Integrand size = 35, antiderivative size = 19 \[ \int \frac {142+2 x-216 x^2+45 x^4}{142 x+x^2-72 x^3+9 x^5} \, dx=\log \left (x \left (2-x-9 \left (4-x^2\right )^2\right )\right ) \]
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Time = 0.01 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.95, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.029, Rules used = {1601} \[ \int \frac {142+2 x-216 x^2+45 x^4}{142 x+x^2-72 x^3+9 x^5} \, dx=\log \left (9 x^5-72 x^3+x^2+142 x\right ) \]
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Rule 1601
Rubi steps \begin{align*} \text {integral}& = \log \left (142 x+x^2-72 x^3+9 x^5\right ) \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.89 \[ \int \frac {142+2 x-216 x^2+45 x^4}{142 x+x^2-72 x^3+9 x^5} \, dx=\log (x)+\log \left (142+x-72 x^2+9 x^4\right ) \]
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Time = 0.12 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.89
method | result | size |
default | \(\ln \left (x \left (9 x^{4}-72 x^{2}+x +142\right )\right )\) | \(17\) |
derivativedivides | \(\ln \left (9 x^{5}-72 x^{3}+x^{2}+142 x \right )\) | \(19\) |
risch | \(\ln \left (9 x^{5}-72 x^{3}+x^{2}+142 x \right )\) | \(19\) |
parallelrisch | \(\ln \left (x \right )+\ln \left (-2+x \right )+\ln \left (x^{3}+2 x^{2}-4 x -\frac {71}{9}\right )\) | \(22\) |
norman | \(\ln \left (x \right )+\ln \left (-2+x \right )+\ln \left (9 x^{3}+18 x^{2}-36 x -71\right )\) | \(24\) |
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none
Time = 0.26 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.95 \[ \int \frac {142+2 x-216 x^2+45 x^4}{142 x+x^2-72 x^3+9 x^5} \, dx=\log \left (9 \, x^{5} - 72 \, x^{3} + x^{2} + 142 \, x\right ) \]
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Time = 0.05 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.89 \[ \int \frac {142+2 x-216 x^2+45 x^4}{142 x+x^2-72 x^3+9 x^5} \, dx=\log {\left (9 x^{5} - 72 x^{3} + x^{2} + 142 x \right )} \]
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none
Time = 0.19 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.95 \[ \int \frac {142+2 x-216 x^2+45 x^4}{142 x+x^2-72 x^3+9 x^5} \, dx=\log \left (9 \, x^{5} - 72 \, x^{3} + x^{2} + 142 \, x\right ) \]
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none
Time = 0.27 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.00 \[ \int \frac {142+2 x-216 x^2+45 x^4}{142 x+x^2-72 x^3+9 x^5} \, dx=\log \left ({\left | 9 \, x^{5} - 72 \, x^{3} + x^{2} + 142 \, x \right |}\right ) \]
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Time = 13.25 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.84 \[ \int \frac {142+2 x-216 x^2+45 x^4}{142 x+x^2-72 x^3+9 x^5} \, dx=\ln \left (x\,\left (9\,x^4-72\,x^2+x+142\right )\right ) \]
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