Optimal. Leaf size=15 \[ \frac{1}{2} \log \left (x^2+1\right )+x \cot ^{-1}(x) \]
[Out]
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Rubi [A] time = 0.00722682, antiderivative size = 15, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 2, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 1. \[ \frac{1}{2} \log \left (x^2+1\right )+x \cot ^{-1}(x) \]
Antiderivative was successfully verified.
[In] Int[ArcCot[x],x]
[Out]
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Rubi in Sympy [A] time = 0.842846, size = 12, normalized size = 0.8 \[ x \operatorname{acot}{\left (x \right )} + \frac{\log{\left (x^{2} + 1 \right )}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(acot(x),x)
[Out]
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Mathematica [A] time = 0.00247219, size = 15, normalized size = 1. \[ \frac{1}{2} \log \left (x^2+1\right )+x \cot ^{-1}(x) \]
Antiderivative was successfully verified.
[In] Integrate[ArcCot[x],x]
[Out]
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Maple [A] time = 0.004, size = 14, normalized size = 0.9 \[ x{\rm arccot} \left (x\right )+{\frac{\ln \left ({x}^{2}+1 \right ) }{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(arccot(x),x)
[Out]
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Maxima [A] time = 1.38675, size = 18, normalized size = 1.2 \[ x \operatorname{arccot}\left (x\right ) + \frac{1}{2} \, \log \left (x^{2} + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(arccot(x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.22433, size = 18, normalized size = 1.2 \[ x \operatorname{arccot}\left (x\right ) + \frac{1}{2} \, \log \left (x^{2} + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(arccot(x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.233644, size = 12, normalized size = 0.8 \[ x \operatorname{acot}{\left (x \right )} + \frac{\log{\left (x^{2} + 1 \right )}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(acot(x),x)
[Out]
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GIAC/XCAS [A] time = 0.218393, size = 20, normalized size = 1.33 \[ x \arctan \left (\frac{1}{x}\right ) + \frac{1}{2} \,{\rm ln}\left (x^{2} + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(arccot(x),x, algorithm="giac")
[Out]