3.241 \(\int \frac{\left (a+b x^3\right )^3}{x} \, dx\)

Optimal. Leaf size=36 \[ a^3 \log (x)+a^2 b x^3+\frac{1}{2} a b^2 x^6+\frac{b^3 x^9}{9} \]

[Out]

a^2*b*x^3 + (a*b^2*x^6)/2 + (b^3*x^9)/9 + a^3*Log[x]

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Rubi [A]  time = 0.0483984, antiderivative size = 36, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154 \[ a^3 \log (x)+a^2 b x^3+\frac{1}{2} a b^2 x^6+\frac{b^3 x^9}{9} \]

Antiderivative was successfully verified.

[In]  Int[(a + b*x^3)^3/x,x]

[Out]

a^2*b*x^3 + (a*b^2*x^6)/2 + (b^3*x^9)/9 + a^3*Log[x]

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{a^{3} \log{\left (x^{3} \right )}}{3} + a^{2} b x^{3} + a b^{2} \int ^{x^{3}} x\, dx + \frac{b^{3} x^{9}}{9} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

a**3*log(x**3)/3 + a**2*b*x**3 + a*b**2*Integral(x, (x, x**3)) + b**3*x**9/9

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Mathematica [A]  time = 0.00714778, size = 36, normalized size = 1. \[ a^3 \log (x)+a^2 b x^3+\frac{1}{2} a b^2 x^6+\frac{b^3 x^9}{9} \]

Antiderivative was successfully verified.

[In]  Integrate[(a + b*x^3)^3/x,x]

[Out]

a^2*b*x^3 + (a*b^2*x^6)/2 + (b^3*x^9)/9 + a^3*Log[x]

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Maple [A]  time = 0.003, size = 33, normalized size = 0.9 \[{a}^{2}b{x}^{3}+{\frac{a{b}^{2}{x}^{6}}{2}}+{\frac{{b}^{3}{x}^{9}}{9}}+{a}^{3}\ln \left ( x \right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((b*x^3+a)^3/x,x)

[Out]

a^2*b*x^3+1/2*a*b^2*x^6+1/9*b^3*x^9+a^3*ln(x)

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Maxima [A]  time = 1.43885, size = 47, normalized size = 1.31 \[ \frac{1}{9} \, b^{3} x^{9} + \frac{1}{2} \, a b^{2} x^{6} + a^{2} b x^{3} + \frac{1}{3} \, a^{3} \log \left (x^{3}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/9*b^3*x^9 + 1/2*a*b^2*x^6 + a^2*b*x^3 + 1/3*a^3*log(x^3)

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Fricas [A]  time = 0.216513, size = 43, normalized size = 1.19 \[ \frac{1}{9} \, b^{3} x^{9} + \frac{1}{2} \, a b^{2} x^{6} + a^{2} b x^{3} + a^{3} \log \left (x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/9*b^3*x^9 + 1/2*a*b^2*x^6 + a^2*b*x^3 + a^3*log(x)

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Sympy [A]  time = 1.07773, size = 32, normalized size = 0.89 \[ a^{3} \log{\left (x \right )} + a^{2} b x^{3} + \frac{a b^{2} x^{6}}{2} + \frac{b^{3} x^{9}}{9} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x**3+a)**3/x,x)

[Out]

a**3*log(x) + a**2*b*x**3 + a*b**2*x**6/2 + b**3*x**9/9

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GIAC/XCAS [A]  time = 0.217218, size = 45, normalized size = 1.25 \[ \frac{1}{9} \, b^{3} x^{9} + \frac{1}{2} \, a b^{2} x^{6} + a^{2} b x^{3} + a^{3}{\rm ln}\left ({\left | x \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/9*b^3*x^9 + 1/2*a*b^2*x^6 + a^2*b*x^3 + a^3*ln(abs(x))