Optimal. Leaf size=19 \[ \frac{2 x^{5/2}}{5}+\frac{2 x^{3/2}}{3} \]
[Out]
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Rubi [A] time = 0.0078335, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ \frac{2 x^{5/2}}{5}+\frac{2 x^{3/2}}{3} \]
Antiderivative was successfully verified.
[In] Int[(x + x^2)/Sqrt[x],x]
[Out]
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Rubi in Sympy [A] time = 1.02458, size = 15, normalized size = 0.79 \[ \frac{2 x^{\frac{5}{2}}}{5} + \frac{2 x^{\frac{3}{2}}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((x**2+x)/x**(1/2),x)
[Out]
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Mathematica [A] time = 0.00382188, size = 14, normalized size = 0.74 \[ \frac{2}{15} x^{3/2} (3 x+5) \]
Antiderivative was successfully verified.
[In] Integrate[(x + x^2)/Sqrt[x],x]
[Out]
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Maple [A] time = 0.003, size = 11, normalized size = 0.6 \[{\frac{10+6\,x}{15}{x}^{{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((x^2+x)/x^(1/2),x)
[Out]
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Maxima [A] time = 1.33123, size = 15, normalized size = 0.79 \[ \frac{2}{5} \, x^{\frac{5}{2}} + \frac{2}{3} \, x^{\frac{3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^2 + x)/sqrt(x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.211054, size = 19, normalized size = 1. \[ \frac{2}{15} \,{\left (3 \, x^{2} + 5 \, x\right )} \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^2 + x)/sqrt(x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.27182, size = 15, normalized size = 0.79 \[ \frac{2 x^{\frac{5}{2}}}{5} + \frac{2 x^{\frac{3}{2}}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x**2+x)/x**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.198108, size = 15, normalized size = 0.79 \[ \frac{2}{5} \, x^{\frac{5}{2}} + \frac{2}{3} \, x^{\frac{3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^2 + x)/sqrt(x),x, algorithm="giac")
[Out]