Optimal. Leaf size=19 \[ \frac{1}{2} e^x \sin (x)+\frac{1}{2} e^x \cos (x) \]
[Out]
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Rubi [A] time = 0.0135202, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 6, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.167 \[ \frac{1}{2} e^x \sin (x)+\frac{1}{2} e^x \cos (x) \]
Antiderivative was successfully verified.
[In] Int[E^x*Cos[x],x]
[Out]
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Rubi in Sympy [A] time = 1.1717, size = 15, normalized size = 0.79 \[ \frac{e^{x} \sin{\left (x \right )}}{2} + \frac{e^{x} \cos{\left (x \right )}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(exp(x)*cos(x),x)
[Out]
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Mathematica [A] time = 0.0071641, size = 12, normalized size = 0.63 \[ \frac{1}{2} e^x (\sin (x)+\cos (x)) \]
Antiderivative was successfully verified.
[In] Integrate[E^x*Cos[x],x]
[Out]
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Maple [A] time = 0.007, size = 14, normalized size = 0.7 \[{\frac{{{\rm e}^{x}}\cos \left ( x \right ) }{2}}+{\frac{{{\rm e}^{x}}\sin \left ( x \right ) }{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(exp(x)*cos(x),x)
[Out]
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Maxima [A] time = 1.36374, size = 12, normalized size = 0.63 \[ \frac{1}{2} \,{\left (\cos \left (x\right ) + \sin \left (x\right )\right )} e^{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cos(x)*e^x,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.213841, size = 18, normalized size = 0.95 \[ \frac{1}{2} \, \cos \left (x\right ) e^{x} + \frac{1}{2} \, e^{x} \sin \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cos(x)*e^x,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.341191, size = 15, normalized size = 0.79 \[ \frac{e^{x} \sin{\left (x \right )}}{2} + \frac{e^{x} \cos{\left (x \right )}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(exp(x)*cos(x),x)
[Out]
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GIAC/XCAS [A] time = 0.216733, size = 12, normalized size = 0.63 \[ \frac{1}{2} \,{\left (\cos \left (x\right ) + \sin \left (x\right )\right )} e^{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cos(x)*e^x,x, algorithm="giac")
[Out]