Optimal. Leaf size=36 \[ \frac {-4 x+x \left (\frac {2 (5-x)}{3}+x^2\right )}{x}-\log \left (\frac {(25+x)^2}{x}\right ) \]
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Rubi [A] time = 0.04, antiderivative size = 17, normalized size of antiderivative = 0.47, number of steps used = 3, number of rules used = 2, integrand size = 27, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.074, Rules used = {1593, 1620} \begin {gather*} x^2-\frac {2 x}{3}+\log (x)-2 \log (x+25) \end {gather*}
Antiderivative was successfully verified.
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Rule 1593
Rule 1620
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {75-53 x+148 x^2+6 x^3}{x (75+3 x)} \, dx\\ &=\int \left (-\frac {2}{3}+\frac {1}{x}+2 x-\frac {2}{25+x}\right ) \, dx\\ &=-\frac {2 x}{3}+x^2+\log (x)-2 \log (25+x)\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 17, normalized size = 0.47 \begin {gather*} -\frac {2 x}{3}+x^2+\log (x)-2 \log (25+x) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.68, size = 15, normalized size = 0.42 \begin {gather*} x^{2} - \frac {2}{3} \, x - 2 \, \log \left (x + 25\right ) + \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.14, size = 17, normalized size = 0.47 \begin {gather*} x^{2} - \frac {2}{3} \, x - 2 \, \log \left ({\left | x + 25 \right |}\right ) + \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 = 0.09, size = 16, normalized size = 0.44
method | result | size |
default | \(x^{2}-\frac {2 x}{3}+\ln \relax (x )-2 \ln \left (x +25\right )\) | \(16\) |
norman | \(x^{2}-\frac {2 x}{3}+\ln \relax (x )-2 \ln \left (x +25\right )\) | \(16\) |
risch | \(x^{2}-\frac {2 x}{3}+\ln \relax (x )-2 \ln \left (x +25\right )\) | \(16\) |
meijerg | \(\ln \relax (x )-2 \ln \relax (5)-2 \ln \left (1+\frac {x}{25}\right )-\frac {25 x \left (-\frac {3 x}{25}+6\right )}{3}+\frac {148 x}{3}\) | \(27\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.48, size = 15, normalized size = 0.42 \begin {gather*} x^{2} - \frac {2}{3} \, x - 2 \, \log \left (x + 25\right ) + \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 7.48, size = 15, normalized size = 0.42 \begin {gather*} \ln \relax (x)-2\,\ln \left (x+25\right )-\frac {2\,x}{3}+x^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 17, normalized size = 0.47 \begin {gather*} x^{2} - \frac {2 x}{3} + \log {\relax (x )} - 2 \log {\left (x + 25 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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