Optimal. Leaf size=7 \[ \tan (x)-\cot (x) \]
[Out]
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Rubi [A] time = 0.0449599, antiderivative size = 7, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.222 \[ \tan (x)-\cot (x) \]
Antiderivative was successfully verified.
[In] Int[Csc[x]^2*Sec[x]^2,x]
[Out]
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Rubi in Sympy [A] time = 1.67775, size = 15, normalized size = 2.14 \[ \frac{2 \sin{\left (x \right )}}{\cos{\left (x \right )}} - \frac{1}{\sin{\left (x \right )} \cos{\left (x \right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/cos(x)**2/sin(x)**2,x)
[Out]
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Mathematica [A] time = 0.00525028, size = 6, normalized size = 0.86 \[ -2 \cot (2 x) \]
Antiderivative was successfully verified.
[In] Integrate[Csc[x]^2*Sec[x]^2,x]
[Out]
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Maple [A] time = 0., size = 15, normalized size = 2.1 \[{\frac{1}{\cos \left ( x \right ) \sin \left ( x \right ) }}-2\,\cot \left ( x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/cos(x)^2/sin(x)^2,x)
[Out]
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Maxima [A] time = 1.36047, size = 12, normalized size = 1.71 \[ -\frac{1}{\tan \left (x\right )} + \tan \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(cos(x)^2*sin(x)^2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.225188, size = 24, normalized size = 3.43 \[ -\frac{2 \, \cos \left (x\right )^{2} - 1}{\cos \left (x\right ) \sin \left (x\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(cos(x)^2*sin(x)^2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.055305, size = 12, normalized size = 1.71 \[ - \frac{2 \cos{\left (2 x \right )}}{\sin{\left (2 x \right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/cos(x)**2/sin(x)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.201517, size = 12, normalized size = 1.71 \[ -\frac{1}{\tan \left (x\right )} + \tan \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(cos(x)^2*sin(x)^2),x, algorithm="giac")
[Out]