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Question Number 107162 by bobhans last updated on 09/Aug/20

Commented by Dwaipayan Shikari last updated on 09/Aug/20

$${\int }_{-5}^5\sqrt[6]{{5\mathrm{x}}^2+6}(5\mathrm{x}-2)\mathrm{dx}={\int }_{-5}^5\sqrt[6]{{5\mathrm{x}}^2+6}(-5\mathrm{x}-2)=\mathrm{I}$$$$2\mathrm{I}={\int }_{-5}^5-4\sqrt[6]{{5\mathrm{x}}^2+6}\mathrm{dx}$$$$\mathrm{I}=-2{\int }_{-5}^5\sqrt[6]{{5\mathrm{x}}^2+6}\mathrm{dx}$$

Answered by john santu last updated on 09/Aug/20

$$⊵\mathrm{JS}⊴$$$$\mathrm{I}=2\underset{0}{\stackrel{5}{\int }}\frac{1}{2}\sqrt[6]{{5\mathrm{x}}^2+6}\mathrm{d}({5\mathrm{x}}^2+6)-2\underset{-5}{\stackrel{5}{\int }}\sqrt[6]{{5\mathrm{x}}^2+6}\mathrm{dx}$$$$\mathrm{I}=\frac{6}{7}{\left[{({5\mathrm{x}}^2+6)}^{7/6}\right]}_0^5-4\underset{0}{\stackrel{5}{\int }}\sqrt[6]{{5\mathrm{x}}^2+6}\mathrm{dx}$$$$$$

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