Optimal. Leaf size=27 \[ -3 x+\log \left (\frac {2+\frac {5}{x^2}-x^5 (-x+\log (x))}{x}\right ) \]
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Rubi [F]
time = 0.47, 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 {15+15 x+2 x^2+6 x^3+x^7-5 x^8+3 x^9+\left (4 x^7-3 x^8\right ) \log (x)}{-5 x-2 x^3-x^9+x^8 \log (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 {4-3 x}{x}+\frac {-35-10 x^2-x^7+x^8}{x \left (5+2 x^2+x^8-x^7 \log (x)\right )}\right ) \, dx\\ &=\int \frac {4-3 x}{x} \, dx+\int \frac {-35-10 x^2-x^7+x^8}{x \left (5+2 x^2+x^8-x^7 \log (x)\right )} \, dx\\ &=\int \left (-3+\frac {4}{x}\right ) \, dx+\int \left (-\frac {35}{x \left (5+2 x^2+x^8-x^7 \log (x)\right )}-\frac {10 x}{5+2 x^2+x^8-x^7 \log (x)}-\frac {x^6}{5+2 x^2+x^8-x^7 \log (x)}+\frac {x^7}{5+2 x^2+x^8-x^7 \log (x)}\right ) \, dx\\ &=-3 x+4 \log (x)-10 \int \frac {x}{5+2 x^2+x^8-x^7 \log (x)} \, dx-35 \int \frac {1}{x \left (5+2 x^2+x^8-x^7 \log (x)\right )} \, dx-\int \frac {x^6}{5+2 x^2+x^8-x^7 \log (x)} \, dx+\int \frac {x^7}{5+2 x^2+x^8-x^7 \log (x)} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.09, size = 26, normalized size = 0.96 \begin {gather*} -3 x-3 \log (x)+\log \left (5+2 x^2+x^8-x^7 \log (x)\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.31, size = 28, normalized size = 1.04
method | result | size |
norman | \(-3 \ln \left (x \right )-3 x +\ln \left (x^{8}-x^{7} \ln \left (x \right )+2 x^{2}+5\right )\) | \(27\) |
default | \(-3 \ln \left (x \right )-3 x +\ln \left (x^{7} \ln \left (x \right )-x^{8}-2 x^{2}-5\right )\) | \(28\) |
risch | \(-3 x +4 \ln \left (x \right )+\ln \left (\ln \left (x \right )-\frac {x^{8}+2 x^{2}+5}{x^{7}}\right )\) | \(28\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 31, normalized size = 1.15 \begin {gather*} -3 \, x + 4 \, \log \left (x\right ) + \log \left (-\frac {x^{8} - x^{7} \log \left (x\right ) + 2 \, x^{2} + 5}{x^{7}}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 31, normalized size = 1.15 \begin {gather*} -3 \, x + 4 \, \log \left (x\right ) + \log \left (-\frac {x^{8} - x^{7} \log \left (x\right ) + 2 \, x^{2} + 5}{x^{7}}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.11, size = 27, normalized size = 1.00 \begin {gather*} - 3 x + 4 \log {\left (x \right )} + \log {\left (\log {\left (x \right )} + \frac {- x^{8} - 2 x^{2} - 5}{x^{7}} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.38, size = 26, normalized size = 0.96 \begin {gather*} -3 \, x + \log \left (x^{8} - x^{7} \log \left (x\right ) + 2 \, x^{2} + 5\right ) - 3 \, \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.09, size = 30, normalized size = 1.11 \begin {gather*} \ln \left (\frac {2\,x^2-x^7\,\ln \left (x\right )+x^8+5}{x^7}\right )-3\,x+4\,\ln \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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