Optimal. Leaf size=17 \[ 3 \left (x+e^x\right )^{2/3} x+3 \log (x) \]
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Rubi [A] time = 1.01534, antiderivative size = 17, normalized size of antiderivative = 1., number of steps used = 8, number of rules used = 4, integrand size = 43, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.093 \[ 3 \left (x+e^x\right )^{2/3} x+3 \log (x) \]
Antiderivative was successfully verified.
[In] Int[(5*x^2 + 3*(E^x + x)^(1/3) + E^x*(3*x + 2*x^2))/(x*(E^x + x)^(1/3)),x]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{5 x^{2} + 3 \sqrt [3]{x + e^{x}} + \left (2 x^{2} + 3 x\right ) e^{x}}{x \sqrt [3]{x + e^{x}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((5*x**2+3*(exp(x)+x)**(1/3)+exp(x)*(2*x**2+3*x))/x/(exp(x)+x)**(1/3),x)
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Mathematica [A] time = 0.123917, size = 17, normalized size = 1. \[ 3 \left (x+e^x\right )^{2/3} x+3 \log (x) \]
Antiderivative was successfully verified.
[In] Integrate[(5*x^2 + 3*(E^x + x)^(1/3) + E^x*(3*x + 2*x^2))/(x*(E^x + x)^(1/3)),x]
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Maple [F] time = 0.024, size = 0, normalized size = 0. \[ \int{\frac{1}{x} \left ( 5\,{x}^{2}+3\,\sqrt [3]{{{\rm e}^{x}}+x}+{{\rm e}^{x}} \left ( 2\,{x}^{2}+3\,x \right ) \right ){\frac{1}{\sqrt [3]{{{\rm e}^{x}}+x}}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((5*x^2+3*(exp(x)+x)^(1/3)+exp(x)*(2*x^2+3*x))/x/(exp(x)+x)^(1/3),x)
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Maxima [A] time = 1.51708, size = 28, normalized size = 1.65 \[ \frac{3 \,{\left (x^{2} + x e^{x}\right )}}{{\left (x + e^{x}\right )}^{\frac{1}{3}}} + 3 \, \log \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x^2 + (2*x^2 + 3*x)*e^x + 3*(x + e^x)^(1/3))/((x + e^x)^(1/3)*x),x, algorithm="maxima")
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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((5*x^2 + (2*x^2 + 3*x)*e^x + 3*(x + e^x)^(1/3))/((x + e^x)^(1/3)*x),x, algorithm="fricas")
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{2 x^{2} e^{x} + 5 x^{2} + 3 x e^{x} + 3 \sqrt [3]{x + e^{x}}}{x \sqrt [3]{x + e^{x}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x**2+3*(exp(x)+x)**(1/3)+exp(x)*(2*x**2+3*x))/x/(exp(x)+x)**(1/3),x)
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{5 \, x^{2} +{\left (2 \, x^{2} + 3 \, x\right )} e^{x} + 3 \,{\left (x + e^{x}\right )}^{\frac{1}{3}}}{{\left (x + e^{x}\right )}^{\frac{1}{3}} x}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x^2 + (2*x^2 + 3*x)*e^x + 3*(x + e^x)^(1/3))/((x + e^x)^(1/3)*x),x, algorithm="giac")
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