Optimal. Leaf size=25 \[ -\frac{2 \tanh ^{-1}\left (\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right )}{\sqrt{55}} \]
[Out]
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Rubi [A] time = 0.0265375, antiderivative size = 25, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.118 \[ -\frac{2 \tanh ^{-1}\left (\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right )}{\sqrt{55}} \]
Antiderivative was successfully verified.
[In] Int[1/(Sqrt[1 - 2*x]*(3 + 5*x)),x]
[Out]
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Rubi in Sympy [A] time = 3.06754, size = 26, normalized size = 1.04 \[ - \frac{2 \sqrt{55} \operatorname{atanh}{\left (\frac{\sqrt{55} \sqrt{- 2 x + 1}}{11} \right )}}{55} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(3+5*x)/(1-2*x)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0112023, size = 25, normalized size = 1. \[ -\frac{2 \tanh ^{-1}\left (\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right )}{\sqrt{55}} \]
Antiderivative was successfully verified.
[In] Integrate[1/(Sqrt[1 - 2*x]*(3 + 5*x)),x]
[Out]
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Maple [A] time = 0.005, size = 19, normalized size = 0.8 \[ -{\frac{2\,\sqrt{55}}{55}{\it Artanh} \left ({\frac{\sqrt{55}}{11}\sqrt{1-2\,x}} \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(3+5*x)/(1-2*x)^(1/2),x)
[Out]
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Maxima [A] time = 1.4794, size = 49, normalized size = 1.96 \[ \frac{1}{55} \, \sqrt{55} \log \left (-\frac{\sqrt{55} - 5 \, \sqrt{-2 \, x + 1}}{\sqrt{55} + 5 \, \sqrt{-2 \, x + 1}}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((5*x + 3)*sqrt(-2*x + 1)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.22675, size = 45, normalized size = 1.8 \[ \frac{1}{55} \, \sqrt{55} \log \left (\frac{\sqrt{55}{\left (5 \, x - 8\right )} + 55 \, \sqrt{-2 \, x + 1}}{5 \, x + 3}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((5*x + 3)*sqrt(-2*x + 1)),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.74909, size = 63, normalized size = 2.52 \[ \begin{cases} - \frac{2 \sqrt{55} \operatorname{acosh}{\left (\frac{\sqrt{110}}{10 \sqrt{x + \frac{3}{5}}} \right )}}{55} & \text{for}\: \frac{11 \left |{\frac{1}{x + \frac{3}{5}}}\right |}{10} > 1 \\\frac{2 \sqrt{55} i \operatorname{asin}{\left (\frac{\sqrt{110}}{10 \sqrt{x + \frac{3}{5}}} \right )}}{55} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(3+5*x)/(1-2*x)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.224098, size = 54, normalized size = 2.16 \[ -\frac{1}{55} \, \sqrt{55}{\rm ln}\left (\frac{1}{5} \, \sqrt{55} + \sqrt{-2 \, x + 1}\right ) + \frac{1}{55} \, \sqrt{55}{\rm ln}\left ({\left | -\frac{1}{5} \, \sqrt{55} + \sqrt{-2 \, x + 1} \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((5*x + 3)*sqrt(-2*x + 1)),x, algorithm="giac")
[Out]