(3-x)dx/ (x^2-6x-9)^5/2

You can use power formula: $\displaystyle \int \dfrac{(3 - x) \, dx}{(x^2 - 6x - 9)^{5/2}}$

$= \displaystyle \int (x^2 - 6x - 9)^{-5/2} \, (3 - x) \, dx$

$= \displaystyle -\dfrac{1}{2} \int (x^2 - 6x - 9)^{-5/2} \, [ \, -2(3 - x) \, ] \, dx$

$= \displaystyle -\dfrac{1}{2} \int (x^2 - 6x - 9)^{-5/2} \, (2x - 6) \, dx$

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MATHalino

You can use power formula:

$\displaystyle \int \dfrac{(3 - x) \, dx}{(x^2 - 6x - 9)^{5/2}}$

$= \displaystyle \int (x^2 - 6x - 9)^{-5/2} \, (3 - x) \, dx$

$= \displaystyle -\dfrac{1}{2} \int (x^2 - 6x - 9)^{-5/2} \, [ \, -2(3 - x) \, ] \, dx$

$= \displaystyle -\dfrac{1}{2} \int (x^2 - 6x - 9)^{-5/2} \, (2x - 6) \, dx$