Optimal. Leaf size=27 \[ e^4+7 x \left (x-\frac {e^4}{1+x-\log (2-x)}\right ) \]
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Rubi [F]
time = 0.44, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps
used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {}
\begin {gather*} \int \frac {e^4 (14-14 x)-28 x-42 x^2+14 x^4+\left (56 x+28 x^2-28 x^3+e^4 (-14+7 x)\right ) \log (2-x)+\left (-28 x+14 x^2\right ) \log ^2(2-x)}{-2-3 x+x^3+\left (4+2 x-2 x^2\right ) \log (2-x)+(-2+x) \log ^2(2-x)} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {7 \left (2 e^4 (-1+x)-2 (-2+x) x (1+x)^2-\left (e^4 (-2+x)+4 x \left (2+x-x^2\right )\right ) \log (2-x)-2 (-2+x) x \log ^2(2-x)\right )}{(2-x) (1+x-\log (2-x))^2} \, dx\\ &=7 \int \frac {2 e^4 (-1+x)-2 (-2+x) x (1+x)^2-\left (e^4 (-2+x)+4 x \left (2+x-x^2\right )\right ) \log (2-x)-2 (-2+x) x \log ^2(2-x)}{(2-x) (1+x-\log (2-x))^2} \, dx\\ &=7 \int \left (2 x+\frac {e^4 (-3+x) x}{(-2+x) (1+x-\log (2-x))^2}-\frac {e^4}{1+x-\log (2-x)}\right ) \, dx\\ &=7 x^2+\left (7 e^4\right ) \int \frac {(-3+x) x}{(-2+x) (1+x-\log (2-x))^2} \, dx-\left (7 e^4\right ) \int \frac {1}{1+x-\log (2-x)} \, dx\\ &=7 x^2+\left (7 e^4\right ) \int \left (-\frac {1}{(1+x-\log (2-x))^2}-\frac {2}{(-2+x) (1+x-\log (2-x))^2}+\frac {x}{(1+x-\log (2-x))^2}\right ) \, dx-\left (7 e^4\right ) \int \frac {1}{1+x-\log (2-x)} \, dx\\ &=7 x^2-\left (7 e^4\right ) \int \frac {1}{(1+x-\log (2-x))^2} \, dx+\left (7 e^4\right ) \int \frac {x}{(1+x-\log (2-x))^2} \, dx-\left (7 e^4\right ) \int \frac {1}{1+x-\log (2-x)} \, dx-\left (14 e^4\right ) \int \frac {1}{(-2+x) (1+x-\log (2-x))^2} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.40, size = 24, normalized size = 0.89 \begin {gather*} 7 \left (x^2+\frac {e^4 x}{-1-x+\log (2-x)}\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. \(80\) vs.
\(2(27)=54\).
time = 2.83, size = 81, normalized size = 3.00
method | result | size |
risch | \(7 x^{2}-\frac {7 \,{\mathrm e}^{4} x}{1+x -\ln \left (2-x \right )}\) | \(25\) |
norman | \(\frac {-7 \,{\mathrm e}^{4} \ln \left (2-x \right )+7 x^{2}+7 x^{3}-7 \ln \left (2-x \right ) x^{2}+7 \,{\mathrm e}^{4}}{1+x -\ln \left (2-x \right )}\) | \(55\) |
derivativedivides | \(-\frac {7 \left (\left ({\mathrm e}^{4}-12\right ) \left (2-x \right )+7 \left (2-x \right )^{2}-\left (2-x \right )^{3}+4 \left (2-x \right ) \ln \left (2-x \right )-\ln \left (2-x \right ) \left (2-x \right )^{2}-2 \,{\mathrm e}^{4}\right )}{\ln \left (2-x \right )-x -1}\) | \(81\) |
default | \(-\frac {7 \left (\left ({\mathrm e}^{4}-12\right ) \left (2-x \right )+7 \left (2-x \right )^{2}-\left (2-x \right )^{3}+4 \left (2-x \right ) \ln \left (2-x \right )-\ln \left (2-x \right ) \left (2-x \right )^{2}-2 \,{\mathrm e}^{4}\right )}{\ln \left (2-x \right )-x -1}\) | \(81\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 38, normalized size = 1.41 \begin {gather*} \frac {7 \, {\left (x^{3} - x^{2} \log \left (-x + 2\right ) + x^{2} - x e^{4}\right )}}{x - \log \left (-x + 2\right ) + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.46, size = 38, normalized size = 1.41 \begin {gather*} \frac {7 \, {\left (x^{3} - x^{2} \log \left (-x + 2\right ) + x^{2} - x e^{4}\right )}}{x - \log \left (-x + 2\right ) + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.06, size = 19, normalized size = 0.70 \begin {gather*} 7 x^{2} + \frac {7 x e^{4}}{- x + \log {\left (2 - x \right )} - 1} \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. 67 vs.
\(2 (25) = 50\).
time = 0.42, size = 67, normalized size = 2.48 \begin {gather*} \frac {7 \, {\left ({\left (x - 2\right )}^{3} - {\left (x - 2\right )}^{2} \log \left (-x + 2\right ) + 7 \, {\left (x - 2\right )}^{2} - {\left (x - 2\right )} e^{4} - 4 \, {\left (x - 2\right )} \log \left (-x + 2\right ) + 12 \, x - 2 \, e^{4} - 24\right )}}{x - \log \left (-x + 2\right ) + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.31, size = 45, normalized size = 1.67 \begin {gather*} \frac {7\,\left ({\mathrm {e}}^4-{\mathrm {e}}^4\,\ln \left (2-x\right )+x^2+x^3-x^2\,\ln \left (2-x\right )\right )}{x-\ln \left (2-x\right )+1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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