Optimal. Leaf size=47 \[ -\frac{2 a^3}{\sqrt{x}}+2 a^2 b x^{3/2}+\frac{6}{7} a b^2 x^{7/2}+\frac{2}{11} b^3 x^{11/2} \]
[Out]
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Rubi [A] time = 0.0451163, antiderivative size = 47, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067 \[ -\frac{2 a^3}{\sqrt{x}}+2 a^2 b x^{3/2}+\frac{6}{7} a b^2 x^{7/2}+\frac{2}{11} b^3 x^{11/2} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^2)^3/x^(3/2),x]
[Out]
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Rubi in Sympy [A] time = 6.34066, size = 46, normalized size = 0.98 \[ - \frac{2 a^{3}}{\sqrt{x}} + 2 a^{2} b x^{\frac{3}{2}} + \frac{6 a b^{2} x^{\frac{7}{2}}}{7} + \frac{2 b^{3} x^{\frac{11}{2}}}{11} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**2+a)**3/x**(3/2),x)
[Out]
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Mathematica [A] time = 0.0148207, size = 41, normalized size = 0.87 \[ \frac{2 \left (-77 a^3+77 a^2 b x^2+33 a b^2 x^4+7 b^3 x^6\right )}{77 \sqrt{x}} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^2)^3/x^(3/2),x]
[Out]
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Maple [A] time = 0.007, size = 38, normalized size = 0.8 \[ -{\frac{-14\,{b}^{3}{x}^{6}-66\,a{b}^{2}{x}^{4}-154\,{a}^{2}b{x}^{2}+154\,{a}^{3}}{77}{\frac{1}{\sqrt{x}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^2+a)^3/x^(3/2),x)
[Out]
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Maxima [A] time = 1.3336, size = 47, normalized size = 1. \[ \frac{2}{11} \, b^{3} x^{\frac{11}{2}} + \frac{6}{7} \, a b^{2} x^{\frac{7}{2}} + 2 \, a^{2} b x^{\frac{3}{2}} - \frac{2 \, a^{3}}{\sqrt{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)^3/x^(3/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.213242, size = 50, normalized size = 1.06 \[ \frac{2 \,{\left (7 \, b^{3} x^{6} + 33 \, a b^{2} x^{4} + 77 \, a^{2} b x^{2} - 77 \, a^{3}\right )}}{77 \, \sqrt{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)^3/x^(3/2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 8.35432, size = 46, normalized size = 0.98 \[ - \frac{2 a^{3}}{\sqrt{x}} + 2 a^{2} b x^{\frac{3}{2}} + \frac{6 a b^{2} x^{\frac{7}{2}}}{7} + \frac{2 b^{3} x^{\frac{11}{2}}}{11} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**2+a)**3/x**(3/2),x)
[Out]
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GIAC/XCAS [A] time = 0.211612, size = 47, normalized size = 1. \[ \frac{2}{11} \, b^{3} x^{\frac{11}{2}} + \frac{6}{7} \, a b^{2} x^{\frac{7}{2}} + 2 \, a^{2} b x^{\frac{3}{2}} - \frac{2 \, a^{3}}{\sqrt{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)^3/x^(3/2),x, algorithm="giac")
[Out]