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Step-by-step Solution

Integral of $\frac{3x}{\sqrt{\left(9-2x^2\right)^3}}$ with respect to x

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Answer

$\frac{\frac{3}{2}}{3\sqrt{1-\frac{2}{9}x^2}}+C_0$

Step-by-step explanation

Problem to solve:

$\int\frac{\left(3x\right)}{\sqrt{\left(9-2x^2\right)^3}}dx$
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Applying the power of a power property

$\int\frac{3x}{\sqrt{\left(9-2x^2\right)^{3}}}dx$
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Taking the constant out of the integral

$3\int\frac{x}{\sqrt{\left(9-2x^2\right)^{3}}}dx$

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Answer

$\frac{\frac{3}{2}}{3\sqrt{1-\frac{2}{9}x^2}}+C_0$