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Math Help - Help with Integration

  1. #1
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    Help with Integration

    How do you integrate (x-1)/sqrt(x)?

    Thanks.
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  2. #2
    Behold, the power of SARDINES!
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    Quote Originally Posted by Savior_Self View Post
    How do you integrate (x-1)/sqrt(x)?

    Thanks.
    Hint:

    \displaystyle \frac{x-1}{\sqrt{x}}=x^{\frac{1}{2}}-x^\frac{-1}{2}

    Now use the power rule!
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  3. #3
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    wait, how does \frac{x-1}{\sqrt{x}}  = x^{1/2} - x^{-1/2}?

    I get that it equals (x-1)(x^{-1/2})... I just don't see the steps you took to get past that.
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  4. #4
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    Quote Originally Posted by Savior_Self View Post
    wait, how does \frac{x-1}{\sqrt{x}}  = x^{1/2} - x^{-1/2}?

    I get that it equals (x-1)(x^{-1/2})... I just don't see the steps you took to get past that.
    Expand the brackets, using the rule that (x^a)(x^b)=x^{a+b}
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  5. #5
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    Thanks. So the answer is: \frac{2x^{3/2}}{3}-2x^{1/2}+C

    correct?
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  6. #6
    Behold, the power of SARDINES!
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    Quote Originally Posted by Savior_Self View Post
    Thanks. So the answer is: \frac{2x^{3/2}}{3}-2x^{1/2}+C

    correct?
    yes you can check by taking the derivative!
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