Optimal. Leaf size=36 \[ \frac{e^{2 x}}{16}-\frac{1}{40} e^{2 x} \sin (4 x)-\frac{1}{80} e^{2 x} \cos (4 x) \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0705463, antiderivative size = 36, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 3, integrand size = 14, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.214 \[ \frac{e^{2 x}}{16}-\frac{1}{40} e^{2 x} \sin (4 x)-\frac{1}{80} e^{2 x} \cos (4 x) \]
Antiderivative was successfully verified.
[In] Int[E^(2*x)*Cos[x]^2*Sin[x]^2,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 5.31334, size = 29, normalized size = 0.81 \[ - \frac{e^{2 x} \sin{\left (4 x \right )}}{40} - \frac{e^{2 x} \cos{\left (4 x \right )}}{80} + \frac{e^{2 x}}{16} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(exp(2*x)*cos(x)**2*sin(x)**2,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0298775, size = 21, normalized size = 0.58 \[ -\frac{1}{80} e^{2 x} (2 \sin (4 x)+\cos (4 x)-5) \]
Antiderivative was successfully verified.
[In] Integrate[E^(2*x)*Cos[x]^2*Sin[x]^2,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.008, size = 28, normalized size = 0.8 \[ -{\frac{{{\rm e}^{2\,x}}\cos \left ( 4\,x \right ) }{80}}-{\frac{{{\rm e}^{2\,x}}\sin \left ( 4\,x \right ) }{40}}+{\frac{ \left ({{\rm e}^{x}} \right ) ^{2}}{16}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(exp(2*x)*cos(x)^2*sin(x)^2,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.34544, size = 36, normalized size = 1. \[ -\frac{1}{80} \, \cos \left (4 \, x\right ) e^{\left (2 \, x\right )} - \frac{1}{40} \, e^{\left (2 \, x\right )} \sin \left (4 \, x\right ) + \frac{1}{16} \, e^{\left (2 \, x\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cos(x)^2*e^(2*x)*sin(x)^2,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.218727, size = 54, normalized size = 1.5 \[ -\frac{1}{10} \,{\left (2 \, \cos \left (x\right )^{3} - \cos \left (x\right )\right )} e^{\left (2 \, x\right )} \sin \left (x\right ) - \frac{1}{20} \,{\left (2 \, \cos \left (x\right )^{4} - 2 \, \cos \left (x\right )^{2} - 1\right )} e^{\left (2 \, x\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cos(x)^2*e^(2*x)*sin(x)^2,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 8.3612, size = 70, normalized size = 1.94 \[ \frac{e^{2 x} \sin ^{4}{\left (x \right )}}{20} + \frac{e^{2 x} \sin ^{3}{\left (x \right )} \cos{\left (x \right )}}{10} + \frac{e^{2 x} \sin ^{2}{\left (x \right )} \cos ^{2}{\left (x \right )}}{5} - \frac{e^{2 x} \sin{\left (x \right )} \cos ^{3}{\left (x \right )}}{10} + \frac{e^{2 x} \cos ^{4}{\left (x \right )}}{20} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(exp(2*x)*cos(x)**2*sin(x)**2,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.209015, size = 32, normalized size = 0.89 \[ -\frac{1}{80} \,{\left (\cos \left (4 \, x\right ) + 2 \, \sin \left (4 \, x\right )\right )} e^{\left (2 \, x\right )} + \frac{1}{16} \, e^{\left (2 \, x\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cos(x)^2*e^(2*x)*sin(x)^2,x, algorithm="giac")
[Out]