Optimal. Leaf size=53 \[ a^4 x+4 a^3 b e^x+3 a^2 b^2 e^{2 x}+\frac{4}{3} a b^3 e^{3 x}+\frac{1}{4} b^4 e^{4 x} \]
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Rubi [A] time = 0.050668, antiderivative size = 53, 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 \[ a^4 x+4 a^3 b e^x+3 a^2 b^2 e^{2 x}+\frac{4}{3} a b^3 e^{3 x}+\frac{1}{4} b^4 e^{4 x} \]
Antiderivative was successfully verified.
[In] Int[(a + b*E^x)^4,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ a^{4} \log{\left (e^{x} \right )} + 4 a^{3} b e^{x} + 6 a^{2} b^{2} \int ^{e^{x}} x\, dx + \frac{4 a b^{3} e^{3 x}}{3} + \frac{b^{4} e^{4 x}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b*exp(x))**4,x)
[Out]
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Mathematica [A] time = 0.0123917, size = 53, normalized size = 1. \[ a^4 x+4 a^3 b e^x+3 a^2 b^2 e^{2 x}+\frac{4}{3} a b^3 e^{3 x}+\frac{1}{4} b^4 e^{4 x} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*E^x)^4,x]
[Out]
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Maple [A] time = 0.003, size = 48, normalized size = 0.9 \[{\frac{{b}^{4} \left ({{\rm e}^{x}} \right ) ^{4}}{4}}+{\frac{4\,a{b}^{3} \left ({{\rm e}^{x}} \right ) ^{3}}{3}}+3\,{a}^{2}{b}^{2} \left ({{\rm e}^{x}} \right ) ^{2}+4\,{a}^{3}b{{\rm e}^{x}}+{a}^{4}\ln \left ({{\rm e}^{x}} \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b*exp(x))^4,x)
[Out]
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Maxima [A] time = 0.762892, size = 61, normalized size = 1.15 \[ a^{4} x + \frac{1}{4} \, b^{4} e^{\left (4 \, x\right )} + \frac{4}{3} \, a b^{3} e^{\left (3 \, x\right )} + 3 \, a^{2} b^{2} e^{\left (2 \, x\right )} + 4 \, a^{3} b e^{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*e^x + a)^4,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.241483, size = 61, normalized size = 1.15 \[ a^{4} x + \frac{1}{4} \, b^{4} e^{\left (4 \, x\right )} + \frac{4}{3} \, a b^{3} e^{\left (3 \, x\right )} + 3 \, a^{2} b^{2} e^{\left (2 \, x\right )} + 4 \, a^{3} b e^{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*e^x + a)^4,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.166968, size = 51, normalized size = 0.96 \[ a^{4} x + 4 a^{3} b e^{x} + 3 a^{2} b^{2} e^{2 x} + \frac{4 a b^{3} e^{3 x}}{3} + \frac{b^{4} e^{4 x}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b*exp(x))**4,x)
[Out]
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GIAC/XCAS [A] time = 0.301992, size = 61, normalized size = 1.15 \[ a^{4} x + \frac{1}{4} \, b^{4} e^{\left (4 \, x\right )} + \frac{4}{3} \, a b^{3} e^{\left (3 \, x\right )} + 3 \, a^{2} b^{2} e^{\left (2 \, x\right )} + 4 \, a^{3} b e^{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*e^x + a)^4,x, algorithm="giac")
[Out]