Optimal. Leaf size=22 \[ 2-x-\frac {1}{e^4 \log \left (x+\frac {9 x^2}{5}\right )} \]
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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 {\frac {5+18 x}{e^4 \log \left (\frac {1}{5} \left (5 x+9 x^2\right )\right )}+\left (-5 x-9 x^2\right ) \log \left (\frac {1}{5} \left (5 x+9 x^2\right )\right )}{\left (5 x+9 x^2\right ) \log \left (\frac {1}{5} \left (5 x+9 x^2\right )\right )} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {\frac {5+18 x}{e^4 \log \left (\frac {1}{5} \left (5 x+9 x^2\right )\right )}+\left (-5 x-9 x^2\right ) \log \left (\frac {1}{5} \left (5 x+9 x^2\right )\right )}{x (5+9 x) \log \left (\frac {1}{5} \left (5 x+9 x^2\right )\right )} \, dx\\ &=\int \frac {5+18 x-e^4 x (5+9 x) \log ^2\left (x+\frac {9 x^2}{5}\right )}{e^4 x (5+9 x) \log ^2\left (x \left (1+\frac {9 x}{5}\right )\right )} \, dx\\ &=\frac {\int \frac {5+18 x-e^4 x (5+9 x) \log ^2\left (x+\frac {9 x^2}{5}\right )}{x (5+9 x) \log ^2\left (x \left (1+\frac {9 x}{5}\right )\right )} \, dx}{e^4}\\ &=\frac {\int \left (-e^4+\frac {5+18 x}{x (5+9 x) \log ^2\left (x \left (1+\frac {9 x}{5}\right )\right )}\right ) \, dx}{e^4}\\ &=-x+\frac {\int \frac {5+18 x}{x (5+9 x) \log ^2\left (x \left (1+\frac {9 x}{5}\right )\right )} \, dx}{e^4}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.07, size = 25, normalized size = 1.14 \begin {gather*} \frac {-e^4 x-\frac {1}{\log \left (x+\frac {9 x^2}{5}\right )}}{e^4} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.19, size = 24, normalized size = 1.09
method | result | size |
default | \(-x -\frac {{\mathrm e}^{-4}}{-\ln \left (5\right )+\ln \left (x \left (9 x +5\right )\right )}\) | \(24\) |
norman | \(\frac {-{\mathrm e}^{-4}-x \ln \left (\frac {9}{5} x^{2}+x \right )}{\ln \left (\frac {9}{5} x^{2}+x \right )}\) | \(30\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.53, size = 28, normalized size = 1.27 \begin {gather*} -x + \frac {1}{e^{4} \log \left (5\right ) - e^{4} \log \left (9 \, x + 5\right ) - e^{4} \log \left (x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 28, normalized size = 1.27 \begin {gather*} -\frac {{\left (x e^{4} \log \left (\frac {9}{5} \, x^{2} + x\right ) + 1\right )} e^{\left (-4\right )}}{\log \left (\frac {9}{5} \, x^{2} + x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.04, size = 17, normalized size = 0.77 \begin {gather*} - x - \frac {1}{e^{4} \log {\left (\frac {9 x^{2}}{5} + x \right )}} \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. 52 vs.
\(2 (21) = 42\).
time = 0.42, size = 52, normalized size = 2.36 \begin {gather*} -\frac {x e^{4} \log \left (5\right ) - x e^{4} \log \left (9 \, x + 5\right ) - x e^{4} \log \left (x\right ) - 1}{e^{4} \log \left (5\right ) - e^{4} \log \left (9 \, x + 5\right ) - e^{4} \log \left (x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.51, size = 18, normalized size = 0.82 \begin {gather*} -x-\frac {{\mathrm {e}}^{-4}}{\ln \left (\frac {9\,x^2}{5}+x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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