Optimal. Leaf size=22 \[ \frac {2 e^{-3-x}}{(-5+x) \log (7+2 x)} \]
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Rubi [F] time = 1.21, 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^{-3-x} \left (20-4 x+\left (56+2 x-4 x^2\right ) \log (7+2 x)\right )}{\left (175-20 x-13 x^2+2 x^3\right ) \log ^2(7+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 \left (-\frac {4 e^{-3-x}}{(-5+x) (7+2 x) \log ^2(7+2 x)}-\frac {2 e^{-3-x} (-4+x)}{(-5+x)^2 \log (7+2 x)}\right ) \, dx\\ &=-\left (2 \int \frac {e^{-3-x} (-4+x)}{(-5+x)^2 \log (7+2 x)} \, dx\right )-4 \int \frac {e^{-3-x}}{(-5+x) (7+2 x) \log ^2(7+2 x)} \, dx\\ &=-\left (2 \int \left (\frac {e^{-3-x}}{(-5+x)^2 \log (7+2 x)}+\frac {e^{-3-x}}{(-5+x) \log (7+2 x)}\right ) \, dx\right )-4 \int \left (\frac {e^{-3-x}}{17 (-5+x) \log ^2(7+2 x)}-\frac {2 e^{-3-x}}{17 (7+2 x) \log ^2(7+2 x)}\right ) \, dx\\ &=-\left (\frac {4}{17} \int \frac {e^{-3-x}}{(-5+x) \log ^2(7+2 x)} \, dx\right )+\frac {8}{17} \int \frac {e^{-3-x}}{(7+2 x) \log ^2(7+2 x)} \, dx-2 \int \frac {e^{-3-x}}{(-5+x)^2 \log (7+2 x)} \, dx-2 \int \frac {e^{-3-x}}{(-5+x) \log (7+2 x)} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.38, size = 22, normalized size = 1.00 \begin {gather*} \frac {2 e^{-3-x}}{(-5+x) \log (7+2 x)} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.56, size = 21, normalized size = 0.95 \begin {gather*} \frac {2 \, e^{\left (-x - 3\right )}}{{\left (x - 5\right )} \log \left (2 \, x + 7\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.20, size = 29, normalized size = 1.32 \begin {gather*} \frac {2 \, e^{\left (-x\right )}}{x e^{3} \log \left (2 \, x + 7\right ) - 5 \, e^{3} \log \left (2 \, x + 7\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 22, normalized size = 1.00
method | result | size |
risch | \(\frac {2 \,{\mathrm e}^{-3-x}}{\left (x -5\right ) \ln \left (7+2 x \right )}\) | \(22\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.44, size = 25, normalized size = 1.14 \begin {gather*} \frac {2 \, e^{\left (-x\right )}}{{\left (x e^{3} - 5 \, e^{3}\right )} \log \left (2 \, x + 7\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.81, size = 28, normalized size = 1.27 \begin {gather*} -\frac {2\,{\mathrm {e}}^{-x}\,{\mathrm {e}}^{-3}}{5\,\ln \left (2\,x+7\right )-x\,\ln \left (2\,x+7\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.32, size = 24, normalized size = 1.09 \begin {gather*} \frac {2 e^{- x - 3}}{x \log {\left (2 x + 7 \right )} - 5 \log {\left (2 x + 7 \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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