Optimal. Leaf size=37 \[ a^3 \log (x)+6 a^2 b \sqrt{x}+3 a b^2 x+\frac{2}{3} b^3 x^{3/2} \]
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Rubi [A] time = 0.049088, antiderivative size = 37, 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 \[ a^3 \log (x)+6 a^2 b \sqrt{x}+3 a b^2 x+\frac{2}{3} b^3 x^{3/2} \]
Antiderivative was successfully verified.
[In] Int[(a + b*Sqrt[x])^3/x,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ 2 a^{3} \log{\left (\sqrt{x} \right )} + 6 a^{2} b \sqrt{x} + 6 a b^{2} \int ^{\sqrt{x}} x\, dx + \frac{2 b^{3} x^{\frac{3}{2}}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b*x**(1/2))**3/x,x)
[Out]
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Mathematica [A] time = 0.0152542, size = 37, normalized size = 1. \[ a^3 \log (x)+6 a^2 b \sqrt{x}+3 a b^2 x+\frac{2}{3} b^3 x^{3/2} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*Sqrt[x])^3/x,x]
[Out]
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Maple [A] time = 0.003, size = 32, normalized size = 0.9 \[ 3\,a{b}^{2}x+{\frac{2\,{b}^{3}}{3}{x}^{{\frac{3}{2}}}}+{a}^{3}\ln \left ( x \right ) +6\,{a}^{2}b\sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b*x^(1/2))^3/x,x)
[Out]
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Maxima [A] time = 1.42985, size = 42, normalized size = 1.14 \[ \frac{2}{3} \, b^{3} x^{\frac{3}{2}} + 3 \, a b^{2} x + a^{3} \log \left (x\right ) + 6 \, a^{2} b \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*sqrt(x) + a)^3/x,x, algorithm="maxima")
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Fricas [A] time = 0.235659, size = 46, normalized size = 1.24 \[ 3 \, a b^{2} x + 2 \, a^{3} \log \left (\sqrt{x}\right ) + \frac{2}{3} \,{\left (b^{3} x + 9 \, a^{2} b\right )} \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*sqrt(x) + a)^3/x,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.665255, size = 37, normalized size = 1. \[ a^{3} \log{\left (x \right )} + 6 a^{2} b \sqrt{x} + 3 a b^{2} x + \frac{2 b^{3} x^{\frac{3}{2}}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b*x**(1/2))**3/x,x)
[Out]
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GIAC/XCAS [A] time = 0.217069, size = 43, normalized size = 1.16 \[ \frac{2}{3} \, b^{3} x^{\frac{3}{2}} + 3 \, a b^{2} x + a^{3}{\rm ln}\left ({\left | x \right |}\right ) + 6 \, a^{2} b \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*sqrt(x) + a)^3/x,x, algorithm="giac")
[Out]