Optimal. Leaf size=6 \[ \tan ^{-1}\left (\sqrt{x}\right ) \]
[Out]
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Rubi [A] time = 0.00837332, antiderivative size = 6, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 14, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.214 \[ \tan ^{-1}\left (\sqrt{x}\right ) \]
Antiderivative was successfully verified.
[In] Int[1/(2*Sqrt[x]*(1 + x)),x]
[Out]
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Rubi in Sympy [A] time = 1.03338, size = 5, normalized size = 0.83 \[ \operatorname{atan}{\left (\sqrt{x} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/2/(1+x)/x**(1/2),x)
[Out]
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Mathematica [A] time = 0.00637886, size = 6, normalized size = 1. \[ \tan ^{-1}\left (\sqrt{x}\right ) \]
Antiderivative was successfully verified.
[In] Integrate[1/(2*Sqrt[x]*(1 + x)),x]
[Out]
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Maple [A] time = 0.005, size = 5, normalized size = 0.8 \[ \arctan \left ( \sqrt{x} \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/2/(1+x)/x^(1/2),x)
[Out]
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Maxima [A] time = 0.774768, size = 5, normalized size = 0.83 \[ \arctan \left (\sqrt{x}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/2/((x + 1)*sqrt(x)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.270482, size = 5, normalized size = 0.83 \[ \arctan \left (\sqrt{x}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/2/((x + 1)*sqrt(x)),x, algorithm="fricas")
[Out]
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Sympy [A] time = 3.30272, size = 32, normalized size = 5.33 \[ \frac{\begin{cases} 2 i \operatorname{acosh}{\left (\frac{1}{\sqrt{x + 1}} \right )} & \text{for}\: \left |{\frac{1}{x + 1}}\right | > 1 \\- 2 \operatorname{asin}{\left (\frac{1}{\sqrt{x + 1}} \right )} & \text{otherwise} \end{cases}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/2/(1+x)/x**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.259751, size = 5, normalized size = 0.83 \[ \arctan \left (\sqrt{x}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/2/((x + 1)*sqrt(x)),x, algorithm="giac")
[Out]