Optimal. Leaf size=14 \[ \frac {3 \left (2+\frac {5 e^{12}}{256}\right )}{x} \]
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Rubi [A]
time = 0.01, antiderivative size = 14, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 2, integrand size = 14, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {12, 30}
\begin {gather*} \frac {3 \left (512+5 e^{12}\right )}{256 x} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 30
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\left (\frac {1}{256} \left (3 \left (512+5 e^{12}\right )\right ) \int \frac {1}{x^2} \, dx\right )\\ &=\frac {3 \left (512+5 e^{12}\right )}{256 x}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 14, normalized size = 1.00 \begin {gather*} \frac {3 \left (512+5 e^{12}\right )}{256 x} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.19, size = 14, normalized size = 1.00
method | result | size |
norman | \(\frac {\frac {15 \,{\mathrm e}^{12}}{256}+6}{x}\) | \(13\) |
gosper | \(\frac {\frac {15 \,{\mathrm e}^{12}}{256}+6}{x}\) | \(14\) |
default | \(-\frac {-\frac {15 \,{\mathrm e}^{12}}{256}-6}{x}\) | \(14\) |
risch | \(\frac {15 \,{\mathrm e}^{12}}{256 x}+\frac {6}{x}\) | \(14\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 11, normalized size = 0.79 \begin {gather*} \frac {3 \, {\left (5 \, e^{12} + 512\right )}}{256 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.38, size = 11, normalized size = 0.79 \begin {gather*} \frac {3 \, {\left (5 \, e^{12} + 512\right )}}{256 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 12, normalized size = 0.86 \begin {gather*} - \frac {- \frac {15 e^{12}}{256} - 6}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 11, normalized size = 0.79 \begin {gather*} \frac {3 \, {\left (5 \, e^{12} + 512\right )}}{256 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.03, size = 10, normalized size = 0.71 \begin {gather*} \frac {\frac {15\,{\mathrm {e}}^{12}}{256}+6}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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