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

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

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Rubi [A]  time = 0.01, antiderivative size = 14, normalized size of antiderivative = 1.00, 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} \begin {gather*} \frac {\pi x}{\sqrt {16-e^2}} \end {gather*}

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*}

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Mathematica [A]  time = 0.00, size = 14, normalized size = 1.00 \begin {gather*} \frac {\pi x}{\sqrt {16-e^2}} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[Pi/Sqrt[16 - E^2],x]

[Out]

(Pi*x)/Sqrt[16 - E^2]

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IntegrateAlgebraic [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\pi }{\sqrt {16-e^2}} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

IntegrateAlgebraic[Pi/Sqrt[16 - E^2],x]

[Out]

IntegrateAlgebraic[Pi/Sqrt[16 - E^2], x]

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fricas [A]  time = 1.20, size = 18, normalized size = 1.29 \begin {gather*} -\frac {\pi x \sqrt {-e^{2} + 16}}{e^{2} - 16} \end {gather*}

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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giac [A]  time = 1.08, size = 11, normalized size = 0.79 \begin {gather*} \frac {\pi x}{\sqrt {-e^{2} + 16}} \end {gather*}

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)

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maple [A]  time = 0.00, size = 12, normalized size = 0.86 \begin {gather*} \frac {\pi x}{\sqrt {16-{\mathrm e}^{2}}} \end {gather*}

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 = 0.45, size = 11, normalized size = 0.79 \begin {gather*} \frac {\pi x}{\sqrt {-e^{2} + 16}} \end {gather*}

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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mupad [B]  time = 0.00, size = 11, normalized size = 0.79 \begin {gather*} \frac {\Pi \,x}{\sqrt {16-{\mathrm {e}}^2}} \end {gather*}

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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sympy [A]  time = 0.06, size = 10, normalized size = 0.71 \begin {gather*} \frac {\pi x}{\sqrt {16 - e^{2}}} \end {gather*}

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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