Optimal. Leaf size=27 \[ \frac{3}{10} e^x \sin (3 x+4)+\frac{1}{10} e^x \cos (3 x+4) \]
[Out]
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Rubi [A] time = 0.0192777, 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 \[ \frac{3}{10} e^x \sin (3 x+4)+\frac{1}{10} e^x \cos (3 x+4) \]
Antiderivative was successfully verified.
[In] Int[E^x*Cos[4 + 3*x],x]
[Out]
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Rubi in Sympy [A] time = 2.52161, 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.
[In] rubi_integrate(exp(x)*cos(4+3*x),x)
[Out]
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Mathematica [A] time = 0.0260844, size = 22, normalized size = 0.81 \[ \frac{1}{10} e^x (3 \sin (3 x+4)+\cos (3 x+4)) \]
Antiderivative was successfully verified.
[In] Integrate[E^x*Cos[4 + 3*x],x]
[Out]
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Maple [A] time = 0.007, size = 22, normalized size = 0.8 \[{\frac{{{\rm e}^{x}}\cos \left ( 4+3\,x \right ) }{10}}+{\frac{3\,{{\rm e}^{x}}\sin \left ( 4+3\,x \right ) }{10}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(exp(x)*cos(4+3*x),x)
[Out]
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Maxima [A] time = 0.772715, size = 26, normalized size = 0.96 \[ \frac{1}{10} \,{\left (\cos \left (3 \, x + 4\right ) + 3 \, \sin \left (3 \, x + 4\right )\right )} e^{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cos(3*x + 4)*e^x,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.240848, size = 28, normalized size = 1.04 \[ \frac{1}{10} \, \cos \left (3 \, x + 4\right ) e^{x} + \frac{3}{10} \, e^{x} \sin \left (3 \, x + 4\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cos(3*x + 4)*e^x,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.319667, 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.
[In] integrate(exp(x)*cos(4+3*x),x)
[Out]
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GIAC/XCAS [A] time = 0.440208, size = 26, normalized size = 0.96 \[ \frac{1}{10} \,{\left (\cos \left (3 \, x + 4\right ) + 3 \, \sin \left (3 \, x + 4\right )\right )} e^{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cos(3*x + 4)*e^x,x, algorithm="giac")
[Out]