Optimal. Leaf size=20 \[ -\frac{1}{4} \csc ^4(x)+6 \csc ^2(x)+16 \log (\sin (x)) \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0908678, antiderivative size = 20, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 3, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.333 \[ -\frac{1}{4} \csc ^4(x)+6 \csc ^2(x)+16 \log (\sin (x)) \]
Antiderivative was successfully verified.
[In] Int[Cos[5*x]*Csc[x]^5,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 23.4735, size = 29, normalized size = 1.45 \[ 8 \log{\left (- \cos ^{2}{\left (x \right )} + 1 \right )} + \frac{6}{- \cos ^{2}{\left (x \right )} + 1} - \frac{1}{4 \left (- \cos ^{2}{\left (x \right )} + 1\right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(cos(5*x)/sin(x)**5,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0125984, size = 20, normalized size = 1. \[ -\frac{1}{4} \csc ^4(x)+6 \csc ^2(x)+16 \log (\sin (x)) \]
Antiderivative was successfully verified.
[In] Integrate[Cos[5*x]*Csc[x]^5,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.066, size = 35, normalized size = 1.8 \[ -{\frac{5}{4\, \left ( \sin \left ( x \right ) \right ) ^{4}}}+5\,{\frac{ \left ( \cos \left ( x \right ) \right ) ^{4}}{ \left ( \sin \left ( x \right ) \right ) ^{4}}}-4\, \left ( \cot \left ( x \right ) \right ) ^{4}+8\, \left ( \cot \left ( x \right ) \right ) ^{2}+16\,\ln \left ( \sin \left ( x \right ) \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(cos(5*x)/sin(x)^5,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.34561, size = 45, normalized size = 2.25 \[ \frac{5}{\sin \left (x\right )^{2}} + \frac{4 \, \sin \left (x\right )^{2} - 1}{4 \, \sin \left (x\right )^{4}} + \frac{11}{2} \, \log \left (\sin \left (x\right )^{2}\right ) + 5 \, \log \left (\sin \left (x\right )\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cos(5*x)/sin(x)^5,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.230294, size = 58, normalized size = 2.9 \[ -\frac{24 \, \cos \left (x\right )^{2} - 64 \,{\left (\cos \left (x\right )^{4} - 2 \, \cos \left (x\right )^{2} + 1\right )} \log \left (\frac{1}{2} \, \sin \left (x\right )\right ) - 23}{4 \,{\left (\cos \left (x\right )^{4} - 2 \, \cos \left (x\right )^{2} + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cos(5*x)/sin(x)^5,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cos(5*x)/sin(x)**5,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.204975, size = 136, normalized size = 6.8 \[ -\frac{{\left (\frac{92 \,{\left (\cos \left (x\right ) - 1\right )}}{\cos \left (x\right ) + 1} + \frac{768 \,{\left (\cos \left (x\right ) - 1\right )}^{2}}{{\left (\cos \left (x\right ) + 1\right )}^{2}} + 1\right )}{\left (\cos \left (x\right ) + 1\right )}^{2}}{64 \,{\left (\cos \left (x\right ) - 1\right )}^{2}} - \frac{23 \,{\left (\cos \left (x\right ) - 1\right )}}{16 \,{\left (\cos \left (x\right ) + 1\right )}} - \frac{{\left (\cos \left (x\right ) - 1\right )}^{2}}{64 \,{\left (\cos \left (x\right ) + 1\right )}^{2}} - 16 \,{\rm ln}\left (-\frac{\cos \left (x\right ) - 1}{\cos \left (x\right ) + 1} + 1\right ) + 8 \,{\rm ln}\left (-\frac{\cos \left (x\right ) - 1}{\cos \left (x\right ) + 1}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cos(5*x)/sin(x)^5,x, algorithm="giac")
[Out]