Optimal. Leaf size=21 \[ a^2 \log (x)+4 a b \sqrt{x}+b^2 x \]
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Rubi [A] time = 0.0380703, antiderivative size = 21, 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 \[ a^2 \log (x)+4 a b \sqrt{x}+b^2 x \]
Antiderivative was successfully verified.
[In] Int[(a + b*Sqrt[x])^2/x,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ 2 a^{2} \log{\left (\sqrt{x} \right )} + 4 a b \sqrt{x} + 2 b^{2} \int ^{\sqrt{x}} x\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b*x**(1/2))**2/x,x)
[Out]
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Mathematica [A] time = 0.0102791, size = 21, normalized size = 1. \[ a^2 \log (x)+4 a b \sqrt{x}+b^2 x \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*Sqrt[x])^2/x,x]
[Out]
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Maple [A] time = 0.002, size = 20, normalized size = 1. \[{b}^{2}x+{a}^{2}\ln \left ( x \right ) +4\,ab\sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b*x^(1/2))^2/x,x)
[Out]
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Maxima [A] time = 1.45189, size = 26, normalized size = 1.24 \[ b^{2} x + a^{2} \log \left (x\right ) + 4 \, a b \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*sqrt(x) + a)^2/x,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.235815, size = 30, normalized size = 1.43 \[ b^{2} x + 2 \, a^{2} \log \left (\sqrt{x}\right ) + 4 \, a b \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*sqrt(x) + a)^2/x,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.473696, size = 20, normalized size = 0.95 \[ a^{2} \log{\left (x \right )} + 4 a b \sqrt{x} + b^{2} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b*x**(1/2))**2/x,x)
[Out]
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GIAC/XCAS [A] time = 0.218265, size = 27, normalized size = 1.29 \[ b^{2} x + a^{2}{\rm ln}\left ({\left | x \right |}\right ) + 4 \, a b \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*sqrt(x) + a)^2/x,x, algorithm="giac")
[Out]