Optimal. Leaf size=13 \[ \frac {1}{e^{16}+\frac {x^2}{64}} \]
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Rubi [A]
time = 0.00, antiderivative size = 13, normalized size of antiderivative = 1.00, number of steps
used = 3, number of rules used = 3, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.136, Rules used = {12, 28, 267}
\begin {gather*} \frac {64}{x^2+64 e^{16}} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 28
Rule 267
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\left (128 \int \frac {x}{4096 e^{32}+128 e^{16} x^2+x^4} \, dx\right )\\ &=-\left (128 \int \frac {x}{\left (64 e^{16}+x^2\right )^2} \, dx\right )\\ &=\frac {64}{64 e^{16}+x^2}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 13, normalized size = 1.00 \begin {gather*} \frac {64}{64 e^{16}+x^2} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.28, size = 11, normalized size = 0.85
method | result | size |
risch | \(\frac {1}{{\mathrm e}^{16}+\frac {x^{2}}{64}}\) | \(11\) |
gosper | \(\frac {64}{x^{2}+64 \,{\mathrm e}^{16}}\) | \(13\) |
norman | \(\frac {64}{x^{2}+64 \,{\mathrm e}^{16}}\) | \(13\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 12, normalized size = 0.92 \begin {gather*} \frac {64}{x^{2} + 64 \, e^{16}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 12, normalized size = 0.92 \begin {gather*} \frac {64}{x^{2} + 64 \, e^{16}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.05, size = 10, normalized size = 0.77 \begin {gather*} \frac {128}{2 x^{2} + 128 e^{16}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 12, normalized size = 0.92 \begin {gather*} \frac {64}{x^{2} + 64 \, e^{16}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.05, size = 12, normalized size = 0.92 \begin {gather*} \frac {64}{x^2+64\,{\mathrm {e}}^{16}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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