Integrand size = 38, antiderivative size = 22 \[ \int \frac {950-60 x-180 x^2+24 x^3}{725+475 x-15 x^2-30 x^3+3 x^4} \, dx=2 \log \left (2+x+3 \left (-3-x+\frac {x^2}{5}\right )^2\right ) \]
[Out]
Time = 0.01 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.05, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.026, Rules used = {1601} \[ \int \frac {950-60 x-180 x^2+24 x^3}{725+475 x-15 x^2-30 x^3+3 x^4} \, dx=2 \log \left (3 x^4-30 x^3-15 x^2+475 x+725\right ) \]
[In]
[Out]
Rule 1601
Rubi steps \begin{align*} \text {integral}& = 2 \log \left (725+475 x-15 x^2-30 x^3+3 x^4\right ) \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.05 \[ \int \frac {950-60 x-180 x^2+24 x^3}{725+475 x-15 x^2-30 x^3+3 x^4} \, dx=2 \log \left (725+475 x-15 x^2-30 x^3+3 x^4\right ) \]
[In]
[Out]
Time = 0.02 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.00
method | result | size |
parallelrisch | \(2 \ln \left (x^{4}-10 x^{3}-5 x^{2}+\frac {475}{3} x +\frac {725}{3}\right )\) | \(22\) |
default | \(2 \ln \left (3 x^{4}-30 x^{3}-15 x^{2}+475 x +725\right )\) | \(24\) |
norman | \(2 \ln \left (3 x^{4}-30 x^{3}-15 x^{2}+475 x +725\right )\) | \(24\) |
risch | \(2 \ln \left (3 x^{4}-30 x^{3}-15 x^{2}+475 x +725\right )\) | \(24\) |
[In]
[Out]
none
Time = 0.25 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.05 \[ \int \frac {950-60 x-180 x^2+24 x^3}{725+475 x-15 x^2-30 x^3+3 x^4} \, dx=2 \, \log \left (3 \, x^{4} - 30 \, x^{3} - 15 \, x^{2} + 475 \, x + 725\right ) \]
[In]
[Out]
Time = 0.05 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.00 \[ \int \frac {950-60 x-180 x^2+24 x^3}{725+475 x-15 x^2-30 x^3+3 x^4} \, dx=2 \log {\left (3 x^{4} - 30 x^{3} - 15 x^{2} + 475 x + 725 \right )} \]
[In]
[Out]
none
Time = 0.20 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.05 \[ \int \frac {950-60 x-180 x^2+24 x^3}{725+475 x-15 x^2-30 x^3+3 x^4} \, dx=2 \, \log \left (3 \, x^{4} - 30 \, x^{3} - 15 \, x^{2} + 475 \, x + 725\right ) \]
[In]
[Out]
none
Time = 0.26 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.09 \[ \int \frac {950-60 x-180 x^2+24 x^3}{725+475 x-15 x^2-30 x^3+3 x^4} \, dx=2 \, \log \left ({\left | 3 \, x^{4} - 30 \, x^{3} - 15 \, x^{2} + 475 \, x + 725 \right |}\right ) \]
[In]
[Out]
Time = 0.12 (sec) , antiderivative size = 21, normalized size of antiderivative = 0.95 \[ \int \frac {950-60 x-180 x^2+24 x^3}{725+475 x-15 x^2-30 x^3+3 x^4} \, dx=2\,\ln \left (x^4-10\,x^3-5\,x^2+\frac {475\,x}{3}+\frac {725}{3}\right ) \]
[In]
[Out]