Optimal. Leaf size=63 \[ -\frac{a^3 x^{-6 n}}{6 n}-\frac{3 a^2 b x^{-5 n}}{5 n}-\frac{3 a b^2 x^{-4 n}}{4 n}-\frac{b^3 x^{-3 n}}{3 n} \]
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Rubi [A] time = 0.0666669, antiderivative size = 63, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.118 \[ -\frac{a^3 x^{-6 n}}{6 n}-\frac{3 a^2 b x^{-5 n}}{5 n}-\frac{3 a b^2 x^{-4 n}}{4 n}-\frac{b^3 x^{-3 n}}{3 n} \]
Antiderivative was successfully verified.
[In] Int[x^(-1 - 6*n)*(a + b*x^n)^3,x]
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Rubi in Sympy [A] time = 10.8654, size = 54, normalized size = 0.86 \[ - \frac{a^{3} x^{- 6 n}}{6 n} - \frac{3 a^{2} b x^{- 5 n}}{5 n} - \frac{3 a b^{2} x^{- 4 n}}{4 n} - \frac{b^{3} x^{- 3 n}}{3 n} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**(-1-6*n)*(a+b*x**n)**3,x)
[Out]
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Mathematica [A] time = 0.0276948, size = 48, normalized size = 0.76 \[ -\frac{x^{-6 n} \left (10 a^3+36 a^2 b x^n+45 a b^2 x^{2 n}+20 b^3 x^{3 n}\right )}{60 n} \]
Antiderivative was successfully verified.
[In] Integrate[x^(-1 - 6*n)*(a + b*x^n)^3,x]
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Maple [A] time = 0.031, size = 56, normalized size = 0.9 \[ -{\frac{{b}^{3}}{3\,n \left ({x}^{n} \right ) ^{3}}}-{\frac{3\,a{b}^{2}}{4\,n \left ({x}^{n} \right ) ^{4}}}-{\frac{3\,{a}^{2}b}{5\,n \left ({x}^{n} \right ) ^{5}}}-{\frac{{a}^{3}}{6\,n \left ({x}^{n} \right ) ^{6}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^(-1-6*n)*(a+b*x^n)^3,x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: ValueError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^n + a)^3*x^(-6*n - 1),x, algorithm="maxima")
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Fricas [A] time = 0.223979, size = 65, normalized size = 1.03 \[ -\frac{20 \, b^{3} x^{3 \, n} + 45 \, a b^{2} x^{2 \, n} + 36 \, a^{2} b x^{n} + 10 \, a^{3}}{60 \, n x^{6 \, n}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^n + a)^3*x^(-6*n - 1),x, algorithm="fricas")
[Out]
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Sympy [A] time = 117.865, size = 63, normalized size = 1. \[ \begin{cases} - \frac{a^{3} x^{- 6 n}}{6 n} - \frac{3 a^{2} b x^{- 5 n}}{5 n} - \frac{3 a b^{2} x^{- 4 n}}{4 n} - \frac{b^{3} x^{- 3 n}}{3 n} & \text{for}\: n \neq 0 \\\left (a + b\right )^{3} \log{\left (x \right )} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**(-1-6*n)*(a+b*x**n)**3,x)
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GIAC/XCAS [A] time = 0.22154, size = 69, normalized size = 1.1 \[ -\frac{{\left (20 \, b^{3} e^{\left (3 \, n{\rm ln}\left (x\right )\right )} + 45 \, a b^{2} e^{\left (2 \, n{\rm ln}\left (x\right )\right )} + 36 \, a^{2} b e^{\left (n{\rm ln}\left (x\right )\right )} + 10 \, a^{3}\right )} e^{\left (-6 \, n{\rm ln}\left (x\right )\right )}}{60 \, n} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^n + a)^3*x^(-6*n - 1),x, algorithm="giac")
[Out]