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Question Number 128826 by benjo_mathlover last updated on 10/Jan/21

$${\int }_{-1}^5\sqrt{\frac{{2\mathrm{x}}^2-8}{\mathrm{x}}}\mathrm{dx}=?$$

Answered by bobhans last updated on 10/Jan/21

$$\int \sqrt{\frac{{\left(x\sqrt{2}\right)}^2-{\left(\sqrt{8}\right)}^2}{x}}dx$$$$letx\sqrt{2}=\sqrt{8}\sec h$$$$\int \sqrt{\frac{8(\sec {}^{2}h-1)}{2\sec h}}\left(2\sec h\tan hdh\right)$$$$=4\int \tan {}^{2}h\sqrt{\sec h}dh$$$$$$

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