Optimal. Leaf size=15 \[ \frac {6+x^2}{-5+2 x+\log (x)} \]
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Rubi [F]
time = 0.37, 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 {-6-12 x-11 x^2+2 x^3+2 x^2 \log (x)}{25 x-20 x^2+4 x^3+\left (-10 x+4 x^2\right ) \log (x)+x \log ^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 {-6-12 x-11 x^2+2 x^3+2 x^2 \log (x)}{x (5-2 x-\log (x))^2} \, dx\\ &=\int \left (\frac {-6-12 x-x^2-2 x^3}{x (-5+2 x+\log (x))^2}+\frac {2 x}{-5+2 x+\log (x)}\right ) \, dx\\ &=2 \int \frac {x}{-5+2 x+\log (x)} \, dx+\int \frac {-6-12 x-x^2-2 x^3}{x (-5+2 x+\log (x))^2} \, dx\\ &=2 \int \frac {x}{-5+2 x+\log (x)} \, dx+\int \left (-\frac {12}{(-5+2 x+\log (x))^2}-\frac {6}{x (-5+2 x+\log (x))^2}-\frac {x}{(-5+2 x+\log (x))^2}-\frac {2 x^2}{(-5+2 x+\log (x))^2}\right ) \, dx\\ &=-\left (2 \int \frac {x^2}{(-5+2 x+\log (x))^2} \, dx\right )+2 \int \frac {x}{-5+2 x+\log (x)} \, dx-6 \int \frac {1}{x (-5+2 x+\log (x))^2} \, dx-12 \int \frac {1}{(-5+2 x+\log (x))^2} \, dx-\int \frac {x}{(-5+2 x+\log (x))^2} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.05, size = 15, normalized size = 1.00 \begin {gather*} \frac {6+x^2}{-5+2 x+\log (x)} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.24, size = 16, normalized size = 1.07
method | result | size |
default | \(\frac {x^{2}+6}{2 x +\ln \left (x \right )-5}\) | \(16\) |
norman | \(\frac {x^{2}+6}{2 x +\ln \left (x \right )-5}\) | \(16\) |
risch | \(\frac {x^{2}+6}{2 x +\ln \left (x \right )-5}\) | \(16\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.31, size = 15, normalized size = 1.00 \begin {gather*} \frac {x^{2} + 6}{2 \, x + \log \left (x\right ) - 5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 15, normalized size = 1.00 \begin {gather*} \frac {x^{2} + 6}{2 \, x + \log \left (x\right ) - 5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.04, size = 12, normalized size = 0.80 \begin {gather*} \frac {x^{2} + 6}{2 x + \log {\left (x \right )} - 5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.38, size = 15, normalized size = 1.00 \begin {gather*} \frac {x^{2} + 6}{2 \, x + \log \left (x\right ) - 5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.85, size = 15, normalized size = 1.00 \begin {gather*} \frac {x^2+6}{2\,x+\ln \left (x\right )-5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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