Optimal. Leaf size=56 \[ -4 x+21 \log (x)-9 \log (x+1)+12 \sin ^{-1}\left (\frac{1-x}{2}\right )-24 \sqrt{3} \tanh ^{-1}\left (\frac{\sqrt{3} \sqrt{x+1}}{\sqrt{3-x}}\right ) \]
[Out]
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Rubi [A] time = 0.408798, antiderivative size = 56, normalized size of antiderivative = 1., number of steps used = 11, number of rules used = 10, integrand size = 27, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.37 \[ -4 x+21 \log (x)-9 \log (x+1)+12 \sin ^{-1}\left (\frac{1-x}{2}\right )-24 \sqrt{3} \tanh ^{-1}\left (\frac{\sqrt{3} \sqrt{x+1}}{\sqrt{3-x}}\right ) \]
Antiderivative was successfully verified.
[In] Int[(2*Sqrt[3 - x] + 3/Sqrt[1 + x])^2/x,x]
[Out]
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Rubi in Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((2*(3-x)**(1/2)+3/(1+x)**(1/2))**2/x,x)
[Out]
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Mathematica [A] time = 0.104082, size = 69, normalized size = 1.23 \[ -12 \sqrt{3} \log \left (\sqrt{-3 x^2+6 x+9}+x+3\right )-4 x+3 \left (7+4 \sqrt{3}\right ) \log (x)-9 \log (x+1)+12 \tan ^{-1}\left (\frac{1-x}{\sqrt{-(x-3) (x+1)}}\right ) \]
Antiderivative was successfully verified.
[In] Integrate[(2*Sqrt[3 - x] + 3/Sqrt[1 + x])^2/x,x]
[Out]
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Maple [A] time = 0.025, size = 76, normalized size = 1.4 \[ -9\,\ln \left ( 1+x \right ) +21\,\ln \left ( x \right ) +12\,{\frac{\sqrt{3-x}\sqrt{1+x}}{\sqrt{-{x}^{2}+2\,x+3}} \left ( -\arcsin \left ( -1/2+x/2 \right ) -\sqrt{3}{\it Artanh} \left ( 1/3\,{\frac{ \left ( 3+x \right ) \sqrt{3}}{\sqrt{-{x}^{2}+2\,x+3}}} \right ) \right ) }-4\,x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2*(3-x)^(1/2)+3/(1+x)^(1/2))^2/x,x)
[Out]
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Maxima [A] time = 0.843976, size = 77, normalized size = 1.38 \[ -12 \, \sqrt{3} \log \left (\frac{2 \, \sqrt{3} \sqrt{-x^{2} + 2 \, x + 3}}{{\left | x \right |}} + \frac{6}{{\left | x \right |}} + 2\right ) - 4 \, x + 12 \, \arcsin \left (-\frac{1}{2} \, x + \frac{1}{2}\right ) - 9 \, \log \left (x + 1\right ) + 21 \, \log \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*sqrt(-x + 3) + 3/sqrt(x + 1))^2/x,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.283814, size = 96, normalized size = 1.71 \[ 6 \, \sqrt{3} \log \left (-\frac{\sqrt{3}{\left (x + 3\right )} \sqrt{x + 1} \sqrt{-x + 3} + x^{2} - 6 \, x - 9}{x^{2}}\right ) - 4 \, x - 12 \, \arctan \left (\frac{x - 1}{\sqrt{x + 1} \sqrt{-x + 3}}\right ) - 9 \, \log \left (x + 1\right ) + 21 \, \log \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*sqrt(-x + 3) + 3/sqrt(x + 1))^2/x,x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\left (2 \sqrt{- x + 3} \sqrt{x + 1} + 3\right )^{2}}{x \left (x + 1\right )}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*(3-x)**(1/2)+3/(1+x)**(1/2))**2/x,x)
[Out]
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GIAC/XCAS [F(-2)] time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: NotImplementedError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*sqrt(-x + 3) + 3/sqrt(x + 1))^2/x,x, algorithm="giac")
[Out]