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x-3x-3-2-dx-




Question Number 56523 by arvinddayama02@gmail.com last updated on 18/Mar/19
∫x(√(3x^3 +2)) dx=?
$$\int{x}\sqrt{\mathrm{3}{x}^{\mathrm{3}} +\mathrm{2}}\:{dx}=? \\ $$
Commented by MJS last updated on 18/Mar/19
it seems impossible to solve
$$\mathrm{it}\:\mathrm{seems}\:\mathrm{impossible}\:\mathrm{to}\:\mathrm{solve} \\ $$
Commented by MJS last updated on 18/Mar/19
possible are these:  ∫x(√(3x^2 +2))dx  ∫x^2 (√(3x^3 +2))dx  (both are easy)  and, harder:  ∫x((3x^3 +2))^(1/3) dx
$$\mathrm{possible}\:\mathrm{are}\:\mathrm{these}: \\ $$$$\int{x}\sqrt{\mathrm{3}{x}^{\mathrm{2}} +\mathrm{2}}{dx} \\ $$$$\int{x}^{\mathrm{2}} \sqrt{\mathrm{3}{x}^{\mathrm{3}} +\mathrm{2}}{dx} \\ $$$$\left(\mathrm{both}\:\mathrm{are}\:\mathrm{easy}\right) \\ $$$$\mathrm{and},\:\mathrm{harder}: \\ $$$$\int{x}\sqrt[{\mathrm{3}}]{\mathrm{3}{x}^{\mathrm{3}} +\mathrm{2}}{dx} \\ $$

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