Integrand size = 66, antiderivative size = 22 \[ \int \frac {1171875+777500 x+3750 x^3+2503 x^4+3 x^6+2 x^7}{11328125+1171875 x+388750 x^2+36250 x^3+3750 x^4+1247 x^5+29 x^6+3 x^7+x^8} \, dx=\log \left (-25+x-(2+x)^2+\frac {3}{\frac {625}{x^2}+x}\right ) \]
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Time = 0.10 (sec) , antiderivative size = 33, normalized size of antiderivative = 1.50, number of steps used = 4, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {2099, 266, 1601} \[ \int \frac {1171875+777500 x+3750 x^3+2503 x^4+3 x^6+2 x^7}{11328125+1171875 x+388750 x^2+36250 x^3+3750 x^4+1247 x^5+29 x^6+3 x^7+x^8} \, dx=\log \left (x^5+3 x^4+29 x^3+622 x^2+1875 x+18125\right )-\log \left (x^3+625\right ) \]
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Rule 266
Rule 1601
Rule 2099
Rubi steps \begin{align*} \text {integral}& = \int \left (-\frac {3 x^2}{625+x^3}+\frac {1875+1244 x+87 x^2+12 x^3+5 x^4}{18125+1875 x+622 x^2+29 x^3+3 x^4+x^5}\right ) \, dx \\ & = -\left (3 \int \frac {x^2}{625+x^3} \, dx\right )+\int \frac {1875+1244 x+87 x^2+12 x^3+5 x^4}{18125+1875 x+622 x^2+29 x^3+3 x^4+x^5} \, dx \\ & = -\log \left (625+x^3\right )+\log \left (18125+1875 x+622 x^2+29 x^3+3 x^4+x^5\right ) \\ \end{align*}
Time = 0.04 (sec) , antiderivative size = 33, normalized size of antiderivative = 1.50 \[ \int \frac {1171875+777500 x+3750 x^3+2503 x^4+3 x^6+2 x^7}{11328125+1171875 x+388750 x^2+36250 x^3+3750 x^4+1247 x^5+29 x^6+3 x^7+x^8} \, dx=-\log \left (625+x^3\right )+\log \left (18125+1875 x+622 x^2+29 x^3+3 x^4+x^5\right ) \]
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Time = 0.04 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.55
method | result | size |
default | \(\ln \left (x^{5}+3 x^{4}+29 x^{3}+622 x^{2}+1875 x +18125\right )-\ln \left (x^{3}+625\right )\) | \(34\) |
norman | \(\ln \left (x^{5}+3 x^{4}+29 x^{3}+622 x^{2}+1875 x +18125\right )-\ln \left (x^{3}+625\right )\) | \(34\) |
risch | \(\ln \left (x^{5}+3 x^{4}+29 x^{3}+622 x^{2}+1875 x +18125\right )-\ln \left (x^{3}+625\right )\) | \(34\) |
parallelrisch | \(\ln \left (x^{5}+3 x^{4}+29 x^{3}+622 x^{2}+1875 x +18125\right )-\ln \left (x^{3}+625\right )\) | \(34\) |
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Time = 0.25 (sec) , antiderivative size = 33, normalized size of antiderivative = 1.50 \[ \int \frac {1171875+777500 x+3750 x^3+2503 x^4+3 x^6+2 x^7}{11328125+1171875 x+388750 x^2+36250 x^3+3750 x^4+1247 x^5+29 x^6+3 x^7+x^8} \, dx=\log \left (x^{5} + 3 \, x^{4} + 29 \, x^{3} + 622 \, x^{2} + 1875 \, x + 18125\right ) - \log \left (x^{3} + 625\right ) \]
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Time = 0.09 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.41 \[ \int \frac {1171875+777500 x+3750 x^3+2503 x^4+3 x^6+2 x^7}{11328125+1171875 x+388750 x^2+36250 x^3+3750 x^4+1247 x^5+29 x^6+3 x^7+x^8} \, dx=- \log {\left (x^{3} + 625 \right )} + \log {\left (x^{5} + 3 x^{4} + 29 x^{3} + 622 x^{2} + 1875 x + 18125 \right )} \]
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Time = 0.19 (sec) , antiderivative size = 33, normalized size of antiderivative = 1.50 \[ \int \frac {1171875+777500 x+3750 x^3+2503 x^4+3 x^6+2 x^7}{11328125+1171875 x+388750 x^2+36250 x^3+3750 x^4+1247 x^5+29 x^6+3 x^7+x^8} \, dx=\log \left (x^{5} + 3 \, x^{4} + 29 \, x^{3} + 622 \, x^{2} + 1875 \, x + 18125\right ) - \log \left (x^{3} + 625\right ) \]
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Time = 0.26 (sec) , antiderivative size = 35, normalized size of antiderivative = 1.59 \[ \int \frac {1171875+777500 x+3750 x^3+2503 x^4+3 x^6+2 x^7}{11328125+1171875 x+388750 x^2+36250 x^3+3750 x^4+1247 x^5+29 x^6+3 x^7+x^8} \, dx=\log \left ({\left | x^{5} + 3 \, x^{4} + 29 \, x^{3} + 622 \, x^{2} + 1875 \, x + 18125 \right |}\right ) - \log \left ({\left | x^{3} + 625 \right |}\right ) \]
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Time = 0.17 (sec) , antiderivative size = 33, normalized size of antiderivative = 1.50 \[ \int \frac {1171875+777500 x+3750 x^3+2503 x^4+3 x^6+2 x^7}{11328125+1171875 x+388750 x^2+36250 x^3+3750 x^4+1247 x^5+29 x^6+3 x^7+x^8} \, dx=\ln \left (x^5+3\,x^4+29\,x^3+622\,x^2+1875\,x+18125\right )-\ln \left (x^3+625\right ) \]
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