Question

РЕШИТЕ   2X³-∛X +3√X      dx
                     5x²                        НЕОПРЕДЕЛЕНЫЙ ИНТЕГРАЛ

Answer 1

∫ (2X³-∛X +3√X ) / 5x²  = ∫ 2X³/5x² dx -∫ ∛X/5x² dx +∫ 3√X/5x² dx =
= 2/5 ∫ X³/x² dx  - 1/5 ∫ ∛X/x² dx + 3/5 ∫√X/x² dx =
=2/5 ∫ X dx  - 1/5 ∫ ∛X/x² dx + 3/5 ∫√X/x² dx =
= 1/5 x^2 + 3/10 ∛x/x - 6/5 *1/√x =
= x^2/5 + 3∛x/10x - 6/5√x 

Answer 2

$intlimits { frac{2x^3- sqrt[3]{x}+3 sqrt{x} }{5x^2} } , dx = intlimits frac{2x^3}{5x^2}dx -intlimits frac{ sqrt[3]{x} }{5x^2}dx+intlimits frac{3 sqrt{x} }{5x^2}dx = \ \ = intlimits frac{2}{5}xdx-intlimits frac{1}{5}x^{- frac{5}{3} }dx+intlimits frac{3}{5}x^{- frac{3}{2} }dx= frac{x^2}{5} + frac{3 sqrt[3]{x} }{10x}- frac{6 sqrt{x} }{5x} = \ \ = frac{2x^3+3 sqrt[3]{x}- 12 sqrt{x} }{10x}$