Optimal. Leaf size=27 \[ \frac {3}{10} e^x \sin (3 x+4)+\frac {1}{10} e^x \cos (3 x+4) \]
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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} \[ \frac {3}{10} e^x \sin (3 x+4)+\frac {1}{10} e^x \cos (3 x+4) \]
Antiderivative was successfully verified.
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Rule 4433
Rubi steps
\begin {align*} \int e^x \cos (4+3 x) \, dx &=\frac {1}{10} e^x \cos (4+3 x)+\frac {3}{10} e^x \sin (4+3 x)\\ \end {align*}
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Mathematica [A] time = 0.04, size = 22, normalized size = 0.81 \[ \frac {1}{10} e^x (3 \sin (3 x+4)+\cos (3 x+4)) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.40, size = 21, normalized size = 0.78 \[ \frac {1}{10} \, \cos \left (3 \, x + 4\right ) e^{x} + \frac {3}{10} \, e^{x} \sin \left (3 \, x + 4\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.18, size = 19, normalized size = 0.70 \[ \frac {1}{10} \, {\left (\cos \left (3 \, x + 4\right ) + 3 \, \sin \left (3 \, x + 4\right )\right )} e^{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.12, size = 22, normalized size = 0.81 \[ \frac {\cos \left (3 x +4\right ) {\mathrm e}^{x}}{10}+\frac {3 \,{\mathrm e}^{x} \sin \left (3 x +4\right )}{10} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.86, size = 19, normalized size = 0.70 \[ \frac {1}{10} \, {\left (\cos \left (3 \, x + 4\right ) + 3 \, \sin \left (3 \, x + 4\right )\right )} e^{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.53, size = 19, normalized size = 0.70 \[ \frac {{\mathrm {e}}^x\,\left (\cos \left (3\,x+4\right )+3\,\sin \left (3\,x+4\right )\right )}{10} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.29, size = 24, normalized size = 0.89 \[ \frac {3 e^{x} \sin {\left (3 x + 4 \right )}}{10} + \frac {e^{x} \cos {\left (3 x + 4 \right )}}{10} \]
Verification of antiderivative is not currently implemented for this CAS.
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