Optimal. Leaf size=40 \[ a^3 x+3 a^2 b e^x+\frac{3}{2} a b^2 e^{2 x}+\frac{1}{3} b^3 e^{3 x} \]
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Rubi [A] time = 0.0393371, antiderivative size = 40, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.222 \[ a^3 x+3 a^2 b e^x+\frac{3}{2} a b^2 e^{2 x}+\frac{1}{3} b^3 e^{3 x} \]
Antiderivative was successfully verified.
[In] Int[(a + b*E^x)^3,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ a^{3} \log{\left (e^{x} \right )} + 3 a^{2} b e^{x} + 3 a b^{2} \int ^{e^{x}} x\, dx + \frac{b^{3} e^{3 x}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b*exp(x))**3,x)
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Mathematica [A] time = 0.0101908, size = 40, normalized size = 1. \[ a^3 x+3 a^2 b e^x+\frac{3}{2} a b^2 e^{2 x}+\frac{1}{3} b^3 e^{3 x} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*E^x)^3,x]
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Maple [A] time = 0.001, size = 36, normalized size = 0.9 \[{\frac{{b}^{3} \left ({{\rm e}^{x}} \right ) ^{3}}{3}}+{\frac{3\,a{b}^{2} \left ({{\rm e}^{x}} \right ) ^{2}}{2}}+3\,{a}^{2}b{{\rm e}^{x}}+{a}^{3}\ln \left ({{\rm e}^{x}} \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b*exp(x))^3,x)
[Out]
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Maxima [A] time = 0.746033, size = 45, normalized size = 1.12 \[ a^{3} x + \frac{1}{3} \, b^{3} e^{\left (3 \, x\right )} + \frac{3}{2} \, a b^{2} e^{\left (2 \, x\right )} + 3 \, a^{2} b e^{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*e^x + a)^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.257728, size = 45, normalized size = 1.12 \[ a^{3} x + \frac{1}{3} \, b^{3} e^{\left (3 \, x\right )} + \frac{3}{2} \, a b^{2} e^{\left (2 \, x\right )} + 3 \, a^{2} b e^{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*e^x + a)^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.13468, size = 37, normalized size = 0.92 \[ a^{3} x + 3 a^{2} b e^{x} + \frac{3 a b^{2} e^{2 x}}{2} + \frac{b^{3} e^{3 x}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b*exp(x))**3,x)
[Out]
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GIAC/XCAS [A] time = 0.220614, size = 45, normalized size = 1.12 \[ a^{3} x + \frac{1}{3} \, b^{3} e^{\left (3 \, x\right )} + \frac{3}{2} \, a b^{2} e^{\left (2 \, x\right )} + 3 \, a^{2} b e^{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*e^x + a)^3,x, algorithm="giac")
[Out]