Optimal. Leaf size=15 \[ \frac{2}{3} \left (x^5+2 x\right )^{3/2} \]
[Out]
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Rubi [A] time = 0.00718842, antiderivative size = 15, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 19, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.053 \[ \frac{2}{3} \left (x^5+2 x\right )^{3/2} \]
Antiderivative was successfully verified.
[In] Int[(2 + 5*x^4)*Sqrt[2*x + x^5],x]
[Out]
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Rubi in Sympy [A] time = 1.43104, size = 12, normalized size = 0.8 \[ \frac{2 \left (x^{5} + 2 x\right )^{\frac{3}{2}}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((5*x**4+2)*(x**5+2*x)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0158078, size = 15, normalized size = 1. \[ \frac{2}{3} \left (x \left (x^4+2\right )\right )^{3/2} \]
Antiderivative was successfully verified.
[In] Integrate[(2 + 5*x^4)*Sqrt[2*x + x^5],x]
[Out]
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Maple [A] time = 0.006, size = 18, normalized size = 1.2 \[{\frac{2\,x \left ({x}^{4}+2 \right ) }{3}\sqrt{{x}^{5}+2\,x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((5*x^4+2)*(x^5+2*x)^(1/2),x)
[Out]
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Maxima [A] time = 0.690947, size = 15, normalized size = 1. \[ \frac{2}{3} \,{\left (x^{5} + 2 \, x\right )}^{\frac{3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(x^5 + 2*x)*(5*x^4 + 2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.258986, size = 15, normalized size = 1. \[ \frac{2}{3} \,{\left (x^{5} + 2 \, x\right )}^{\frac{3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(x^5 + 2*x)*(5*x^4 + 2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.678819, size = 31, normalized size = 2.07 \[ \frac{2 x^{5} \sqrt{x^{5} + 2 x}}{3} + \frac{4 x \sqrt{x^{5} + 2 x}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x**4+2)*(x**5+2*x)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.272422, size = 15, normalized size = 1. \[ \frac{2}{3} \,{\left (x^{5} + 2 \, x\right )}^{\frac{3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(x^5 + 2*x)*(5*x^4 + 2),x, algorithm="giac")
[Out]