Optimal. Leaf size=47 \[ -\frac{a^3}{5 x^5}-\frac{2 a^2 b}{3 x^{9/2}}-\frac{3 a b^2}{4 x^4}-\frac{2 b^3}{7 x^{7/2}} \]
[Out]
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Rubi [A] time = 0.0554863, antiderivative size = 47, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133 \[ -\frac{a^3}{5 x^5}-\frac{2 a^2 b}{3 x^{9/2}}-\frac{3 a b^2}{4 x^4}-\frac{2 b^3}{7 x^{7/2}} \]
Antiderivative was successfully verified.
[In] Int[(a + b*Sqrt[x])^3/x^6,x]
[Out]
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Rubi in Sympy [A] time = 8.57145, size = 46, normalized size = 0.98 \[ - \frac{a^{3}}{5 x^{5}} - \frac{2 a^{2} b}{3 x^{\frac{9}{2}}} - \frac{3 a b^{2}}{4 x^{4}} - \frac{2 b^{3}}{7 x^{\frac{7}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b*x**(1/2))**3/x**6,x)
[Out]
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Mathematica [A] time = 0.0161598, size = 41, normalized size = 0.87 \[ -\frac{84 a^3+280 a^2 b \sqrt{x}+315 a b^2 x+120 b^3 x^{3/2}}{420 x^5} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*Sqrt[x])^3/x^6,x]
[Out]
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Maple [A] time = 0.003, size = 36, normalized size = 0.8 \[ -{\frac{{a}^{3}}{5\,{x}^{5}}}-{\frac{2\,{a}^{2}b}{3}{x}^{-{\frac{9}{2}}}}-{\frac{3\,a{b}^{2}}{4\,{x}^{4}}}-{\frac{2\,{b}^{3}}{7}{x}^{-{\frac{7}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b*x^(1/2))^3/x^6,x)
[Out]
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Maxima [A] time = 1.53289, size = 47, normalized size = 1. \[ -\frac{120 \, b^{3} x^{\frac{3}{2}} + 315 \, a b^{2} x + 280 \, a^{2} b \sqrt{x} + 84 \, a^{3}}{420 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*sqrt(x) + a)^3/x^6,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.233722, size = 49, normalized size = 1.04 \[ -\frac{315 \, a b^{2} x + 84 \, a^{3} + 40 \,{\left (3 \, b^{3} x + 7 \, a^{2} b\right )} \sqrt{x}}{420 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*sqrt(x) + a)^3/x^6,x, algorithm="fricas")
[Out]
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Sympy [A] time = 7.58204, size = 46, normalized size = 0.98 \[ - \frac{a^{3}}{5 x^{5}} - \frac{2 a^{2} b}{3 x^{\frac{9}{2}}} - \frac{3 a b^{2}}{4 x^{4}} - \frac{2 b^{3}}{7 x^{\frac{7}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b*x**(1/2))**3/x**6,x)
[Out]
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GIAC/XCAS [A] time = 0.21653, size = 47, normalized size = 1. \[ -\frac{120 \, b^{3} x^{\frac{3}{2}} + 315 \, a b^{2} x + 280 \, a^{2} b \sqrt{x} + 84 \, a^{3}}{420 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*sqrt(x) + a)^3/x^6,x, algorithm="giac")
[Out]