Optimal. Leaf size=14 \[ \frac{(a+b x)^7}{7 b} \]
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Rubi [A] time = 0.0169498, antiderivative size = 14, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 29, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.069 \[ \frac{(a+b x)^7}{7 b} \]
Antiderivative was successfully verified.
[In] Int[(a^3 + 3*a^2*b*x + 3*a*b^2*x^2 + b^3*x^3)^2,x]
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Rubi in Sympy [A] time = 15.6221, size = 8, normalized size = 0.57 \[ \frac{\left (a + b x\right )^{7}}{7 b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b**3*x**3+3*a*b**2*x**2+3*a**2*b*x+a**3)**2,x)
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Mathematica [A] time = 0.00204501, size = 14, normalized size = 1. \[ \frac{(a+b x)^7}{7 b} \]
Antiderivative was successfully verified.
[In] Integrate[(a^3 + 3*a^2*b*x + 3*a*b^2*x^2 + b^3*x^3)^2,x]
[Out]
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Maple [B] time = 0.001, size = 65, normalized size = 4.6 \[{\frac{{b}^{6}{x}^{7}}{7}}+a{b}^{5}{x}^{6}+3\,{a}^{2}{b}^{4}{x}^{5}+5\,{a}^{3}{b}^{3}{x}^{4}+5\,{a}^{4}{b}^{2}{x}^{3}+3\,{a}^{5}b{x}^{2}+{a}^{6}x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b^3*x^3+3*a*b^2*x^2+3*a^2*b*x+a^3)^2,x)
[Out]
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Maxima [A] time = 0.77603, size = 134, normalized size = 9.57 \[ \frac{1}{7} \, b^{6} x^{7} + a b^{5} x^{6} + \frac{9}{5} \, a^{2} b^{4} x^{5} + 3 \, a^{4} b^{2} x^{3} + a^{6} x + \frac{1}{2} \,{\left (b^{3} x^{4} + 4 \, a b^{2} x^{3} + 6 \, a^{2} b x^{2}\right )} a^{3} + \frac{3}{10} \,{\left (4 \, b^{3} x^{5} + 15 \, a b^{2} x^{4}\right )} a^{2} b \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b^3*x^3 + 3*a*b^2*x^2 + 3*a^2*b*x + a^3)^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.249373, size = 1, normalized size = 0.07 \[ \frac{1}{7} x^{7} b^{6} + x^{6} b^{5} a + 3 x^{5} b^{4} a^{2} + 5 x^{4} b^{3} a^{3} + 5 x^{3} b^{2} a^{4} + 3 x^{2} b a^{5} + x a^{6} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b^3*x^3 + 3*a*b^2*x^2 + 3*a^2*b*x + a^3)^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.125764, size = 66, normalized size = 4.71 \[ a^{6} x + 3 a^{5} b x^{2} + 5 a^{4} b^{2} x^{3} + 5 a^{3} b^{3} x^{4} + 3 a^{2} b^{4} x^{5} + a b^{5} x^{6} + \frac{b^{6} x^{7}}{7} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b**3*x**3+3*a*b**2*x**2+3*a**2*b*x+a**3)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.261963, size = 86, normalized size = 6.14 \[ \frac{1}{7} \, b^{6} x^{7} + a b^{5} x^{6} + 3 \, a^{2} b^{4} x^{5} + 5 \, a^{3} b^{3} x^{4} + 5 \, a^{4} b^{2} x^{3} + 3 \, a^{5} b x^{2} + a^{6} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b^3*x^3 + 3*a*b^2*x^2 + 3*a^2*b*x + a^3)^2,x, algorithm="giac")
[Out]