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Math Help - intergrate with respect to x

  1. #1
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    intergrate with respect to x

    intergrate with respect to x:

    x√1+2x dx

    need the steps how to solve please

    thank you
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  2. #2
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    Re: intergrate with respect to x

    Quote Originally Posted by bobmarly12345 View Post
    intergrate with respect to x:

    x√1+2x dx

    need the steps how to solve please

    thank you
    WA click "show steps"
    Last edited by princeps; April 2nd 2012 at 06:22 AM.
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  3. #3
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    Re: intergrate with respect to x

    Hello, bobmarly12345!

    \text{Integrate: }\:\int x \sqrt{1+2x^2}\,dx

    We have: . \int (1 + 2x^2)^{\frac{1}{2}}(x\,dx)

    Let: . u \,=\,1+2x^2 \quad\Rightarrow\quad du \,=\,4x\,dx \quad\Rightarrow\quad x\,dx \,=\,\tfrac{1}{4}du

    Substitute: . \int \!u^{\frac{1}{2}}\left(\tfrac{1}{4}du\right) \;=\;\tfrac{1}{4} \!\!\int \!u^{\frac{1}{2}}du  \;=\;\tfrac{1}{6}u^{\frac{3}{2}} + C

    Back-substitute: . \tfrac{1}{6}(1 + 2x^2)^{\frac{3}{2}} + C

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  4. #4
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    Re: intergrate with respect to x

    Write question as 1/4 Integral of 4x(1+2x^2)^1/2
    There is a rule which says as 4x is the derivative of the expression in the bracket then this part integrates to (1+2x^2)^3/2 divided by 3/2, that is
    2/3(1+2x^2)^3/2
    Hence complete answer is 1/4.2/3(1+2x^2)^3/2=1/6(1+2x^2)^3/2
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  5. #5
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    Re: intergrate with respect to x

    Thankyou very much guys much appreciated
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