Optimal. Leaf size=14 \[ \frac {\pi x}{\sqrt {16-e^2}} \]
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Rubi [A]
time = 0.03, 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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Maple [A]
time = 0.02, size = 12, normalized size = 0.86
method | result | size |
default | \(\frac {\pi x}{\sqrt {16-{\mathrm e}^{2}}}\) | \(12\) |
norman | \(-\frac {\pi \sqrt {16-{\mathrm e}^{2}}\, x}{-16+{\mathrm e}^{2}}\) | \(19\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, 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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Fricas [A]
time = 0.92, 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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Sympy [A]
time = 0.00, 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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Giac [A]
time = 1.81, 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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