Optimal. Leaf size=20 \[ \frac{2}{5} x^2 \sqrt{x^3+5 e^x} \]
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Rubi [A] time = 0.943667, antiderivative size = 20, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 2, integrand size = 50, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.04 \[ \frac{2}{5} x^2 \sqrt{x^3+5 e^x} \]
Antiderivative was successfully verified.
[In] Int[(x^2*(5*E^x + 3*x^2))/(5*Sqrt[5*E^x + x^3]) + (4*x*Sqrt[5*E^x + x^3])/5,x]
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Rubi in Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/5*x**2*(5*exp(x)+3*x**2)/(5*exp(x)+x**3)**(1/2)+4/5*x*(5*exp(x)+x**3)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0462046, size = 20, normalized size = 1. \[ \frac{2}{5} x^2 \sqrt{x^3+5 e^x} \]
Antiderivative was successfully verified.
[In] Integrate[(x^2*(5*E^x + 3*x^2))/(5*Sqrt[5*E^x + x^3]) + (4*x*Sqrt[5*E^x + x^3])/5,x]
[Out]
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Maple [A] time = 0.05, size = 16, normalized size = 0.8 \[{\frac{2\,{x}^{2}}{5}\sqrt{5\,{{\rm e}^{x}}+{x}^{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/5*x^2*(5*exp(x)+3*x^2)/(5*exp(x)+x^3)^(1/2)+4/5*x*(5*exp(x)+x^3)^(1/2),x)
[Out]
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Maxima [A] time = 0.920601, size = 31, normalized size = 1.55 \[ \frac{2 \,{\left (x^{5} + 5 \, x^{2} e^{x}\right )}}{5 \, \sqrt{x^{3} + 5 \, e^{x}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/5*(3*x^2 + 5*e^x)*x^2/sqrt(x^3 + 5*e^x) + 4/5*sqrt(x^3 + 5*e^x)*x,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(1/5*(3*x^2 + 5*e^x)*x^2/sqrt(x^3 + 5*e^x) + 4/5*sqrt(x^3 + 5*e^x)*x,x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{\int \frac{7 x^{4}}{\sqrt{x^{3} + 5 e^{x}}}\, dx + \int \frac{20 x e^{x}}{\sqrt{x^{3} + 5 e^{x}}}\, dx + \int \frac{5 x^{2} e^{x}}{\sqrt{x^{3} + 5 e^{x}}}\, dx}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/5*x**2*(5*exp(x)+3*x**2)/(5*exp(x)+x**3)**(1/2)+4/5*x*(5*exp(x)+x**3)**(1/2),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{{\left (3 \, x^{2} + 5 \, e^{x}\right )} x^{2}}{5 \, \sqrt{x^{3} + 5 \, e^{x}}} + \frac{4}{5} \, \sqrt{x^{3} + 5 \, e^{x}} x\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/5*(3*x^2 + 5*e^x)*x^2/sqrt(x^3 + 5*e^x) + 4/5*sqrt(x^3 + 5*e^x)*x,x, algorithm="giac")
[Out]