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Thread: Few Integration Problems

  1. #1
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    Few Integration Problems

    Hey gang, I'm having a devil of a time solving these following problems. Mostly, I'm having difficulty figuring out how to start them off.

    (excuse me for not yet knowing how to properly type these problems in)

    1) Integrate (x-1)/(x^2-4x+5)

    2) Integrate ((2x-1)^.5)/(2x+3)

    3) Integrate 1/(x+x*x^.5)
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  2. #2
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    Quote Originally Posted by emeryj View Post
    Hey gang, I'm having a devil of a time solving these following problems. Mostly, I'm having difficulty figuring out how to start them off.

    (excuse me for not yet knowing how to properly type these problems in)

    1) Integrate (x-1)/(x^2-4x+5)

    2) Integrate ((2x-1)^.5)/(2x+3)

    3) Integrate 1/(x+x*x^.5)

    (1) \int \frac{x-1}{x^2-4x+5} \, dx = \int \frac{x-2}{x^2-4x+5} + \frac{1}{(x-2)^2+1} \, dx



    (2) \int \frac{\sqrt{2x-1}}{(2x-1) + 4} \, dx

    let u^2 = 2x-1



    (3) \int \frac{1}{x(1+\sqrt{x})} \, dx

    let x = u^2
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  3. #3
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    Quote Originally Posted by emeryj View Post
    Hey gang, I'm having a devil of a time solving these following problems. Mostly, I'm having difficulty figuring out how to start them off.

    (excuse me for not yet knowing how to properly type these problems in)

    1) Integrate (x-1)/(x^2-4x+5)

    \int\frac{x-1}{x^2-4x+5}\,dx

    =\int\frac{x-2}{x^2-4x+5}\,dx+\int\frac{1}{x^2-4x+5}\,dx

    =\int\frac{x-2}{x^2-4x+5}\,dx+\int\frac{1}{(x-2)^2+1}\,dx
    Last edited by ione; Feb 21st 2010 at 05:09 PM.
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