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C3 help urgent!

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    Can some1 please show me how to do question 4b.
    http://store.aqa.org.uk/qual/gceasa/...W-QP-JAN07.PDF

    I can do simple substitution but not the harder ones .
    If you could show me all the steps that you did to get the answer, that would be great.
    Ty for reading
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    (Original post by bahjat93)
    Can some1 please show me how to do question 4b.
    http://store.aqa.org.uk/qual/gceasa/...W-QP-JAN07.PDF

    I can do simple substitution but not the harder ones .
    If you could show me all the steps that you did to get the answer, that would be great.
    Ty for reading
    It isn't a harder one!

     \displaystyle \int x \sqrt{x^2+5} \ dx \ \ \ u = x^2 +5

    Differentiate,  u = x^2 +5
    This gives,  \displaystyle dx = \frac{du}{2x}

    The integral becomes,  \displaystyle \int x \sqrt{x^2+5} \ dx  = \int x u^{\frac12} \times \frac{du}{2x} = \int \frac{u^{\frac12}}{2} \ du

    Now its simple to finish it off.
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    (Original post by raheem94)
    It isn't a harder one!

     \displaystyle \int x \sqrt{x^2+5} \ dx \ \ \ u = x^2 +5

    Differentiate,  u = x^2 +5
    This gives,  \displaystyle dx = \frac{du}{2x}

    The integral becomes,  \displaystyle \int x \sqrt{x^2+5} \ dx  = \int x u^{\frac12} \times \frac{du}{2x} = \int \frac{u^{\frac12}}{2} \ du

    Now its simple to finish it off.
    I don't get maths but i see what you did, LOOOL cheers dude much appreciated

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