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 = 0.0135615, 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*Sin[x],x]
[Out]
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Rubi in Sympy [A] time = 1.17316, 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)*sin(x),x)
[Out]
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Mathematica [A] time = 0.0160791, size = 14, normalized size = 0.74 \[ \frac{1}{2} e^x (\sin (x)-\cos (x)) \]
Antiderivative was successfully verified.
[In] Integrate[E^x*Sin[x],x]
[Out]
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Maple [A] time = 0.029, 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)*sin(x),x)
[Out]
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Maxima [A] time = 1.37677, size = 15, normalized size = 0.79 \[ -\frac{1}{2} \,{\left (\cos \left (x\right ) - \sin \left (x\right )\right )} e^{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(e^x*sin(x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.210022, 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(e^x*sin(x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.3489, 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)*sin(x),x)
[Out]
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GIAC/XCAS [A] time = 0.217649, size = 15, normalized size = 0.79 \[ -\frac{1}{2} \,{\left (\cos \left (x\right ) - \sin \left (x\right )\right )} e^{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(e^x*sin(x),x, algorithm="giac")
[Out]