3.2284 \(\int \frac{a+b \sqrt [3]{x}}{x^2} \, dx\)

Optimal. Leaf size=17 \[ -\frac{a}{x}-\frac{3 b}{2 x^{2/3}} \]

[Out]

-(a/x) - (3*b)/(2*x^(2/3))

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Rubi [A]  time = 0.0164993, antiderivative size = 17, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ -\frac{a}{x}-\frac{3 b}{2 x^{2/3}} \]

Antiderivative was successfully verified.

[In]  Int[(a + b*x^(1/3))/x^2,x]

[Out]

-(a/x) - (3*b)/(2*x^(2/3))

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Rubi in Sympy [A]  time = 3.0318, size = 14, normalized size = 0.82 \[ - \frac{a}{x} - \frac{3 b}{2 x^{\frac{2}{3}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((a+b*x**(1/3))/x**2,x)

[Out]

-a/x - 3*b/(2*x**(2/3))

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Mathematica [A]  time = 0.00750872, size = 17, normalized size = 1. \[ -\frac{a}{x}-\frac{3 b}{2 x^{2/3}} \]

Antiderivative was successfully verified.

[In]  Integrate[(a + b*x^(1/3))/x^2,x]

[Out]

-(a/x) - (3*b)/(2*x^(2/3))

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Maple [A]  time = 0.008, size = 14, normalized size = 0.8 \[ -{\frac{a}{x}}-{\frac{3\,b}{2}{x}^{-{\frac{2}{3}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((a+b*x^(1/3))/x^2,x)

[Out]

-a/x-3/2*b/x^(2/3)

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Maxima [A]  time = 1.44402, size = 20, normalized size = 1.18 \[ -\frac{3 \, b x^{\frac{1}{3}} + 2 \, a}{2 \, x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^(1/3) + a)/x^2,x, algorithm="maxima")

[Out]

-1/2*(3*b*x^(1/3) + 2*a)/x

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Fricas [A]  time = 0.212827, size = 20, normalized size = 1.18 \[ -\frac{3 \, b x^{\frac{1}{3}} + 2 \, a}{2 \, x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^(1/3) + a)/x^2,x, algorithm="fricas")

[Out]

-1/2*(3*b*x^(1/3) + 2*a)/x

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Sympy [A]  time = 2.51015, size = 14, normalized size = 0.82 \[ - \frac{a}{x} - \frac{3 b}{2 x^{\frac{2}{3}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((a+b*x**(1/3))/x**2,x)

[Out]

-a/x - 3*b/(2*x**(2/3))

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GIAC/XCAS [A]  time = 0.246131, size = 20, normalized size = 1.18 \[ -\frac{3 \, b x^{\frac{1}{3}} + 2 \, a}{2 \, x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^(1/3) + a)/x^2,x, algorithm="giac")

[Out]

-1/2*(3*b*x^(1/3) + 2*a)/x