int(x^(3)-2sqrtx)/(x)dx

Split Fraction: Simplify the integral by splitting the fraction. \[ \int \frac{x^3 - 2\sqrt{x}}{x} \, dx = \int \left(x^2 - 2x^{-1/2}\right) \, dx \]Integrate Terms: Integrate each term separately. \[ \int x^2 \, dx = \frac{x^3}{3} \] \[ \int -2x^{-1/2} \, dx = -2 \cdot \frac{x^{1/2}}{1/2} = -4x^{1/2} \]Combine and Add Constant: Combine the integrated terms and add the constant of integration. \[ \frac{x^3}{3} - 4x^{1/2} + C \]

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$\int \frac{x^{3}-2 \sqrt{x}}{x} d x$ =

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Calculus

Find indefinite integrals using the substitution and by parts

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\int \frac{x^{3}-2 \sqrt{x}}{x} d x

Split Fraction: Simplify the integral by splitting the fraction. $\newline$ $\int \frac{x^3 - 2\sqrt{x}}{x} \, dx = \int \left(x^2 - 2x^{-1/2}\right) \, dx$
Integrate Terms: Integrate each term separately. $\newline$ $\int x^2 \, dx = \frac{x^3}{3}$ $\newline$ $\int -2x^{-1/2} \, dx = -2 \cdot \frac{x^{1/2}}{1/2} = -4x^{1/2}$
Combine and Add Constant: Combine the integrated terms and add the constant of integration. $\newline$ $\frac{x^3}{3} - 4x^{1/2} + C$