Optimal. Leaf size=19 \[ 3 \log \left (\frac {5}{4} \left (-1-\frac {3 e^5}{2 x}\right )\right ) \]
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Rubi [A]
time = 0.01, antiderivative size = 17, normalized size of antiderivative = 0.89, number of steps
used = 2, number of rules used = 2, integrand size = 19, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.105, Rules used = {12, 629}
\begin {gather*} 3 \log \left (2 x+3 e^5\right )-3 \log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 629
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\left (\left (9 e^5\right ) \int \frac {1}{3 e^5 x+2 x^2} \, dx\right )\\ &=-3 \log (x)+3 \log \left (3 e^5+2 x\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 32, normalized size = 1.68 \begin {gather*} -9 e^5 \left (\frac {\log (x)}{3 e^5}-\frac {\log \left (3 e^5+2 x\right )}{3 e^5}\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(28\) vs.
\(2(12)=24\).
time = 0.67, size = 29, normalized size = 1.53
method | result | size |
norman | \(-3 \ln \left (x \right )+3 \ln \left (3 \,{\mathrm e}^{5}+2 x \right )\) | \(17\) |
risch | \(-3 \ln \left (x \right )+3 \ln \left (3 \,{\mathrm e}^{5}+2 x \right )\) | \(17\) |
meijerg | \(3 \ln \left (1+\frac {2 x \,{\mathrm e}^{-5}}{3}\right )-3 \ln \left (x \right )+3 \ln \left (3\right )-3 \ln \left (2\right )+15\) | \(25\) |
default | \(-9 \,{\mathrm e}^{5} \left (-\frac {{\mathrm e}^{-5} \ln \left (3 \,{\mathrm e}^{5}+2 x \right )}{3}+\frac {\ln \left (x \right ) {\mathrm e}^{-5}}{3}\right )\) | \(29\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 23, normalized size = 1.21 \begin {gather*} 3 \, {\left (e^{\left (-5\right )} \log \left (2 \, x + 3 \, e^{5}\right ) - e^{\left (-5\right )} \log \left (x\right )\right )} e^{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 16, normalized size = 0.84 \begin {gather*} 3 \, \log \left (2 \, x + 3 \, e^{5}\right ) - 3 \, \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.07, size = 29, normalized size = 1.53 \begin {gather*} - 9 \left (\frac {\log {\left (x \right )}}{3 e^{5}} - \frac {\log {\left (x + \frac {3 e^{5}}{2} \right )}}{3 e^{5}}\right ) e^{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 25 vs.
\(2 (12) = 24\).
time = 0.41, size = 25, normalized size = 1.32 \begin {gather*} 3 \, {\left (e^{\left (-5\right )} \log \left ({\left | 2 \, x + 3 \, e^{5} \right |}\right ) - e^{\left (-5\right )} \log \left ({\left | x \right |}\right )\right )} e^{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 2.38, size = 10, normalized size = 0.53 \begin {gather*} 6\,\mathrm {atanh}\left (\frac {4\,x\,{\mathrm {e}}^{-5}}{3}+1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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