Integrand size = 22, antiderivative size = 21 \[ \int \frac {-144-289 x+e (1+2 x)}{-144 x+e x} \, dx=2 x+\frac {1+x}{144-e}+\log \left (\frac {x}{4}\right ) \]
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Time = 0.01 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.81, number of steps used = 5, number of rules used = 4, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.182, Rules used = {6, 12, 192, 45} \[ \int \frac {-144-289 x+e (1+2 x)}{-144 x+e x} \, dx=\frac {(289-2 e) x}{144-e}+\log (x) \]
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Rule 6
Rule 12
Rule 45
Rule 192
Rubi steps \begin{align*} \text {integral}& = \int \frac {-144-289 x+e (1+2 x)}{(-144+e) x} \, dx \\ & = \frac {\int \frac {-144-289 x+e (1+2 x)}{x} \, dx}{-144+e} \\ & = \frac {\int \frac {-144+e-(289-2 e) x}{x} \, dx}{-144+e} \\ & = \frac {\int \left (-289+2 e+\frac {-144+e}{x}\right ) \, dx}{-144+e} \\ & = \frac {(289-2 e) x}{144-e}+\log (x) \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.95 \[ \int \frac {-144-289 x+e (1+2 x)}{-144 x+e x} \, dx=\frac {(-289+2 e) x+(-144+e) \log (x)}{-144+e} \]
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Time = 0.06 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.86
method | result | size |
norman | \(\frac {\left (2 \,{\mathrm e}-289\right ) x}{{\mathrm e}-144}+\ln \left (x \right )\) | \(18\) |
default | \(\frac {2 x \,{\mathrm e}-289 x +\left ({\mathrm e}-144\right ) \ln \left (x \right )}{{\mathrm e}-144}\) | \(24\) |
risch | \(\frac {2 x \,{\mathrm e}}{{\mathrm e}-144}-\frac {289 x}{{\mathrm e}-144}+\ln \left (x \right )\) | \(24\) |
parallelrisch | \(\frac {{\mathrm e} \ln \left (x \right )+2 x \,{\mathrm e}-144 \ln \left (x \right )-289 x}{{\mathrm e}-144}\) | \(26\) |
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Time = 0.25 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.10 \[ \int \frac {-144-289 x+e (1+2 x)}{-144 x+e x} \, dx=\frac {2 \, x e + {\left (e - 144\right )} \log \left (x\right ) - 289 \, x}{e - 144} \]
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Time = 0.05 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.05 \[ \int \frac {-144-289 x+e (1+2 x)}{-144 x+e x} \, dx=\frac {- x \left (289 - 2 e\right ) - \left (144 - e\right ) \log {\left (x \right )}}{-144 + e} \]
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Time = 0.19 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.81 \[ \int \frac {-144-289 x+e (1+2 x)}{-144 x+e x} \, dx=\frac {x {\left (2 \, e - 289\right )}}{e - 144} + \log \left (x\right ) \]
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Time = 0.26 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.95 \[ \int \frac {-144-289 x+e (1+2 x)}{-144 x+e x} \, dx=\frac {2 \, x e - 289 \, x}{e - 144} + \log \left ({\left | x \right |}\right ) \]
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Time = 0.07 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.81 \[ \int \frac {-144-289 x+e (1+2 x)}{-144 x+e x} \, dx=\ln \left (x\right )+\frac {x\,\left (2\,\mathrm {e}-289\right )}{\mathrm {e}-144} \]
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