Optimal. Leaf size=27 \[ \frac {5}{34} e^{3 x} \sin (5 x)+\frac {3}{34} e^{3 x} \cos (5 x) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.01, antiderivative size = 27, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 10, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {4433} \[ \frac {5}{34} e^{3 x} \sin (5 x)+\frac {3}{34} e^{3 x} \cos (5 x) \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 4433
Rubi steps
\begin {align*} \int e^{3 x} \cos (5 x) \, dx &=\frac {3}{34} e^{3 x} \cos (5 x)+\frac {5}{34} e^{3 x} \sin (5 x)\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.03, size = 22, normalized size = 0.81 \[ \frac {1}{34} e^{3 x} (5 \sin (5 x)+3 \cos (5 x)) \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.42, size = 21, normalized size = 0.78 \[ \frac {3}{34} \, \cos \left (5 \, x\right ) e^{\left (3 \, x\right )} + \frac {5}{34} \, e^{\left (3 \, x\right )} \sin \left (5 \, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.21, size = 19, normalized size = 0.70 \[ \frac {1}{34} \, {\left (3 \, \cos \left (5 \, x\right ) + 5 \, \sin \left (5 \, x\right )\right )} e^{\left (3 \, x\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.08, size = 22, normalized size = 0.81 \[ \frac {3 \cos \left (5 x \right ) {\mathrm e}^{3 x}}{34}+\frac {5 \,{\mathrm e}^{3 x} \sin \left (5 x \right )}{34} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.75, size = 19, normalized size = 0.70 \[ \frac {1}{34} \, {\left (3 \, \cos \left (5 \, x\right ) + 5 \, \sin \left (5 \, x\right )\right )} e^{\left (3 \, x\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.03, size = 19, normalized size = 0.70 \[ \frac {{\mathrm {e}}^{3\,x}\,\left (3\,\cos \left (5\,x\right )+5\,\sin \left (5\,x\right )\right )}{34} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.30, size = 26, normalized size = 0.96 \[ \frac {5 e^{3 x} \sin {\left (5 x \right )}}{34} + \frac {3 e^{3 x} \cos {\left (5 x \right )}}{34} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________