Optimal. Leaf size=63 \[ \frac{a^3 x^{3 n}}{3 n}+\frac{3 a^2 b x^{4 n}}{4 n}+\frac{3 a b^2 x^{5 n}}{5 n}+\frac{b^3 x^{6 n}}{6 n} \]
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Rubi [A] time = 0.0721114, 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 \[ \frac{a^3 x^{3 n}}{3 n}+\frac{3 a^2 b x^{4 n}}{4 n}+\frac{3 a b^2 x^{5 n}}{5 n}+\frac{b^3 x^{6 n}}{6 n} \]
Antiderivative was successfully verified.
[In] Int[x^(-1 + 3*n)*(a + b*x^n)^3,x]
[Out]
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Rubi in Sympy [A] time = 11.2901, size = 53, normalized size = 0.84 \[ \frac{a^{3} x^{3 n}}{3 n} + \frac{3 a^{2} b x^{4 n}}{4 n} + \frac{3 a b^{2} x^{5 n}}{5 n} + \frac{b^{3} x^{6 n}}{6 n} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**(-1+3*n)*(a+b*x**n)**3,x)
[Out]
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Mathematica [A] time = 0.0234826, size = 48, normalized size = 0.76 \[ \frac{x^{3 n} \left (20 a^3+45 a^2 b x^n+36 a b^2 x^{2 n}+10 b^3 x^{3 n}\right )}{60 n} \]
Antiderivative was successfully verified.
[In] Integrate[x^(-1 + 3*n)*(a + b*x^n)^3,x]
[Out]
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Maple [A] time = 0.03, size = 56, normalized size = 0.9 \[{\frac{{b}^{3} \left ({x}^{n} \right ) ^{6}}{6\,n}}+{\frac{3\,a{b}^{2} \left ({x}^{n} \right ) ^{5}}{5\,n}}+{\frac{3\,{a}^{2}b \left ({x}^{n} \right ) ^{4}}{4\,n}}+{\frac{{a}^{3} \left ({x}^{n} \right ) ^{3}}{3\,n}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^(-1+3*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^(3*n - 1),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.22497, size = 65, normalized size = 1.03 \[ \frac{10 \, b^{3} x^{6 \, n} + 36 \, a b^{2} x^{5 \, n} + 45 \, a^{2} b x^{4 \, n} + 20 \, a^{3} x^{3 \, n}}{60 \, n} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^n + a)^3*x^(3*n - 1),x, algorithm="fricas")
[Out]
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Sympy [A] time = 116.467, size = 61, normalized size = 0.97 \[ \begin{cases} \frac{a^{3} x^{3 n}}{3 n} + \frac{3 a^{2} b x^{4 n}}{4 n} + \frac{3 a b^{2} x^{5 n}}{5 n} + \frac{b^{3} x^{6 n}}{6 n} & \text{for}\: n \neq 0 \\\left (a + b\right )^{3} \log{\left (x \right )} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**(-1+3*n)*(a+b*x**n)**3,x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int{\left (b x^{n} + a\right )}^{3} x^{3 \, n - 1}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^n + a)^3*x^(3*n - 1),x, algorithm="giac")
[Out]