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Math Help - Help Solving Integral

  1. #1
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    Help Solving Integral

    Before I ask the problem, I also want to know how to post or what program to use to show the integral sign and square root sign etc...

    Now to the problem

    X^7 / fifth root of 2X^4+5

    If possible, please show using the U-Substitution Method. If another is easier, post as well.
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  2. #2
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    Quote Originally Posted by gammaman View Post
    Before I ask the problem, I also want to know how to post or what program to use to show the integral sign and square root sign etc...

    Now to the problem

    X^7 / third root of 2X^4+5

    If possible, please show using the U-Substitution Method. If another is easier, post as well.
    To check to make sure what you're talking about, you have
    x^7 / (2x^4 +5)^1/3 dx ?
    If so, start by substituting
    x^4 for u
    x^4 = u
    4x^3dx = du
    dx = du/4x^3

    Substitute back in. We're only going to substitute dx at first
    x^7/ (2x^4 +5)^1/3 * du/4x^3
    Note that the x^7/4x^3 will reduce to x^4/4, which allows us to substitute it for u.

    1/4 (integral ( u/(2u +5)^1/3 du)) = 1/4 * 3/40 (2u +5)^(2/3) * (4u -15)

    Substitute u back in and we arrive at

    1/4 * 3/40 * (2x^4 +5)^(2/3) * (4x^4 -15)

    Hope that helped. -Edit-
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  3. #3
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    Quote Originally Posted by gammaman View Post
    Before I ask the problem, I also want to know how to post or what program to use to show the integral sign and square root sign etc...

    [snip]
    Read this: http://www.mathhelpforum.com/math-he...-tutorial.html
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  4. #4
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    Quote Originally Posted by gammaman View Post

    Now to the problem

    X^7 / fifth root of 2X^4+5
    \int{\frac{x^{7}}{\sqrt[5]{2x^{4}+5}}\,dx}=\int{\frac{x^{4}\cdot x^{3}}{\sqrt[5]{2x^{4}+5}}\,dx}, and then put u^5=2x^4+5.
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  5. #5
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    Quote Originally Posted by gammaman View Post
    Before I ask the problem, I also want to know how to post or what program to use to show the integral sign and square root sign etc...

    Now to the problem

    X^7 / fifth root of 2X^4+5

    If possible, please show using the U-Substitution Method. If another is easier, post as well.
    When you edit a question after getting a reply you make the person who gave the reply look foolish. You originally posted third root .....
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  6. #6
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    Quote Originally Posted by mr fantastic View Post
    When you edit a question after getting a reply you make the person who gave the reply look foolish. You originally posted third root .....

    Yes I realized that but it was too late, sorry.
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  7. #7
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    That's not a problem actually, it's always a worth of try, may be that'd help some other people.

    But, the idea is essentially the same for both integrals. Both methods work.
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  8. #8
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    Quote Originally Posted by Krizalid View Post
    \int{\frac{x^{7}}{\sqrt[5]{2x^{4}+5}}\,dx}=\int{\frac{x^{4}\cdot x^{3}}{\sqrt[5]{2x^{4}+5}}\,dx}, and then put u^5=2x^4+5.
    would you mind showing me how to solve it through?
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  9. #9
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    5u^4\,du=8x^3\,dx and \frac58u^4\,du=x^3\,dx. Furthermore, we have x^4=\frac{u^5-5}{2} and \sqrt[5]{2x^4+5} becomes u. Now put these together.
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