3.9 \(\int \frac{\pi }{\sqrt{16-e^2}} \, dx\)

Optimal. Leaf size=14 \[ \frac{\pi x}{\sqrt{16-e^2}} \]

[Out]

(Pi*x)/Sqrt[16 - E^2]

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Rubi [A]  time = 0.0161089, antiderivative size = 14, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ \frac{\pi x}{\sqrt{16-e^2}} \]

Antiderivative was successfully verified.

[In]  Int[Pi/Sqrt[16 - E^2],x]

[Out]

(Pi*x)/Sqrt[16 - E^2]

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{\int \pi \, dx}{\sqrt{- e^{2} + 16}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(pi/(16-exp(2))**(1/2),x)

[Out]

Integral(pi, x)/sqrt(-exp(2) + 16)

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Mathematica [A]  time = 0.0000435177, size = 14, normalized size = 1. \[ \frac{\pi x}{\sqrt{16-e^2}} \]

Antiderivative was successfully verified.

[In]  Integrate[Pi/Sqrt[16 - E^2],x]

[Out]

(Pi*x)/Sqrt[16 - E^2]

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Maple [A]  time = 0.001, size = 12, normalized size = 0.9 \[{\frac{\pi \,x}{\sqrt{16-{{\rm e}^{2}}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(Pi/(16-exp(2))^(1/2),x)

[Out]

Pi*x/(16-exp(2))^(1/2)

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Maxima [A]  time = 1.33101, size = 15, normalized size = 1.07 \[ \frac{\pi x}{\sqrt{-e^{2} + 16}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(pi/sqrt(-e^2 + 16),x, algorithm="maxima")

[Out]

pi*x/sqrt(-e^2 + 16)

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Fricas [A]  time = 0.214672, size = 15, normalized size = 1.07 \[ \frac{\pi x}{\sqrt{-e^{2} + 16}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(pi/sqrt(-e^2 + 16),x, algorithm="fricas")

[Out]

pi*x/sqrt(-e^2 + 16)

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Sympy [A]  time = 0.023166, size = 10, normalized size = 0.71 \[ \frac{\pi x}{\sqrt{- e^{2} + 16}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(pi/(16-exp(2))**(1/2),x)

[Out]

pi*x/sqrt(-exp(2) + 16)

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GIAC/XCAS [A]  time = 0.214826, size = 15, normalized size = 1.07 \[ \frac{\pi x}{\sqrt{-e^{2} + 16}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(pi/sqrt(-e^2 + 16),x, algorithm="giac")

[Out]

pi*x/sqrt(-e^2 + 16)