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Math Help - integrating by assumed knowledge

  1. #1
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    integrating by assumed knowledge

    ok i've this question:

    \int \frac{3x^2}{\sqrt{1-x^6}}

    I know that the answer is sin^-1(x^3) + c

    I see the relationship between sin^-1(x) and sin^-1(x^3) and their integrals and this question...But what would be the best method to use to integrate and if it is substitution, what will u equal?

    Thanks in advance!!
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  2. #2
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    Quote Originally Posted by tsal15 View Post
    ok i've this question:

    \int \frac{3x^2}{\sqrt{1-x^6}}

    I know that the answer is sin^-1(x^3) + c

    I see the relationship between sin^-1(x) and sin^-1(x^3) and their integrals and this question...But what would be the best method to use to integrate and if it is substitution, what will u equal?

    Thanks in advance!!
    Substitute u = x^3 \Rightarrow dx = \frac{du}{3x^2}.
    Last edited by mr fantastic; December 15th 2008 at 05:30 PM.
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  3. #3
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    Quote Originally Posted by mr fantastic View Post
    Substitute u = x^3 \Rightarrow dx = \frac{1}{3x^2}.
    Actually if \frac{du}{dx} = 3x^2 then dx = \frac{du}{3x^2}.
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  4. #4
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    Quote Originally Posted by Prove It View Post
    Actually if \frac{du}{dx} = 3x^2 then dx = \frac{du}{3x^2}.
    Carelss of me. Fixed.
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