Optimal. Leaf size=37 \[ \frac{2 \left (x^3+x^2\right )^{3/2}}{5 x^2}-\frac{4 \left (x^3+x^2\right )^{3/2}}{15 x^3} \]
[Out]
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Rubi [A] time = 0.0455966, antiderivative size = 37, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.182 \[ \frac{2 \left (x^3+x^2\right )^{3/2}}{5 x^2}-\frac{4 \left (x^3+x^2\right )^{3/2}}{15 x^3} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[x^2 + x^3],x]
[Out]
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Rubi in Sympy [A] time = 3.03249, size = 32, normalized size = 0.86 \[ \frac{2 \left (x^{3} + x^{2}\right )^{\frac{3}{2}}}{5 x^{2}} - \frac{4 \left (x^{3} + x^{2}\right )^{\frac{3}{2}}}{15 x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((x**3+x**2)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0110324, size = 23, normalized size = 0.62 \[ \frac{2 \left (x^2 (x+1)\right )^{3/2} (3 x-2)}{15 x^3} \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[x^2 + x^3],x]
[Out]
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Maple [A] time = 0.003, size = 23, normalized size = 0.6 \[{\frac{ \left ( 2+2\,x \right ) \left ( 3\,x-2 \right ) }{15\,x}\sqrt{{x}^{3}+{x}^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((x^3+x^2)^(1/2),x)
[Out]
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Maxima [A] time = 0.721156, size = 20, normalized size = 0.54 \[ \frac{2}{15} \,{\left (3 \, x^{2} + x - 2\right )} \sqrt{x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(x^3 + x^2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.265747, size = 30, normalized size = 0.81 \[ \frac{2 \, \sqrt{x^{3} + x^{2}}{\left (3 \, x^{2} + x - 2\right )}}{15 \, x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(x^3 + x^2),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \sqrt{x^{3} + x^{2}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x**3+x**2)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.262637, size = 32, normalized size = 0.86 \[ \frac{2}{15} \,{\left (3 \,{\left (x + 1\right )}^{\frac{5}{2}} - 5 \,{\left (x + 1\right )}^{\frac{3}{2}}\right )}{\rm sign}\left (x\right ) + \frac{4}{15} \,{\rm sign}\left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(x^3 + x^2),x, algorithm="giac")
[Out]