Optimal. Leaf size=21 \[ \log \left (4 \left (-9+\log ^2\left (1-2 \left (-3+e^{5 (-5+x)}\right )\right )\right )\right ) \]
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Rubi [A] time = 0.16, antiderivative size = 19, normalized size of antiderivative = 0.90, number of steps used = 3, number of rules used = 5, integrand size = 60, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.083, Rules used = {12, 2282, 6696, 206, 6684} \begin {gather*} \log \left (9-\log ^2\left (7-2 e^{5 x-25}\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 206
Rule 2282
Rule 6684
Rule 6696
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=20 \int \frac {e^{-25+5 x} \log \left (7-2 e^{-25+5 x}\right )}{63-18 e^{-25+5 x}+\left (-7+2 e^{-25+5 x}\right ) \log ^2\left (7-2 e^{-25+5 x}\right )} \, dx\\ &=4 \operatorname {Subst}\left (\int \frac {\log (7-2 x)}{(7-2 x) \left (9-\log ^2(7-2 x)\right )} \, dx,x,e^{-25+5 x}\right )\\ &=\log \left (9-\log ^2\left (7-2 e^{-25+5 x}\right )\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.06, size = 19, normalized size = 0.90 \begin {gather*} \log \left (9-\log ^2\left (7-2 e^{-25+5 x}\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.70, size = 29, normalized size = 1.38 \begin {gather*} \log \left (\log \left (-2 \, e^{\left (5 \, x - 25\right )} + 7\right ) + 3\right ) + \log \left (\log \left (-2 \, e^{\left (5 \, x - 25\right )} + 7\right ) - 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.26, size = 16, normalized size = 0.76 \begin {gather*} \log \left (\log \left (-2 \, e^{\left (5 \, x - 25\right )} + 7\right )^{2} - 9\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 17, normalized size = 0.81
method | result | size |
derivativedivides | \(\ln \left (\ln \left (-2 \,{\mathrm e}^{5 x -25}+7\right )^{2}-9\right )\) | \(17\) |
default | \(\ln \left (\ln \left (-2 \,{\mathrm e}^{5 x -25}+7\right )^{2}-9\right )\) | \(17\) |
risch | \(\ln \left (\ln \left (-2 \,{\mathrm e}^{5 x -25}+7\right )^{2}-9\right )\) | \(17\) |
norman | \(\ln \left (\ln \left (-2 \,{\mathrm e}^{5 x -25}+7\right )-3\right )+\ln \left (\ln \left (-2 \,{\mathrm e}^{5 x -25}+7\right )+3\right )\) | \(30\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.37, size = 104, normalized size = 4.95 \begin {gather*} -\frac {1}{3} \, {\left (\log \left (\log \left (-2 \, e^{\left (5 \, x - 25\right )} + 7\right ) + 3\right ) - \log \left (\log \left (-2 \, e^{\left (5 \, x - 25\right )} + 7\right ) - 3\right )\right )} \log \left (-2 \, e^{\left (5 \, x - 25\right )} + 7\right ) + \frac {1}{3} \, {\left (\log \left (-2 \, e^{\left (5 \, x - 25\right )} + 7\right ) + 3\right )} \log \left (\log \left (-2 \, e^{\left (5 \, x - 25\right )} + 7\right ) + 3\right ) - \frac {1}{3} \, {\left (\log \left (-2 \, e^{\left (5 \, x - 25\right )} + 7\right ) - 3\right )} \log \left (\log \left (-2 \, e^{\left (5 \, x - 25\right )} + 7\right ) - 3\right ) - 2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 6.30, size = 16, normalized size = 0.76 \begin {gather*} \ln \left ({\ln \left (7-2\,{\mathrm {e}}^{5\,x-25}\right )}^2-9\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.23, size = 15, normalized size = 0.71 \begin {gather*} \log {\left (\log {\left (7 - 2 e^{5 x - 25} \right )}^{2} - 9 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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