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 = 0.011464, 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, Rules used = {4432} \[ \frac{2}{13} e^{2 t} \sin (3 t)-\frac{3}{13} e^{2 t} \cos (3 t) \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 4432
Rubi steps
\begin{align*} \int e^{2 t} \sin (3 t) \, dt &=-\frac{3}{13} e^{2 t} \cos (3 t)+\frac{2}{13} e^{2 t} \sin (3 t)\\ \end{align*}
Mathematica [A] time = 0.0324587, 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]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.004, size = 22, normalized size = 0.8 \begin{align*} -{\frac{3\,{{\rm e}^{2\,t}}\cos \left ( 3\,t \right ) }{13}}+{\frac{2\,{{\rm e}^{2\,t}}\sin \left ( 3\,t \right ) }{13}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0.925916, size = 26, normalized size = 0.96 \begin{align*} -\frac{1}{13} \,{\left (3 \, \cos \left (3 \, t\right ) - 2 \, \sin \left (3 \, t\right )\right )} e^{\left (2 \, t\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.92505, size = 65, normalized size = 2.41 \begin{align*} -\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 ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.293081, size = 26, normalized size = 0.96 \begin{align*} \frac{2 e^{2 t} \sin{\left (3 t \right )}}{13} - \frac{3 e^{2 t} \cos{\left (3 t \right )}}{13} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.0594, size = 26, normalized size = 0.96 \begin{align*} -\frac{1}{13} \,{\left (3 \, \cos \left (3 \, t\right ) - 2 \, \sin \left (3 \, t\right )\right )} e^{\left (2 \, t\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]