3.571 \(\int \sinh (x) \, dx\)

Optimal. Leaf size=2 \[ \cosh (x) \]

[Out]

Cosh[x]

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Rubi [A]  time = 0.00627967, antiderivative size = 2, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 2, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.5 \[ \cosh (x) \]

Antiderivative was successfully verified.

[In]  Int[Sinh[x],x]

[Out]

Cosh[x]

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \int \sinh{\left (x \right )}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(sinh(x),x)

[Out]

Integral(sinh(x), x)

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Mathematica [A]  time = 0.0033963, size = 2, normalized size = 1. \[ \cosh (x) \]

Antiderivative was successfully verified.

[In]  Integrate[Sinh[x],x]

[Out]

Cosh[x]

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Maple [A]  time = 0.001, size = 3, normalized size = 1.5 \[ \cosh \left ( x \right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(sinh(x),x)

[Out]

cosh(x)

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Maxima [A]  time = 1.37059, size = 3, normalized size = 1.5 \[ \cosh \left (x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(sinh(x),x, algorithm="maxima")

[Out]

cosh(x)

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Fricas [A]  time = 0.199181, size = 3, normalized size = 1.5 \[ \cosh \left (x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(sinh(x),x, algorithm="fricas")

[Out]

cosh(x)

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Sympy [A]  time = 0.102313, size = 2, normalized size = 1. \[ \cosh{\left (x \right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(sinh(x),x)

[Out]

cosh(x)

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GIAC/XCAS [A]  time = 0.199236, size = 15, normalized size = 7.5 \[ \frac{1}{2} \, e^{\left (-x\right )} + \frac{1}{2} \, e^{x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(sinh(x),x, algorithm="giac")

[Out]

1/2*e^(-x) + 1/2*e^x