Optimal. Leaf size=38 \[ -\frac{a^3}{x}-\frac{6 a^2 b}{\sqrt{x}}+3 a b^2 \log (x)+2 b^3 \sqrt{x} \]
[Out]
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Rubi [A] time = 0.0527943, antiderivative size = 38, 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 \[ -\frac{a^3}{x}-\frac{6 a^2 b}{\sqrt{x}}+3 a b^2 \log (x)+2 b^3 \sqrt{x} \]
Antiderivative was successfully verified.
[In] Int[(a + b*Sqrt[x])^3/x^2,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{a^{3}}{x} - \frac{6 a^{2} b}{\sqrt{x}} + 6 a b^{2} \log{\left (\sqrt{x} \right )} + 2 \int ^{\sqrt{x}} b^{3}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b*x**(1/2))**3/x**2,x)
[Out]
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Mathematica [A] time = 0.0296743, size = 39, normalized size = 1.03 \[ 3 a b^2 \log (x)-\frac{a^3+6 a^2 b \sqrt{x}-2 b^3 x^{3/2}}{x} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*Sqrt[x])^3/x^2,x]
[Out]
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Maple [A] time = 0.003, size = 35, normalized size = 0.9 \[ -{\frac{{a}^{3}}{x}}+3\,a{b}^{2}\ln \left ( x \right ) -6\,{\frac{{a}^{2}b}{\sqrt{x}}}+2\,{b}^{3}\sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b*x^(1/2))^3/x^2,x)
[Out]
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Maxima [A] time = 1.43208, size = 47, normalized size = 1.24 \[ 3 \, a b^{2} \log \left (x\right ) + 2 \, b^{3} \sqrt{x} - \frac{6 \, a^{2} b \sqrt{x} + a^{3}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*sqrt(x) + a)^3/x^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.234188, size = 51, normalized size = 1.34 \[ \frac{6 \, a b^{2} x \log \left (\sqrt{x}\right ) - a^{3} + 2 \,{\left (b^{3} x - 3 \, a^{2} b\right )} \sqrt{x}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*sqrt(x) + a)^3/x^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.68588, size = 36, normalized size = 0.95 \[ - \frac{a^{3}}{x} - \frac{6 a^{2} b}{\sqrt{x}} + 3 a b^{2} \log{\left (x \right )} + 2 b^{3} \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b*x**(1/2))**3/x**2,x)
[Out]
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GIAC/XCAS [A] time = 0.221688, size = 49, normalized size = 1.29 \[ 3 \, a b^{2}{\rm ln}\left ({\left | x \right |}\right ) + 2 \, b^{3} \sqrt{x} - \frac{6 \, a^{2} b \sqrt{x} + a^{3}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*sqrt(x) + a)^3/x^2,x, algorithm="giac")
[Out]