3.2395 \(\int \frac{a+\frac{b}{\sqrt [3]{x}}}{x^4} \, dx\)

Optimal. Leaf size=19 \[ -\frac{a}{3 x^3}-\frac{3 b}{10 x^{10/3}} \]

[Out]

(-3*b)/(10*x^(10/3)) - a/(3*x^3)

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Rubi [A]  time = 0.0164452, 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 \[ -\frac{a}{3 x^3}-\frac{3 b}{10 x^{10/3}} \]

Antiderivative was successfully verified.

[In]  Int[(a + b/x^(1/3))/x^4,x]

[Out]

(-3*b)/(10*x^(10/3)) - a/(3*x^3)

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Rubi in Sympy [A]  time = 2.85443, size = 17, normalized size = 0.89 \[ - \frac{a}{3 x^{3}} - \frac{3 b}{10 x^{\frac{10}{3}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((a+b/x**(1/3))/x**4,x)

[Out]

-a/(3*x**3) - 3*b/(10*x**(10/3))

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Mathematica [A]  time = 0.00966701, size = 19, normalized size = 1. \[ -\frac{a}{3 x^3}-\frac{3 b}{10 x^{10/3}} \]

Antiderivative was successfully verified.

[In]  Integrate[(a + b/x^(1/3))/x^4,x]

[Out]

(-3*b)/(10*x^(10/3)) - a/(3*x^3)

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Maple [A]  time = 0.008, size = 14, normalized size = 0.7 \[ -{\frac{3\,b}{10}{x}^{-{\frac{10}{3}}}}-{\frac{a}{3\,{x}^{3}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((a+b/x^(1/3))/x^4,x)

[Out]

-3/10*b/x^(10/3)-1/3*a/x^3

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Maxima [A]  time = 1.5851, size = 201, normalized size = 10.58 \[ -\frac{3 \,{\left (a + \frac{b}{x^{\frac{1}{3}}}\right )}^{10}}{10 \, b^{9}} + \frac{8 \,{\left (a + \frac{b}{x^{\frac{1}{3}}}\right )}^{9} a}{3 \, b^{9}} - \frac{21 \,{\left (a + \frac{b}{x^{\frac{1}{3}}}\right )}^{8} a^{2}}{2 \, b^{9}} + \frac{24 \,{\left (a + \frac{b}{x^{\frac{1}{3}}}\right )}^{7} a^{3}}{b^{9}} - \frac{35 \,{\left (a + \frac{b}{x^{\frac{1}{3}}}\right )}^{6} a^{4}}{b^{9}} + \frac{168 \,{\left (a + \frac{b}{x^{\frac{1}{3}}}\right )}^{5} a^{5}}{5 \, b^{9}} - \frac{21 \,{\left (a + \frac{b}{x^{\frac{1}{3}}}\right )}^{4} a^{6}}{b^{9}} + \frac{8 \,{\left (a + \frac{b}{x^{\frac{1}{3}}}\right )}^{3} a^{7}}{b^{9}} - \frac{3 \,{\left (a + \frac{b}{x^{\frac{1}{3}}}\right )}^{2} a^{8}}{2 \, b^{9}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((a + b/x^(1/3))/x^4,x, algorithm="maxima")

[Out]

-3/10*(a + b/x^(1/3))^10/b^9 + 8/3*(a + b/x^(1/3))^9*a/b^9 - 21/2*(a + b/x^(1/3)
)^8*a^2/b^9 + 24*(a + b/x^(1/3))^7*a^3/b^9 - 35*(a + b/x^(1/3))^6*a^4/b^9 + 168/
5*(a + b/x^(1/3))^5*a^5/b^9 - 21*(a + b/x^(1/3))^4*a^6/b^9 + 8*(a + b/x^(1/3))^3
*a^7/b^9 - 3/2*(a + b/x^(1/3))^2*a^8/b^9

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Fricas [A]  time = 0.21969, size = 20, normalized size = 1.05 \[ -\frac{10 \, a x^{\frac{1}{3}} + 9 \, b}{30 \, x^{\frac{10}{3}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((a + b/x^(1/3))/x^4,x, algorithm="fricas")

[Out]

-1/30*(10*a*x^(1/3) + 9*b)/x^(10/3)

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Sympy [A]  time = 9.07927, size = 17, normalized size = 0.89 \[ - \frac{a}{3 x^{3}} - \frac{3 b}{10 x^{\frac{10}{3}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((a+b/x**(1/3))/x**4,x)

[Out]

-a/(3*x**3) - 3*b/(10*x**(10/3))

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GIAC/XCAS [A]  time = 0.209772, size = 20, normalized size = 1.05 \[ -\frac{10 \, a x^{\frac{1}{3}} + 9 \, b}{30 \, x^{\frac{10}{3}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((a + b/x^(1/3))/x^4,x, algorithm="giac")

[Out]

-1/30*(10*a*x^(1/3) + 9*b)/x^(10/3)