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Math Help - integration

  1. #1
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    integration

    integral
    2x^2(x^3+1)^(1/2) dx
    Having the hardest time with this is there a simple way to do it.
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  2. #2
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    Quote Originally Posted by Nightasylum View Post
    integral
    2x^2(x^3+1)^(1/2) dx
    Having the hardest time with this is there a simple way to do it.
    For \int 2x^2 \sqrt{x^3+1}\,dx let u = x^3+1. See how that works?
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  3. #3
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    Quote Originally Posted by Nightasylum View Post
    integral
    2x^2(x^3+1)^(1/2) dx
    Having the hardest time with this is there a simple way to do it.
    substitution ...

    u = x^3+1

    du = 3x^2 \, dx

    \frac{2}{3} \int 3x^2\sqrt{x^3+1} \, dx

    \frac{2}{3} \int \sqrt{u} \, du

    finish ...
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  4. #4
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    Quote Originally Posted by skeeter View Post
    substitution ...

    u = x^3+1

    du = 3x^2 \, dx

    \frac{2}{3} \int 3x^2\sqrt{x^3+1} \, dx

    \frac{2}{3} \int \sqrt{u} \, du

    finish ...
    Ill get 2/3 (x^3+1)^3/2 + c But that doesnt work so im a little lost.
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  5. #5
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    Quote Originally Posted by Nightasylum View Post
    Ill get 2/3 (x^3+1)^3/2 + c But that doesnt work so im a little lost.
    ... you ignored the constant in front of the integral.
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  6. #6
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    Quote Originally Posted by skeeter View Post
    ... you ignored the constant in front of the integral.
    O ok I got it. Thanks a ton .
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