Optimal. Leaf size=10 \[ -2 \tanh ^{-1}\left (\sqrt{x+1}\right ) \]
[Out]
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Rubi [A] time = 0.010595, antiderivative size = 10, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.182 \[ -2 \tanh ^{-1}\left (\sqrt{x+1}\right ) \]
Antiderivative was successfully verified.
[In] Int[1/(x*Sqrt[1 + x]),x]
[Out]
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Rubi in Sympy [A] time = 0.975793, size = 10, normalized size = 1. \[ - 2 \operatorname{atanh}{\left (\sqrt{x + 1} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x/(1+x)**(1/2),x)
[Out]
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Mathematica [B] time = 0.00410762, size = 25, normalized size = 2.5 \[ \log \left (1-\sqrt{x+1}\right )-\log \left (\sqrt{x+1}+1\right ) \]
Antiderivative was successfully verified.
[In] Integrate[1/(x*Sqrt[1 + x]),x]
[Out]
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Maple [A] time = 0.006, size = 9, normalized size = 0.9 \[ -2\,{\it Artanh} \left ( \sqrt{1+x} \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x/(1+x)^(1/2),x)
[Out]
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Maxima [A] time = 1.34975, size = 26, normalized size = 2.6 \[ -\log \left (\sqrt{x + 1} + 1\right ) + \log \left (\sqrt{x + 1} - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(x + 1)*x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.206026, size = 26, normalized size = 2.6 \[ -\log \left (\sqrt{x + 1} + 1\right ) + \log \left (\sqrt{x + 1} - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(x + 1)*x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.787056, size = 26, normalized size = 2.6 \[ \begin{cases} - 2 \operatorname{acoth}{\left (\sqrt{x + 1} \right )} & \text{for}\: \left |{x + 1}\right | > 1 \\- 2 \operatorname{atanh}{\left (\sqrt{x + 1} \right )} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x/(1+x)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.214613, size = 27, normalized size = 2.7 \[ -{\rm ln}\left (\sqrt{x + 1} + 1\right ) +{\rm ln}\left ({\left | \sqrt{x + 1} - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(x + 1)*x),x, algorithm="giac")
[Out]