3.2285 \(\int \frac{a+b \sqrt [3]{x}}{x^3} \, dx\)

Optimal. Leaf size=19 \[ -\frac{a}{2 x^2}-\frac{3 b}{5 x^{5/3}} \]

[Out]

-a/(2*x^2) - (3*b)/(5*x^(5/3))

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Rubi [A]  time = 0.0155531, antiderivative size = 19, 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 \[ -\frac{a}{2 x^2}-\frac{3 b}{5 x^{5/3}} \]

Antiderivative was successfully verified.

[In]  Int[(a + b*x^(1/3))/x^3,x]

[Out]

-a/(2*x^2) - (3*b)/(5*x^(5/3))

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Rubi in Sympy [A]  time = 2.94582, size = 17, normalized size = 0.89 \[ - \frac{a}{2 x^{2}} - \frac{3 b}{5 x^{\frac{5}{3}}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-a/(2*x**2) - 3*b/(5*x**(5/3))

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Mathematica [A]  time = 0.00757016, size = 19, normalized size = 1. \[ -\frac{a}{2 x^2}-\frac{3 b}{5 x^{5/3}} \]

Antiderivative was successfully verified.

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

[Out]

-a/(2*x^2) - (3*b)/(5*x^(5/3))

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Maple [A]  time = 0.008, size = 14, normalized size = 0.7 \[ -{\frac{a}{2\,{x}^{2}}}-{\frac{3\,b}{5}{x}^{-{\frac{5}{3}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((a+b*x^(1/3))/x^3,x)

[Out]

-1/2*a/x^2-3/5*b/x^(5/3)

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Maxima [A]  time = 1.43992, size = 20, normalized size = 1.05 \[ -\frac{6 \, b x^{\frac{1}{3}} + 5 \, a}{10 \, x^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/10*(6*b*x^(1/3) + 5*a)/x^2

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Fricas [A]  time = 0.215202, size = 20, normalized size = 1.05 \[ -\frac{6 \, b x^{\frac{1}{3}} + 5 \, a}{10 \, x^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/10*(6*b*x^(1/3) + 5*a)/x^2

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Sympy [A]  time = 4.79186, size = 17, normalized size = 0.89 \[ - \frac{a}{2 x^{2}} - \frac{3 b}{5 x^{\frac{5}{3}}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-a/(2*x**2) - 3*b/(5*x**(5/3))

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GIAC/XCAS [A]  time = 0.237336, size = 20, normalized size = 1.05 \[ -\frac{6 \, b x^{\frac{1}{3}} + 5 \, a}{10 \, x^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/10*(6*b*x^(1/3) + 5*a)/x^2