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Math Help - Integration by substitution

  1. #1
    Junior Member
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    Integration by substitution

    integrate ((x^2+4)^1/2)/x dx ; u^2=x^2+4

    x=(u^2-4)^1/2

    dx=u/(u^2-4)^1/2 du

    =integral u/(u^2-4)^1/2 x u/(u^2-4)^1/2 du
    =integral u^2/u^2 -4 du

    not sure if the above is correct/if it is, how to integrate it?
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  2. #2
    Member
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    Quote Originally Posted by Erghhh View Post
    integrate ((x^2+4)^1/2)/x dx ; u^2=x^2+4

    x=(u^2-4)^1/2

    dx=u/(u^2-4)^1/2 du

    =integral u/(u^2-4)^1/2 x u/(u^2-4)^1/2 du
    =integral u^2/u^2 -4 du

    not sure if the above is correct/if it is, how to integrate it?
    \int (u^2/u^2 -4) du

    = \int (1 -4)du
    =\int -3du
    =-3u+c

    did you mean:
    \int (u^2/(u^2 -4)) du

    ?

    if so, use parentheses.
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