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Step-by-step Solution

Integral of (x^2)/((x^2-6)^0.5)

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Answer

$6\left(\frac{\frac{1}{2}\left(\frac{x}{\sqrt{5}}\right)^{2}\sqrt{x^2-6}}{x}+\frac{1}{2}\ln\left|\frac{x+\sqrt{x^2-6}}{\sqrt{5}}\right|\right)+C_0$

Step-by-step explanation

Problem to solve:

$\int\frac{x^2}{\sqrt{x^2-6}}dx$
1

Solve the integral $\int\frac{x^2}{\sqrt{x^2-6}}dx$ by trigonometric substitution using the substitution

$\begin{matrix}x=\sqrt{5}\sec\left(\theta\right) \\ dx=\sqrt{5}\sec\left(\theta\right)\tan\left(\theta\right)d\theta\end{matrix}$
2

Substituting in the original integral, we get

$\int\frac{14.6969\sec\left(\theta\right)^2\tan\left(\theta\right)\sec\left(\theta\right)}{\sqrt{6\sec\left(\theta\right)^2-6}}d\theta$

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Answer

$6\left(\frac{\frac{1}{2}\left(\frac{x}{\sqrt{5}}\right)^{2}\sqrt{x^2-6}}{x}+\frac{1}{2}\ln\left|\frac{x+\sqrt{x^2-6}}{\sqrt{5}}\right|\right)+C_0$