3.70 \(\int e^{2 \sin (x)} \cos (x) \, dx\)

Optimal. Leaf size=10 \[ \frac{1}{2} e^{2 \sin (x)} \]

[Out]

E^(2*Sin[x])/2

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Rubi [A]  time = 0.0157524, antiderivative size = 10, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.222 \[ \frac{1}{2} e^{2 \sin (x)} \]

Antiderivative was successfully verified.

[In]  Int[E^(2*Sin[x])*Cos[x],x]

[Out]

E^(2*Sin[x])/2

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Rubi in Sympy [A]  time = 1.67072, size = 7, normalized size = 0.7 \[ \frac{e^{2 \sin{\left (x \right )}}}{2} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(exp(2*sin(x))*cos(x),x)

[Out]

exp(2*sin(x))/2

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Mathematica [A]  time = 0.00846611, size = 10, normalized size = 1. \[ \frac{1}{2} e^{2 \sin (x)} \]

Antiderivative was successfully verified.

[In]  Integrate[E^(2*Sin[x])*Cos[x],x]

[Out]

E^(2*Sin[x])/2

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Maple [A]  time = 0.01, size = 8, normalized size = 0.8 \[{\frac{{{\rm e}^{2\,\sin \left ( x \right ) }}}{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(exp(2*sin(x))*cos(x),x)

[Out]

1/2*exp(2*sin(x))

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Maxima [A]  time = 1.419, size = 9, normalized size = 0.9 \[ \frac{1}{2} \, e^{\left (2 \, \sin \left (x\right )\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(cos(x)*e^(2*sin(x)),x, algorithm="maxima")

[Out]

1/2*e^(2*sin(x))

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Fricas [A]  time = 0.214045, size = 9, normalized size = 0.9 \[ \frac{1}{2} \, e^{\left (2 \, \sin \left (x\right )\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(cos(x)*e^(2*sin(x)),x, algorithm="fricas")

[Out]

1/2*e^(2*sin(x))

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Sympy [A]  time = 0.354896, size = 7, normalized size = 0.7 \[ \frac{e^{2 \sin{\left (x \right )}}}{2} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(exp(2*sin(x))*cos(x),x)

[Out]

exp(2*sin(x))/2

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GIAC/XCAS [A]  time = 0.223314, size = 9, normalized size = 0.9 \[ \frac{1}{2} \, e^{\left (2 \, \sin \left (x\right )\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(cos(x)*e^(2*sin(x)),x, algorithm="giac")

[Out]

1/2*e^(2*sin(x))