Optimal. Leaf size=20 \[ \frac {e^{-25+x}}{\log \left ((2+3 (3-x))^2\right )} \]
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Rubi [A] time = 0.18, antiderivative size = 16, normalized size of antiderivative = 0.80, number of steps used = 3, number of rules used = 3, integrand size = 50, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.060, Rules used = {12, 6688, 2288} \begin {gather*} \frac {e^{x-25}}{\log \left ((11-3 x)^2\right )} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2288
Rule 6688
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \frac {-6 e^x+e^x (-11+3 x) \log \left (121-66 x+9 x^2\right )}{(-11+3 x) \log ^2\left (121-66 x+9 x^2\right )} \, dx}{e^{25}}\\ &=\frac {\int \frac {e^x \left (\frac {6}{11-3 x}+\log \left ((11-3 x)^2\right )\right )}{\log ^2\left ((11-3 x)^2\right )} \, dx}{e^{25}}\\ &=\frac {e^{-25+x}}{\log \left ((11-3 x)^2\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.02, size = 16, normalized size = 0.80 \begin {gather*} \frac {e^{-25+x}}{\log \left ((11-3 x)^2\right )} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.63, size = 18, normalized size = 0.90 \begin {gather*} \frac {e^{\left (x - 25\right )}}{\log \left (9 \, x^{2} - 66 \, x + 121\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.21, size = 18, normalized size = 0.90 \begin {gather*} \frac {e^{\left (x - 25\right )}}{\log \left (9 \, x^{2} - 66 \, x + 121\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.27, size = 18, normalized size = 0.90
method | result | size |
default | \(\frac {{\mathrm e}^{-25} {\mathrm e}^{x}}{\ln \left (\left (-11+3 x \right )^{2}\right )}\) | \(18\) |
norman | \(\frac {{\mathrm e}^{-25} {\mathrm e}^{x}}{\ln \left (9 x^{2}-66 x +121\right )}\) | \(21\) |
risch | \(\frac {2 i {\mathrm e}^{x -25}}{\pi \mathrm {csgn}\left (i \left (x -\frac {11}{3}\right )\right )^{2} \mathrm {csgn}\left (i \left (x -\frac {11}{3}\right )^{2}\right )-2 \pi \,\mathrm {csgn}\left (i \left (x -\frac {11}{3}\right )\right ) \mathrm {csgn}\left (i \left (x -\frac {11}{3}\right )^{2}\right )^{2}+\pi \mathrm {csgn}\left (i \left (x -\frac {11}{3}\right )^{2}\right )^{3}+4 i \ln \left (x -\frac {11}{3}\right )}\) | \(72\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.41, size = 14, normalized size = 0.70 \begin {gather*} \frac {e^{\left (x - 25\right )}}{2 \, \log \left (3 \, x - 11\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.92, size = 18, normalized size = 0.90 \begin {gather*} \frac {{\mathrm {e}}^{-25}\,{\mathrm {e}}^x}{\ln \left (9\,x^2-66\,x+121\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.30, size = 17, normalized size = 0.85 \begin {gather*} \frac {e^{x}}{e^{25} \log {\left (9 x^{2} - 66 x + 121 \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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