Optimal. Leaf size=15 \[ \log \left (21-10 e^5 (2-x+\log (4))\right ) \]
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Rubi [A] time = 0.02, antiderivative size = 15, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 3, integrand size = 25, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.120, Rules used = {12, 33, 31} \begin {gather*} \log \left (21-10 e^5 (-x+2+\log (4))\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 31
Rule 33
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\left (\left (10 e^5\right ) \int \frac {1}{-21+e^5 (20-10 x)+10 e^5 \log (4)} \, dx\right )\\ &=e^5 \operatorname {Subst}\left (\int \frac {1}{-21+e^5 x+10 e^5 \log (4)} \, dx,x,20-10 x\right )\\ &=\log \left (21-10 e^5 (2-x+\log (4))\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 15, normalized size = 1.00 \begin {gather*} \log \left (21+10 e^5 (-2+x-\log (4))\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.09, size = 16, normalized size = 1.07 \begin {gather*} \log \left (10 \, {\left (x - 2\right )} e^{5} - 20 \, e^{5} \log \relax (2) + 21\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.12, size = 17, normalized size = 1.13 \begin {gather*} \log \left ({\left | 10 \, {\left (x - 2\right )} e^{5} - 20 \, e^{5} \log \relax (2) + 21 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.20, size = 19, normalized size = 1.27
method | result | size |
default | \(\ln \left (20 \,{\mathrm e}^{5} \ln \relax (2)-10 x \,{\mathrm e}^{5}+20 \,{\mathrm e}^{5}-21\right )\) | \(19\) |
norman | \(\ln \left (20 \,{\mathrm e}^{5} \ln \relax (2)-10 x \,{\mathrm e}^{5}+20 \,{\mathrm e}^{5}-21\right )\) | \(19\) |
risch | \(\ln \left (20 \,{\mathrm e}^{5} \ln \relax (2)-10 x \,{\mathrm e}^{5}+20 \,{\mathrm e}^{5}-21\right )\) | \(19\) |
meijerg | \(\ln \left (1-\frac {10 x \,{\mathrm e}^{5}}{20 \,{\mathrm e}^{5} \ln \relax (2)+20 \,{\mathrm e}^{5}-21}\right )\) | \(23\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.34, size = 16, normalized size = 1.07 \begin {gather*} \log \left (10 \, {\left (x - 2\right )} e^{5} - 20 \, e^{5} \log \relax (2) + 21\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.31, size = 12, normalized size = 0.80 \begin {gather*} \ln \left (x+\frac {21\,{\mathrm {e}}^{-5}}{10}-\ln \relax (4)-2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.07, size = 22, normalized size = 1.47 \begin {gather*} \log {\left (10 x e^{5} - 20 e^{5} - 20 e^{5} \log {\relax (2 )} + 21 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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