3.463 \(\int \frac{-4+5 x^2+x^3}{x^2} \, dx\)

Optimal. Leaf size=16 \[ \frac{x^2}{2}+5 x+\frac{4}{x} \]

[Out]

4/x + 5*x + x^2/2

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Rubi [A]  time = 0.0138338, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 14, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.071 \[ \frac{x^2}{2}+5 x+\frac{4}{x} \]

Antiderivative was successfully verified.

[In]  Int[(-4 + 5*x^2 + x^3)/x^2,x]

[Out]

4/x + 5*x + x^2/2

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ 5 x + \int x\, dx + \frac{4}{x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((x**3+5*x**2-4)/x**2,x)

[Out]

5*x + Integral(x, x) + 4/x

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Mathematica [A]  time = 0.00175415, size = 16, normalized size = 1. \[ \frac{x^2}{2}+5 x+\frac{4}{x} \]

Antiderivative was successfully verified.

[In]  Integrate[(-4 + 5*x^2 + x^3)/x^2,x]

[Out]

4/x + 5*x + x^2/2

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Maple [A]  time = 0.005, size = 15, normalized size = 0.9 \[ 4\,{x}^{-1}+5\,x+{\frac{{x}^{2}}{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((x^3+5*x^2-4)/x^2,x)

[Out]

4/x+5*x+1/2*x^2

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Maxima [A]  time = 0.819913, size = 19, normalized size = 1.19 \[ \frac{1}{2} \, x^{2} + 5 \, x + \frac{4}{x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((x^3 + 5*x^2 - 4)/x^2,x, algorithm="maxima")

[Out]

1/2*x^2 + 5*x + 4/x

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Fricas [A]  time = 0.253396, size = 20, normalized size = 1.25 \[ \frac{x^{3} + 10 \, x^{2} + 8}{2 \, x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((x^3 + 5*x^2 - 4)/x^2,x, algorithm="fricas")

[Out]

1/2*(x^3 + 10*x^2 + 8)/x

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Sympy [A]  time = 0.10831, size = 10, normalized size = 0.62 \[ \frac{x^{2}}{2} + 5 x + \frac{4}{x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((x**3+5*x**2-4)/x**2,x)

[Out]

x**2/2 + 5*x + 4/x

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GIAC/XCAS [A]  time = 0.261158, size = 19, normalized size = 1.19 \[ \frac{1}{2} \, x^{2} + 5 \, x + \frac{4}{x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((x^3 + 5*x^2 - 4)/x^2,x, algorithm="giac")

[Out]

1/2*x^2 + 5*x + 4/x