Optimal. Leaf size=24 \[ -\left (\left (-4+\frac {10}{x}\right ) x\right )+\frac {x}{-\frac {2401}{625}+x}-\log (x) \]
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Rubi [A] time = 0.05, antiderivative size = 17, normalized size of antiderivative = 0.71, number of steps used = 4, number of rules used = 3, integrand size = 32, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.094, Rules used = {1594, 27, 1620} \begin {gather*} 4 x-\frac {2401}{2401-625 x}-\log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 27
Rule 1594
Rule 1620
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-5764801+24559829 x-12395625 x^2+1562500 x^3}{x \left (5764801-3001250 x+390625 x^2\right )} \, dx\\ &=\int \frac {-5764801+24559829 x-12395625 x^2+1562500 x^3}{x (-2401+625 x)^2} \, dx\\ &=\int \left (4-\frac {1}{x}-\frac {1500625}{(-2401+625 x)^2}\right ) \, dx\\ &=-\frac {2401}{2401-625 x}+4 x-\log (x)\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 17, normalized size = 0.71 \begin {gather*} 4 x+\frac {2401}{-2401+625 x}-\log (x) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.65, size = 27, normalized size = 1.12 \begin {gather*} \frac {2500 \, x^{2} - {\left (625 \, x - 2401\right )} \log \relax (x) - 9604 \, x + 2401}{625 \, x - 2401} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.38, size = 18, normalized size = 0.75 \begin {gather*} 4 \, x + \frac {2401}{625 \, x - 2401} - \log \left ({\left | x \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 16, normalized size = 0.67
method | result | size |
risch | \(4 x +\frac {2401}{625 \left (x -\frac {2401}{625}\right )}-\ln \relax (x )\) | \(16\) |
default | \(4 x -\ln \relax (x )+\frac {2401}{625 x -2401}\) | \(18\) |
norman | \(\frac {2500 x^{2}-\frac {21558579}{625}}{625 x -2401}-\ln \relax (x )\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.50, size = 17, normalized size = 0.71 \begin {gather*} 4 \, x + \frac {2401}{625 \, x - 2401} - \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.33, size = 17, normalized size = 0.71 \begin {gather*} 4\,x-\ln \relax (x)+\frac {2401}{625\,\left (x-\frac {2401}{625}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.12, size = 12, normalized size = 0.50 \begin {gather*} 4 x - \log {\relax (x )} + \frac {2401}{625 x - 2401} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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