\(\int \frac {\pi }{\sqrt {16-e^2}} \, dx\) [9]

Optimal result

Integrand size = 13, antiderivative size = 14 \[ \int \frac {\pi }{\sqrt {16-e^2}} \, dx=\frac {\pi x}{\sqrt {16-e^2}} \]

[Out]

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

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {8} \[ \int \frac {\pi }{\sqrt {16-e^2}} \, dx=\frac {\pi x}{\sqrt {16-e^2}} \]

[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*} \text {integral}& = \frac {\pi x}{\sqrt {16-e^2}} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.00 \[ \int \frac {\pi }{\sqrt {16-e^2}} \, dx=\frac {\pi x}{\sqrt {16-e^2}} \]

[In]

Integrate[Pi/Sqrt[16 - E^2],x]

[Out]

(Pi*x)/Sqrt[16 - E^2]

Maple [A] (verified)

Time = 0.17 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.86

method	result	size
default	\(\frac {\pi x}{\sqrt {16-{\mathrm e}^{2}}}\)	\(12\)
parallelrisch	\(\frac {\pi x}{\sqrt {16-{\mathrm e}^{2}}}\)	\(12\)
norman	\(-\frac {\pi \sqrt {16-{\mathrm e}^{2}}\, x}{-16+{\mathrm e}^{2}}\)	\(19\)

[In]

int(Pi/(16-exp(2))^(1/2),x,method=_RETURNVERBOSE)

[Out]

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

Fricas [A] (verification not implemented)

none

Time = 0.22 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.29 \[ \int \frac {\pi }{\sqrt {16-e^2}} \, dx=-\frac {\pi x \sqrt {-e^{2} + 16}}{e^{2} - 16} \]

[In]

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

[Out]

-pi*x*sqrt(-e^2 + 16)/(e^2 - 16)

Sympy [A] (verification not implemented)

Time = 0.01 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.71 \[ \int \frac {\pi }{\sqrt {16-e^2}} \, dx=\frac {\pi x}{\sqrt {16 - e^{2}}} \]

[In]

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

[Out]

pi*x/sqrt(16 - exp(2))

Maxima [A] (verification not implemented)

none

Time = 0.21 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.79 \[ \int \frac {\pi }{\sqrt {16-e^2}} \, dx=\frac {\pi x}{\sqrt {-e^{2} + 16}} \]

[In]

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

[Out]

pi*x/sqrt(-e^2 + 16)

Giac [A] (verification not implemented)

none

Time = 0.32 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.79 \[ \int \frac {\pi }{\sqrt {16-e^2}} \, dx=\frac {\pi x}{\sqrt {-e^{2} + 16}} \]

[In]

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

[Out]

pi*x/sqrt(-e^2 + 16)

Mupad [B] (verification not implemented)

Time = 0.00 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.79 \[ \int \frac {\pi }{\sqrt {16-e^2}} \, dx=\frac {\Pi \,x}{\sqrt {16-{\mathrm {e}}^2}} \]

[In]

int(Pi/(16 - exp(2))^(1/2),x)

[Out]

(Pi*x)/(16 - exp(2))^(1/2)