Optimal. Leaf size=20 \[ \frac{4 \left (x^{5/2}+x\right )^{3/2}}{9 x^{3/2}} \]
[Out]
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Rubi [A] time = 0.00959661, antiderivative size = 20, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ \frac{4 \left (x^{5/2}+x\right )^{3/2}}{9 x^{3/2}} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[x + x^(5/2)],x]
[Out]
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Rubi in Sympy [A] time = 1.02098, size = 17, normalized size = 0.85 \[ \frac{4 \left (x^{\frac{5}{2}} + x\right )^{\frac{3}{2}}}{9 x^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((x+x**(5/2))**(1/2),x)
[Out]
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Mathematica [A] time = 0.0193071, size = 29, normalized size = 1.45 \[ \left (\frac{4 x}{9}+\frac{4}{9 \sqrt{x}}\right ) \sqrt{x \left (x^{3/2}+1\right )} \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[x + x^(5/2)],x]
[Out]
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Maple [A] time = 0.013, size = 18, normalized size = 0.9 \[{\frac{4}{9}\sqrt{x+{x}^{{\frac{5}{2}}}} \left ( 1+{x}^{{\frac{3}{2}}} \right ){\frac{1}{\sqrt{x}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((x+x^(5/2))^(1/2),x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \sqrt{x^{\frac{5}{2}} + x}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(x^(5/2) + x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.253817, size = 26, normalized size = 1.3 \[ \frac{4 \, \sqrt{x^{\frac{5}{2}} + x}{\left (x^{2} + \sqrt{x}\right )}}{9 \, x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(x^(5/2) + x),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \sqrt{x^{\frac{5}{2}} + x}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x+x**(5/2))**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.21918, size = 15, normalized size = 0.75 \[ \frac{4}{9} \,{\left (x^{\frac{3}{2}} + 1\right )}^{\frac{3}{2}} - \frac{4}{9} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(x^(5/2) + x),x, algorithm="giac")
[Out]