Optimal. Leaf size=25 \[ \log \left (\frac {12 e^{-x}}{(25-x) \left (-x+\log \left (x^2\right )\right )}\right ) \]
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Rubi [A]
time = 0.47, antiderivative size = 23, normalized size of antiderivative = 0.92, number of steps
used = 6, number of rules used = 4, integrand size = 53, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.075, Rules used = {6873, 6874, 45,
6816} \begin {gather*} -\log \left (x-\log \left (x^2\right )\right )-x-\log (25-x) \end {gather*}
Antiderivative was successfully verified.
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Rule 45
Rule 6816
Rule 6873
Rule 6874
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {50-27 x-23 x^2+x^3+\left (24 x-x^2\right ) \log \left (x^2\right )}{(25-x) x \left (x-\log \left (x^2\right )\right )} \, dx\\ &=\int \left (\frac {24-x}{-25+x}+\frac {2-x}{x \left (x-\log \left (x^2\right )\right )}\right ) \, dx\\ &=\int \frac {24-x}{-25+x} \, dx+\int \frac {2-x}{x \left (x-\log \left (x^2\right )\right )} \, dx\\ &=-\log \left (x-\log \left (x^2\right )\right )+\int \left (-1+\frac {1}{25-x}\right ) \, dx\\ &=-x-\log (25-x)-\log \left (x-\log \left (x^2\right )\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.04, size = 23, normalized size = 0.92 \begin {gather*} -x-\log (25-x)-\log \left (x-\log \left (x^2\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 1.57, size = 22, normalized size = 0.88
method | result | size |
norman | \(-x -\ln \left (x -25\right )-\ln \left (-\ln \left (x^{2}\right )+x \right )\) | \(22\) |
risch | \(-x -\ln \left (x -25\right )-\ln \left (\ln \left (x^{2}\right )-x \right )\) | \(22\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.32, size = 19, normalized size = 0.76 \begin {gather*} -x - \log \left (x - 25\right ) - \log \left (-\frac {1}{2} \, x + \log \left (x\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.40, size = 21, normalized size = 0.84 \begin {gather*} -x - \log \left (x - 25\right ) - \log \left (-x + \log \left (x^{2}\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.07, size = 15, normalized size = 0.60 \begin {gather*} - x - \log {\left (- x + \log {\left (x^{2} \right )} \right )} - \log {\left (x - 25 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 21, normalized size = 0.84 \begin {gather*} -x - \log \left (x - 25\right ) - \log \left (-x + \log \left (x^{2}\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 3.58, size = 21, normalized size = 0.84 \begin {gather*} -x-\ln \left (x-25\right )-\ln \left (\ln \left (x^2\right )-x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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