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Question Number 146689 by naka3546 last updated on 15/Jul/21

$$\int \frac{-3x+5}{\sqrt[3]{{(3x^2-10x)}^2}}dx=...?$$$$Solveitwithoutsubstitutionmethod.$$

Answered by Ar Brandon last updated on 15/Jul/21

$$\mathcal{I}=\int \frac{-3\mathrm{x}+5}{\sqrt[3]{{({3\mathrm{x}}^2-10\mathrm{x})}^2}}\mathrm{dx}$$$$=-\frac{1}{2}\int \frac{6\mathrm{x}-10}{\sqrt[3]{{({3\mathrm{x}}^2-10\mathrm{x})}^2}}\mathrm{dx}$$$$=-\frac{1}{2}\int \frac{\mathrm{d}({3\mathrm{x}}^2-10\mathrm{x})}{\sqrt[3]{{({3\mathrm{x}}^2-10\mathrm{x})}^2}}$$$$=-\frac{3}{2}\sqrt[3]{{3\mathrm{x}}^2-10\mathrm{x}}+\mathrm{C}$$

Commented by naka3546 last updated on 15/Jul/21

$$thankyou,sir.$$

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