3.2394 \(\int \frac{a+\frac{b}{\sqrt [3]{x}}}{x^3} \, dx\)

Optimal. Leaf size=19 \[ -\frac{a}{2 x^2}-\frac{3 b}{7 x^{7/3}} \]

[Out]

(-3*b)/(7*x^(7/3)) - a/(2*x^2)

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Rubi [A]  time = 0.016074, 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 \[ -\frac{a}{2 x^2}-\frac{3 b}{7 x^{7/3}} \]

Antiderivative was successfully verified.

[In]  Int[(a + b/x^(1/3))/x^3,x]

[Out]

(-3*b)/(7*x^(7/3)) - a/(2*x^2)

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Rubi in Sympy [A]  time = 2.92499, size = 17, normalized size = 0.89 \[ - \frac{a}{2 x^{2}} - \frac{3 b}{7 x^{\frac{7}{3}}} \]

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/(7*x**(7/3))

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Mathematica [A]  time = 0.00952621, size = 19, normalized size = 1. \[ -\frac{a}{2 x^2}-\frac{3 b}{7 x^{7/3}} \]

Antiderivative was successfully verified.

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

[Out]

(-3*b)/(7*x^(7/3)) - a/(2*x^2)

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Maple [A]  time = 0.008, size = 14, normalized size = 0.7 \[ -{\frac{3\,b}{7}{x}^{-{\frac{7}{3}}}}-{\frac{a}{2\,{x}^{2}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((a+b/x^(1/3))/x^3,x)

[Out]

-3/7*b/x^(7/3)-1/2*a/x^2

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Maxima [A]  time = 1.44598, size = 132, normalized size = 6.95 \[ -\frac{3 \,{\left (a + \frac{b}{x^{\frac{1}{3}}}\right )}^{7}}{7 \, b^{6}} + \frac{5 \,{\left (a + \frac{b}{x^{\frac{1}{3}}}\right )}^{6} a}{2 \, b^{6}} - \frac{6 \,{\left (a + \frac{b}{x^{\frac{1}{3}}}\right )}^{5} a^{2}}{b^{6}} + \frac{15 \,{\left (a + \frac{b}{x^{\frac{1}{3}}}\right )}^{4} a^{3}}{2 \, b^{6}} - \frac{5 \,{\left (a + \frac{b}{x^{\frac{1}{3}}}\right )}^{3} a^{4}}{b^{6}} + \frac{3 \,{\left (a + \frac{b}{x^{\frac{1}{3}}}\right )}^{2} a^{5}}{2 \, b^{6}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-3/7*(a + b/x^(1/3))^7/b^6 + 5/2*(a + b/x^(1/3))^6*a/b^6 - 6*(a + b/x^(1/3))^5*a
^2/b^6 + 15/2*(a + b/x^(1/3))^4*a^3/b^6 - 5*(a + b/x^(1/3))^3*a^4/b^6 + 3/2*(a +
b/x^(1/3))^2*a^5/b^6

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Fricas [A]  time = 0.221057, size = 20, normalized size = 1.05 \[ -\frac{7 \, a x^{\frac{1}{3}} + 6 \, b}{14 \, x^{\frac{7}{3}}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/14*(7*a*x^(1/3) + 6*b)/x^(7/3)

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Sympy [A]  time = 4.77961, size = 17, normalized size = 0.89 \[ - \frac{a}{2 x^{2}} - \frac{3 b}{7 x^{\frac{7}{3}}} \]

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/(7*x**(7/3))

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GIAC/XCAS [A]  time = 0.209446, size = 20, normalized size = 1.05 \[ -\frac{7 \, a x^{\frac{1}{3}} + 6 \, b}{14 \, x^{\frac{7}{3}}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/14*(7*a*x^(1/3) + 6*b)/x^(7/3)