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Math Help - integration by substitution

  1. #1
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    integration by substitution

    would you possibly be able to show me a step by step solution for the following??

    Integrate: 2x((x^2)+1)^23 dx with respect to x

    thanks

    Dave
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  2. #2
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    Quote Originally Posted by daaavo View Post
    would you possibly be able to show me a step by step solution for the following??

    Integrate: 2x((x^2)+1)^23 dx with respect to x

    thanks

    Dave
    Try the u substition


    u=x^2+1 then du=2xdx

    so making the substition


    \int 2x(x^2+1)^{23}dx=\int u^{23}du=\frac{1}{24}u^{24}+C

    subbing u back in we get...

    \frac{1}{24}(x^2+1)^{24}+C
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