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 = 0.0077652, 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, Rules used = {8} \[ \frac{\pi x}{\sqrt{16-e^2}} \]

Antiderivative was successfully verified.

[In]

Int[Pi/Sqrt[16 - E^2],x]

[Out]

(Pi*x)/Sqrt[16 - E^2]

Rule 8

Int[a_, x_Symbol] :> Simp[a*x, x] /; FreeQ[a, x]

Rubi steps

\begin{align*} \int \frac{\pi }{\sqrt{16-e^2}} \, dx &=\frac{\pi x}{\sqrt{16-e^2}}\\ \end{align*}

Mathematica [A]  time = 0.0000276, 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., size = 12, normalized size = 0.9 \begin{align*}{\frac{\pi \,x}{\sqrt{16-{{\rm e}^{2}}}}} \end{align*}

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 = 0.943684, size = 15, normalized size = 1.07 \begin{align*} \frac{\pi x}{\sqrt{-e^{2} + 16}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(pi/(16-exp(2))^(1/2),x, algorithm="maxima")

[Out]

pi*x/sqrt(-e^2 + 16)

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Fricas [A]  time = 1.54692, size = 46, normalized size = 3.29 \begin{align*} -\frac{\pi x \sqrt{-e^{2} + 16}}{e^{2} - 16} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(pi/(16-exp(2))^(1/2),x, algorithm="fricas")

[Out]

-pi*x*sqrt(-e^2 + 16)/(e^2 - 16)

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Sympy [A]  time = 0.045001, size = 10, normalized size = 0.71 \begin{align*} \frac{\pi x}{\sqrt{16 - e^{2}}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

pi*x/sqrt(16 - exp(2))

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Giac [A]  time = 1.11218, size = 15, normalized size = 1.07 \begin{align*} \frac{\pi x}{\sqrt{-e^{2} + 16}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(pi/(16-exp(2))^(1/2),x, algorithm="giac")

[Out]

pi*x/sqrt(-e^2 + 16)