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.
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Rule 8
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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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