Optimal. Leaf size=12 \[ 3 x \left (x+e^x\right )^{2/3} \]
[Out]
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Rubi [A] time = 0.50272, antiderivative size = 12, normalized size of antiderivative = 1., number of steps used = 8, number of rules used = 4, integrand size = 23, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.174 \[ 3 x \left (x+e^x\right )^{2/3} \]
Antiderivative was successfully verified.
[In] Int[(5*x + E^x*(3 + 2*x))/(E^x + x)^(1/3),x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{5 x + \left (2 x + 3\right ) e^{x}}{\sqrt [3]{x + e^{x}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((5*x+exp(x)*(3+2*x))/(exp(x)+x)**(1/3),x)
[Out]
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Mathematica [A] time = 0.0249667, size = 12, normalized size = 1. \[ 3 x \left (x+e^x\right )^{2/3} \]
Antiderivative was successfully verified.
[In] Integrate[(5*x + E^x*(3 + 2*x))/(E^x + x)^(1/3),x]
[Out]
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Maple [A] time = 0.014, size = 10, normalized size = 0.8 \[ 3\,x \left ({{\rm e}^{x}}+x \right ) ^{2/3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((5*x+exp(x)*(3+2*x))/(exp(x)+x)^(1/3),x)
[Out]
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Maxima [A] time = 0.82782, size = 22, normalized size = 1.83 \[ \frac{3 \,{\left (x^{2} + x e^{x}\right )}}{{\left (x + e^{x}\right )}^{\frac{1}{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(((2*x + 3)*e^x + 5*x)/(x + e^x)^(1/3),x, algorithm="maxima")
[Out]
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Fricas [F(-2)] time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: TypeError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(((2*x + 3)*e^x + 5*x)/(x + e^x)^(1/3),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{2 x e^{x} + 5 x + 3 e^{x}}{\sqrt [3]{x + e^{x}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x+exp(x)*(3+2*x))/(exp(x)+x)**(1/3),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{{\left (2 \, x + 3\right )} e^{x} + 5 \, x}{{\left (x + e^{x}\right )}^{\frac{1}{3}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(((2*x + 3)*e^x + 5*x)/(x + e^x)^(1/3),x, algorithm="giac")
[Out]