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Math Help - Integration by substitution?

  1. #1
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    Integration by substitution?

    Hi

    I have this function which I am asked to integrate, I think Integration by substitution is the way to go but I'm not sure where to begin?

    \displaystyle\int\dfrac{\arctan x}{1 + x^2}dx

    Thanks in advance.

    James
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  2. #2
    MHF Contributor alexmahone's Avatar
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    let arctan x=u
    du=\frac{dx}{1+x^2}
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  3. #3
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    Thanks, its obvious now.
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  4. #4
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    Sorry, I might have been a bit hasty, I going round in circles again. Any chance you cound ellaborate on that a little?

    Thanks
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  5. #5
    MHF Contributor alexmahone's Avatar
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    Quote Originally Posted by bobred View Post
    Sorry, I might have been a bit hasty, I going round in circles again. Any chance you cound ellaborate on that a little?

    Thanks
    \displaystyle\int\dfrac{\arctan x}{1 + x^2}dx
    =\displaystyle\int u du
    =\frac{u^2}{2}+C
    =\frac{(arctanx)^2}{2}+C
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  6. #6
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    Quote Originally Posted by bobred View Post
    Sorry, I might have been a bit hasty, I going round in circles again. Any chance you cound ellaborate on that a little?

    Thanks
    Let u = arctanx
    du = \frac {dx}{1+x^2}

    Therefore

    \int udu

    \frac {1}{2} u^2+c

    \frac {\arctan^2 x}{2} +c
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