Integrand size = 27, antiderivative size = 36 \[ \int \frac {75-53 x+148 x^2+6 x^3}{75 x+3 x^2} \, dx=\frac {-4 x+x \left (\frac {2 (5-x)}{3}+x^2\right )}{x}-\log \left (\frac {(25+x)^2}{x}\right ) \]
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Time = 0.02 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.47, number of steps used = 3, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.074, Rules used = {1607, 1634} \[ \int \frac {75-53 x+148 x^2+6 x^3}{75 x+3 x^2} \, dx=x^2-\frac {2 x}{3}+\log (x)-2 \log (x+25) \]
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Rule 1607
Rule 1634
Rubi steps \begin{align*} \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{align*}
Time = 0.01 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.47 \[ \int \frac {75-53 x+148 x^2+6 x^3}{75 x+3 x^2} \, dx=-\frac {2 x}{3}+x^2+\log (x)-2 \log (25+x) \]
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Time = 0.86 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.44
method | result | size |
default | \(x^{2}-\frac {2 x}{3}+\ln \left (x \right )-2 \ln \left (x +25\right )\) | \(16\) |
norman | \(x^{2}-\frac {2 x}{3}+\ln \left (x \right )-2 \ln \left (x +25\right )\) | \(16\) |
risch | \(x^{2}-\frac {2 x}{3}+\ln \left (x \right )-2 \ln \left (x +25\right )\) | \(16\) |
parallelrisch | \(x^{2}-\frac {2 x}{3}+\ln \left (x \right )-2 \ln \left (x +25\right )\) | \(16\) |
meijerg | \(\ln \left (x \right )-2 \ln \left (5\right )-2 \ln \left (1+\frac {x}{25}\right )-\frac {25 x \left (-\frac {3 x}{25}+6\right )}{3}+\frac {148 x}{3}\) | \(27\) |
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none
Time = 0.23 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.42 \[ \int \frac {75-53 x+148 x^2+6 x^3}{75 x+3 x^2} \, dx=x^{2} - \frac {2}{3} \, x - 2 \, \log \left (x + 25\right ) + \log \left (x\right ) \]
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Time = 0.05 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.47 \[ \int \frac {75-53 x+148 x^2+6 x^3}{75 x+3 x^2} \, dx=x^{2} - \frac {2 x}{3} + \log {\left (x \right )} - 2 \log {\left (x + 25 \right )} \]
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none
Time = 0.21 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.42 \[ \int \frac {75-53 x+148 x^2+6 x^3}{75 x+3 x^2} \, dx=x^{2} - \frac {2}{3} \, x - 2 \, \log \left (x + 25\right ) + \log \left (x\right ) \]
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none
Time = 0.27 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.47 \[ \int \frac {75-53 x+148 x^2+6 x^3}{75 x+3 x^2} \, dx=x^{2} - \frac {2}{3} \, x - 2 \, \log \left ({\left | x + 25 \right |}\right ) + \log \left ({\left | x \right |}\right ) \]
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Time = 14.28 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.42 \[ \int \frac {75-53 x+148 x^2+6 x^3}{75 x+3 x^2} \, dx=\ln \left (x\right )-2\,\ln \left (x+25\right )-\frac {2\,x}{3}+x^2 \]
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