Optimal. Leaf size=14 \[ \frac{\pi x}{\sqrt{16-e^2}} \]
[Out]
________________________________________________________________________________________
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]
[Out]
Rule 8
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]
[Out]
________________________________________________________________________________________
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]
[Out]
________________________________________________________________________________________
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]
[Out]
________________________________________________________________________________________
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]
[Out]
________________________________________________________________________________________
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]
[Out]
________________________________________________________________________________________
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]
[Out]