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Math Help - finding the integral

  1. #1
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    finding the integral

    Find the integral of:

    x * sqrt(5x^2 - 4) * dx
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  2. #2
    GAMMA Mathematics
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    Let u = 5x^2 - 4

    du = 10x dx

    OR

    x dx = \frac{du}{10}
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  3. #3
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    would it be:

    1/10 * (5x^2 - 4)^(3/2) + c
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  4. #4
    GAMMA Mathematics
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    Quote Originally Posted by DINOCALC09 View Post
    would it be:

    1/10 * (5x^2 - 4)^(3/2) + c
    Almost, you forgot to divide by the three halves.
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  5. #5
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    Quote Originally Posted by DINOCALC09 View Post
    Find the integral of:

    x * sqrt(5x^2 - 4) * dx
    Make-up

    \int {x\sqrt {5x^2  - 4} \,dx}  = \frac{1}<br />
{5}\int {5x\sqrt {5x^2  - 4} \,dx} .

    Set u^2=5x^2-4\implies u\,du=5x\,dx,

    \int {x\sqrt {5x^2  - 4} \,dx}  = \frac{1}<br />
{5}\int {u^2 \,du}  = \frac{u^3 }<br />
{{15}} + k = \frac{{\left( {5x^2  - 4} \right)^{3/2} }}<br />
{{15}} + k.
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