Optimal. Leaf size=9 \[ \frac{1}{2} \log ^2(\tan (x)) \]
[Out]
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Rubi [A] time = 0.0329528, antiderivative size = 9, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 3, integrand size = 8, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.375 \[ \frac{1}{2} \log ^2(\tan (x)) \]
Antiderivative was successfully verified.
[In] Int[Csc[x]*Log[Tan[x]]*Sec[x],x]
[Out]
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Rubi in Sympy [A] time = 9.2886, size = 48, normalized size = 5.33 \[ - \frac{\left (\log{\left (- \cos{\left (2 x \right )} + 1 \right )} - \log{\left (\cos{\left (2 x \right )} + 1 \right )}\right )^{2}}{8} - \frac{\log{\left (- \sin ^{2}{\left (x \right )} + 1 \right )} \log{\left (\tan{\left (x \right )} \right )}}{2} + \frac{\log{\left (\sin ^{2}{\left (x \right )} \right )} \log{\left (\tan{\left (x \right )} \right )}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(ln(tan(x))/cos(x)/sin(x),x)
[Out]
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Mathematica [A] time = 0.00588257, size = 9, normalized size = 1. \[ \frac{1}{2} \log ^2(\tan (x)) \]
Antiderivative was successfully verified.
[In] Integrate[Csc[x]*Log[Tan[x]]*Sec[x],x]
[Out]
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Maple [A] time = 0.024, size = 8, normalized size = 0.9 \[{\frac{ \left ( \ln \left ( \tan \left ( x \right ) \right ) \right ) ^{2}}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(ln(tan(x))/cos(x)/sin(x),x)
[Out]
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Maxima [A] time = 1.34224, size = 9, normalized size = 1. \[ \frac{1}{2} \, \log \left (\tan \left (x\right )\right )^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(log(tan(x))/(cos(x)*sin(x)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.223696, size = 16, normalized size = 1.78 \[ \frac{1}{2} \, \log \left (\frac{\sin \left (x\right )}{\cos \left (x\right )}\right )^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(log(tan(x))/(cos(x)*sin(x)),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\log{\left (\tan{\left (x \right )} \right )}}{\sin{\left (x \right )} \cos{\left (x \right )}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(ln(tan(x))/cos(x)/sin(x),x)
[Out]
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GIAC/XCAS [A] time = 0.205264, size = 9, normalized size = 1. \[ \frac{1}{2} \,{\rm ln}\left (\tan \left (x\right )\right )^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(log(tan(x))/(cos(x)*sin(x)),x, algorithm="giac")
[Out]