Integrand size = 48, antiderivative size = 27 \[ \int \frac {3970-2520 x-9360 x^2-6400 x^3-1440 x^4}{-33-463 x-315 x^2+298 x^3+316 x^4+72 x^5} \, dx=5 \log \left (\frac {2}{\left (-4-x+\left (3 x-\frac {5}{3+2 x}\right )^2\right )^2}\right ) \]
[Out]
Time = 0.06 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.19, number of steps used = 3, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.042, Rules used = {2099, 1601} \[ \int \frac {3970-2520 x-9360 x^2-6400 x^3-1440 x^4}{-33-463 x-315 x^2+298 x^3+316 x^4+72 x^5} \, dx=20 \log (2 x+3)-10 \log \left (-36 x^4-104 x^3+7 x^2+147 x+11\right ) \]
[In]
[Out]
Rule 1601
Rule 2099
Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {40}{3+2 x}-\frac {10 \left (-147-14 x+312 x^2+144 x^3\right )}{-11-147 x-7 x^2+104 x^3+36 x^4}\right ) \, dx \\ & = 20 \log (3+2 x)-10 \int \frac {-147-14 x+312 x^2+144 x^3}{-11-147 x-7 x^2+104 x^3+36 x^4} \, dx \\ & = 20 \log (3+2 x)-10 \log \left (11+147 x+7 x^2-104 x^3-36 x^4\right ) \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.19 \[ \int \frac {3970-2520 x-9360 x^2-6400 x^3-1440 x^4}{-33-463 x-315 x^2+298 x^3+316 x^4+72 x^5} \, dx=-10 \left (-2 \log (3+2 x)+\log \left (11+147 x+7 x^2-104 x^3-36 x^4\right )\right ) \]
[In]
[Out]
Time = 0.08 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.07
method | result | size |
parallelrisch | \(20 \ln \left (x +\frac {3}{2}\right )-10 \ln \left (x^{4}+\frac {26}{9} x^{3}-\frac {7}{36} x^{2}-\frac {49}{12} x -\frac {11}{36}\right )\) | \(29\) |
default | \(-10 \ln \left (36 x^{4}+104 x^{3}-7 x^{2}-147 x -11\right )+20 \ln \left (3+2 x \right )\) | \(33\) |
norman | \(-10 \ln \left (36 x^{4}+104 x^{3}-7 x^{2}-147 x -11\right )+20 \ln \left (3+2 x \right )\) | \(33\) |
risch | \(-10 \ln \left (36 x^{4}+104 x^{3}-7 x^{2}-147 x -11\right )+20 \ln \left (3+2 x \right )\) | \(33\) |
[In]
[Out]
none
Time = 0.27 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.19 \[ \int \frac {3970-2520 x-9360 x^2-6400 x^3-1440 x^4}{-33-463 x-315 x^2+298 x^3+316 x^4+72 x^5} \, dx=-10 \, \log \left (36 \, x^{4} + 104 \, x^{3} - 7 \, x^{2} - 147 \, x - 11\right ) + 20 \, \log \left (2 \, x + 3\right ) \]
[In]
[Out]
Time = 0.07 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.15 \[ \int \frac {3970-2520 x-9360 x^2-6400 x^3-1440 x^4}{-33-463 x-315 x^2+298 x^3+316 x^4+72 x^5} \, dx=20 \log {\left (2 x + 3 \right )} - 10 \log {\left (36 x^{4} + 104 x^{3} - 7 x^{2} - 147 x - 11 \right )} \]
[In]
[Out]
none
Time = 0.18 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.19 \[ \int \frac {3970-2520 x-9360 x^2-6400 x^3-1440 x^4}{-33-463 x-315 x^2+298 x^3+316 x^4+72 x^5} \, dx=-10 \, \log \left (36 \, x^{4} + 104 \, x^{3} - 7 \, x^{2} - 147 \, x - 11\right ) + 20 \, \log \left (2 \, x + 3\right ) \]
[In]
[Out]
none
Time = 0.30 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.26 \[ \int \frac {3970-2520 x-9360 x^2-6400 x^3-1440 x^4}{-33-463 x-315 x^2+298 x^3+316 x^4+72 x^5} \, dx=-10 \, \log \left ({\left | 36 \, x^{4} + 104 \, x^{3} - 7 \, x^{2} - 147 \, x - 11 \right |}\right ) + 20 \, \log \left ({\left | 2 \, x + 3 \right |}\right ) \]
[In]
[Out]
Time = 0.14 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.11 \[ \int \frac {3970-2520 x-9360 x^2-6400 x^3-1440 x^4}{-33-463 x-315 x^2+298 x^3+316 x^4+72 x^5} \, dx=20\,\ln \left (x+\frac {3}{2}\right )-10\,\ln \left (36\,x^4+104\,x^3-7\,x^2-147\,x-11\right ) \]
[In]
[Out]