n+1}+k=\frac{x^{n+1}}{n+1}+k.
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  3. #3
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    I'm sorry, but I don't quite understand how you got the natural constant (e) (I'm not sure if that is what it's called in English) or how you got the +1 later on.
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