Optimal. Leaf size=11 \[ -\frac{3}{4} \tanh ^{-1}\left (\cos \left (\frac{x}{3}\right )\right ) \]
[Out]
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Rubi [A] time = 0.00796438, antiderivative size = 11, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 10, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.2 \[ -\frac{3}{4} \tanh ^{-1}\left (\cos \left (\frac{x}{3}\right )\right ) \]
Antiderivative was successfully verified.
[In] Int[Csc[x/3]/4,x]
[Out]
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Rubi in Sympy [A] time = 0.659701, size = 10, normalized size = 0.91 \[ - \frac{3 \operatorname{atanh}{\left (\cos{\left (\frac{x}{3} \right )} \right )}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/4/sin(1/3*x),x)
[Out]
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Mathematica [B] time = 0.00549987, size = 23, normalized size = 2.09 \[ \frac{1}{4} \left (3 \log \left (\sin \left (\frac{x}{6}\right )\right )-3 \log \left (\cos \left (\frac{x}{6}\right )\right )\right ) \]
Antiderivative was successfully verified.
[In] Integrate[Csc[x/3]/4,x]
[Out]
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Maple [A] time = 0.01, size = 15, normalized size = 1.4 \[{\frac{3}{4}\ln \left ( \csc \left ({\frac{x}{3}} \right ) -\cot \left ({\frac{x}{3}} \right ) \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/4/sin(1/3*x),x)
[Out]
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Maxima [A] time = 1.37099, size = 26, normalized size = 2.36 \[ -\frac{3}{8} \, \log \left (\cos \left (\frac{1}{3} \, x\right ) + 1\right ) + \frac{3}{8} \, \log \left (\cos \left (\frac{1}{3} \, x\right ) - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/4/sin(1/3*x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.24232, size = 31, normalized size = 2.82 \[ -\frac{3}{8} \, \log \left (\frac{1}{2} \, \cos \left (\frac{1}{3} \, x\right ) + \frac{1}{2}\right ) + \frac{3}{8} \, \log \left (-\frac{1}{2} \, \cos \left (\frac{1}{3} \, x\right ) + \frac{1}{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/4/sin(1/3*x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.099579, size = 22, normalized size = 2. \[ \frac{3 \log{\left (\cos{\left (\frac{x}{3} \right )} - 1 \right )}}{8} - \frac{3 \log{\left (\cos{\left (\frac{x}{3} \right )} + 1 \right )}}{8} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/4/sin(1/3*x),x)
[Out]
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GIAC/XCAS [A] time = 0.208553, size = 31, normalized size = 2.82 \[ -\frac{3}{8} \,{\rm ln}\left (3 \, \cos \left (\frac{1}{3} \, x\right ) + 3\right ) + \frac{3}{8} \,{\rm ln}\left (-3 \, \cos \left (\frac{1}{3} \, x\right ) + 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/4/sin(1/3*x),x, algorithm="giac")
[Out]