Optimal. Leaf size=13 \[ -\frac{1}{3} \cot ^3(x)-\cot (x) \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0115975, antiderivative size = 13, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 4, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.25 \[ -\frac{1}{3} \cot ^3(x)-\cot (x) \]
Antiderivative was successfully verified.
[In] Int[Csc[x]^4,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 0.537123, size = 20, normalized size = 1.54 \[ - \frac{2 \cos{\left (x \right )}}{3 \sin{\left (x \right )}} - \frac{\cos{\left (x \right )}}{3 \sin ^{3}{\left (x \right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/sin(x)**4,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.00387051, size = 17, normalized size = 1.31 \[ -\frac{2 \cot (x)}{3}-\frac{1}{3} \cot (x) \csc ^2(x) \]
Antiderivative was successfully verified.
[In] Integrate[Csc[x]^4,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.045, size = 12, normalized size = 0.9 \[ \left ( -{\frac{2}{3}}-{\frac{ \left ( \csc \left ( x \right ) \right ) ^{2}}{3}} \right ) \cot \left ( x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/sin(x)^4,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.34744, size = 19, normalized size = 1.46 \[ -\frac{3 \, \tan \left (x\right )^{2} + 1}{3 \, \tan \left (x\right )^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sin(x)^(-4),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.219669, size = 34, normalized size = 2.62 \[ -\frac{2 \, \cos \left (x\right )^{3} - 3 \, \cos \left (x\right )}{3 \,{\left (\cos \left (x\right )^{2} - 1\right )} \sin \left (x\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sin(x)^(-4),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.043178, size = 20, normalized size = 1.54 \[ - \frac{2 \cos{\left (x \right )}}{3 \sin{\left (x \right )}} - \frac{\cos{\left (x \right )}}{3 \sin ^{3}{\left (x \right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/sin(x)**4,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.201392, size = 19, normalized size = 1.46 \[ -\frac{3 \, \tan \left (x\right )^{2} + 1}{3 \, \tan \left (x\right )^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sin(x)^(-4),x, algorithm="giac")
[Out]