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

∫x3−2xxdx \int \frac{x^{3}-2 \sqrt{x}}{x} d x =

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Find indefinite integrals using the substitution and by partsright chevron icon

Full solution

Q. ∫x3−2xxdx \int \frac{x^{3}-2 \sqrt{x}}{x} d x =
  1. Split Fraction: Simplify the integral by splitting the fraction.\newline∫x3−2xx dx=∫(x2−2x−1/2) dx \int \frac{x^3 - 2\sqrt{x}}{x} \, dx = \int \left(x^2 - 2x^{-1/2}\right) \, dx
  2. Integrate Terms: Integrate each term separately.\newline∫x2 dx=x33 \int x^2 \, dx = \frac{x^3}{3} \newline∫−2x−1/2 dx=−2⋅x1/21/2=−4x1/2 \int -2x^{-1/2} \, dx = -2 \cdot \frac{x^{1/2}}{1/2} = -4x^{1/2}
  3. Combine and Add Constant: Combine the integrated terms and add the constant of integration.\newlinex33−4x1/2+C \frac{x^3}{3} - 4x^{1/2} + C

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