Optimal. Leaf size=25 \[ \frac{2 \left (x^2 \left (a+b x^3\right )\right )^{3/2}}{9 b x^3} \]
[Out]
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Rubi [A] time = 0.0137916, antiderivative size = 25, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.059 \[ \frac{2 \left (x^2 \left (a+b x^3\right )\right )^{3/2}}{9 b x^3} \]
Antiderivative was successfully verified.
[In] Int[x*Sqrt[x^2*(a + b*x^3)],x]
[Out]
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Rubi in Sympy [A] time = 6.72121, size = 20, normalized size = 0.8 \[ \frac{2 \left (a x^{2} + b x^{5}\right )^{\frac{3}{2}}}{9 b x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x*(x**2*(b*x**3+a))**(1/2),x)
[Out]
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Mathematica [A] time = 0.0231226, size = 25, normalized size = 1. \[ \frac{2 \left (x^2 \left (a+b x^3\right )\right )^{3/2}}{9 b x^3} \]
Antiderivative was successfully verified.
[In] Integrate[x*Sqrt[x^2*(a + b*x^3)],x]
[Out]
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Maple [A] time = 0.008, size = 29, normalized size = 1.2 \[{\frac{2\,b{x}^{3}+2\,a}{9\,bx}\sqrt{{x}^{2} \left ( b{x}^{3}+a \right ) }} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x*(x^2*(b*x^3+a))^(1/2),x)
[Out]
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Maxima [A] time = 1.39294, size = 19, normalized size = 0.76 \[ \frac{2 \,{\left (b x^{3} + a\right )}^{\frac{3}{2}}}{9 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt((b*x^3 + a)*x^2)*x,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.227703, size = 38, normalized size = 1.52 \[ \frac{2 \, \sqrt{b x^{5} + a x^{2}}{\left (b x^{3} + a\right )}}{9 \, b x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt((b*x^3 + a)*x^2)*x,x, algorithm="fricas")
[Out]
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x*(x**2*(b*x**3+a))**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.223694, size = 36, normalized size = 1.44 \[ \frac{2 \,{\left (b x^{3} + a\right )}^{\frac{3}{2}}{\rm sign}\left (x\right )}{9 \, b} - \frac{2 \, a^{\frac{3}{2}}{\rm sign}\left (x\right )}{9 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt((b*x^3 + a)*x^2)*x,x, algorithm="giac")
[Out]