Optimal. Leaf size=27 \[ \frac{2}{13} e^{2 t} \sin (3 t)-\frac{3}{13} e^{2 t} \cos (3 t) \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0206872, antiderivative size = 27, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 10, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.1 \[ \frac{2}{13} e^{2 t} \sin (3 t)-\frac{3}{13} e^{2 t} \cos (3 t) \]
Antiderivative was successfully verified.
[In] Int[E^(2*t)*Sin[3*t],t]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 1.44696, size = 26, normalized size = 0.96 \[ \frac{2 e^{2 t} \sin{\left (3 t \right )}}{13} - \frac{3 e^{2 t} \cos{\left (3 t \right )}}{13} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(exp(2*t)*sin(3*t),t)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0288039, size = 22, normalized size = 0.81 \[ \frac{1}{13} e^{2 t} (2 \sin (3 t)-3 \cos (3 t)) \]
Antiderivative was successfully verified.
[In] Integrate[E^(2*t)*Sin[3*t],t]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.009, size = 22, normalized size = 0.8 \[ -{\frac{3\,{{\rm e}^{2\,t}}\cos \left ( 3\,t \right ) }{13}}+{\frac{2\,{{\rm e}^{2\,t}}\sin \left ( 3\,t \right ) }{13}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(exp(2*t)*sin(3*t),t)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.40284, size = 26, normalized size = 0.96 \[ -\frac{1}{13} \,{\left (3 \, \cos \left (3 \, t\right ) - 2 \, \sin \left (3 \, t\right )\right )} e^{\left (2 \, t\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(e^(2*t)*sin(3*t),t, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.217567, size = 28, normalized size = 1.04 \[ -\frac{3}{13} \, \cos \left (3 \, t\right ) e^{\left (2 \, t\right )} + \frac{2}{13} \, e^{\left (2 \, t\right )} \sin \left (3 \, t\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(e^(2*t)*sin(3*t),t, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.373493, size = 26, normalized size = 0.96 \[ \frac{2 e^{2 t} \sin{\left (3 t \right )}}{13} - \frac{3 e^{2 t} \cos{\left (3 t \right )}}{13} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(exp(2*t)*sin(3*t),t)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.201499, size = 26, normalized size = 0.96 \[ -\frac{1}{13} \,{\left (3 \, \cos \left (3 \, t\right ) - 2 \, \sin \left (3 \, t\right )\right )} e^{\left (2 \, t\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(e^(2*t)*sin(3*t),t, algorithm="giac")
[Out]