Optimal. Leaf size=17 \[ -\frac{1}{7} \cot ^7(x)-\frac{\cot ^5(x)}{5} \]
[Out]
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Rubi [A] time = 0.0395665, antiderivative size = 17, 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 \[ -\frac{1}{7} \cot ^7(x)-\frac{\cot ^5(x)}{5} \]
Antiderivative was successfully verified.
[In] Int[Cot[x]^4*Csc[x]^4,x]
[Out]
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Rubi in Sympy [A] time = 2.84001, size = 44, normalized size = 2.59 \[ - \frac{2 \cos{\left (x \right )}}{35 \sin{\left (x \right )}} - \frac{\cos{\left (x \right )}}{35 \sin ^{3}{\left (x \right )}} + \frac{3}{35 \sin ^{4}{\left (x \right )} \tan{\left (x \right )}} - \frac{1}{7 \sin ^{4}{\left (x \right )} \tan ^{3}{\left (x \right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(cot(x)**4*csc(x)**4,x)
[Out]
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Mathematica [B] time = 0.0199545, size = 37, normalized size = 2.18 \[ -\frac{2 \cot (x)}{35}-\frac{1}{7} \cot (x) \csc ^6(x)+\frac{8}{35} \cot (x) \csc ^4(x)-\frac{1}{35} \cot (x) \csc ^2(x) \]
Antiderivative was successfully verified.
[In] Integrate[Cot[x]^4*Csc[x]^4,x]
[Out]
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Maple [A] time = 0.019, size = 22, normalized size = 1.3 \[ -{\frac{ \left ( \cos \left ( x \right ) \right ) ^{5}}{7\, \left ( \sin \left ( x \right ) \right ) ^{7}}}-{\frac{2\, \left ( \cos \left ( x \right ) \right ) ^{5}}{35\, \left ( \sin \left ( x \right ) \right ) ^{5}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(cot(x)^4*csc(x)^4,x)
[Out]
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Maxima [A] time = 1.45815, size = 19, normalized size = 1.12 \[ -\frac{7 \, \tan \left (x\right )^{2} + 5}{35 \, \tan \left (x\right )^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cot(x)^4*csc(x)^4,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.234645, size = 53, normalized size = 3.12 \[ -\frac{2 \, \cos \left (x\right )^{7} - 7 \, \cos \left (x\right )^{5}}{35 \,{\left (\cos \left (x\right )^{6} - 3 \, \cos \left (x\right )^{4} + 3 \, \cos \left (x\right )^{2} - 1\right )} \sin \left (x\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cot(x)^4*csc(x)^4,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.057872, size = 41, normalized size = 2.41 \[ - \frac{2 \cos{\left (x \right )}}{35 \sin{\left (x \right )}} - \frac{\cos{\left (x \right )}}{35 \sin ^{3}{\left (x \right )}} + \frac{8 \cos{\left (x \right )}}{35 \sin ^{5}{\left (x \right )}} - \frac{\cos{\left (x \right )}}{7 \sin ^{7}{\left (x \right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cot(x)**4*csc(x)**4,x)
[Out]
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GIAC/XCAS [A] time = 0.213308, size = 19, normalized size = 1.12 \[ -\frac{7 \, \tan \left (x\right )^{2} + 5}{35 \, \tan \left (x\right )^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cot(x)^4*csc(x)^4,x, algorithm="giac")
[Out]