Optimal. Leaf size=25 \[ \frac{2 \sqrt{a x^2+b x^5}}{3 b x} \]
[Out]
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Rubi [A] time = 0.0149602, antiderivative size = 25, 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 \[ \frac{2 \sqrt{a x^2+b x^5}}{3 b x} \]
Antiderivative was successfully verified.
[In] Int[x^3/Sqrt[a*x^2 + b*x^5],x]
[Out]
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Rubi in Sympy [A] time = 7.05235, size = 19, normalized size = 0.76 \[ \frac{2 \sqrt{a x^{2} + b x^{5}}}{3 b x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**3/(b*x**5+a*x**2)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0148376, size = 25, normalized size = 1. \[ \frac{2 \sqrt{x^2 \left (a+b x^3\right )}}{3 b x} \]
Antiderivative was successfully verified.
[In] Integrate[x^3/Sqrt[a*x^2 + b*x^5],x]
[Out]
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Maple [A] time = 0.008, size = 27, normalized size = 1.1 \[{\frac{2\,x \left ( b{x}^{3}+a \right ) }{3\,b}{\frac{1}{\sqrt{b{x}^{5}+a{x}^{2}}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^3/(b*x^5+a*x^2)^(1/2),x)
[Out]
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Maxima [A] time = 1.39405, size = 19, normalized size = 0.76 \[ \frac{2 \, \sqrt{b x^{3} + a}}{3 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^3/sqrt(b*x^5 + a*x^2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.215296, size = 28, normalized size = 1.12 \[ \frac{2 \, \sqrt{b x^{5} + a x^{2}}}{3 \, b x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^3/sqrt(b*x^5 + a*x^2),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{x^{3}}{\sqrt{x^{2} \left (a + b x^{3}\right )}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**3/(b*x**5+a*x**2)**(1/2),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{x^{3}}{\sqrt{b x^{5} + a x^{2}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^3/sqrt(b*x^5 + a*x^2),x, algorithm="giac")
[Out]