Integrand size = 64, antiderivative size = 25 \[ \int \frac {436+784 x-13 x^2+4 x^3+2 x^4+\left (-16+8 x+7 x^2-2 x^3-x^4\right ) \log (3)}{16-8 x-7 x^2+2 x^3+x^4} \, dx=2 x+\frac {400+x}{4-x-x^2}-x \log (3) \]
[Out]
Time = 0.05 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.08, number of steps used = 4, number of rules used = 4, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.062, Rules used = {1694, 1828, 21, 8} \[ \int \frac {436+784 x-13 x^2+4 x^3+2 x^4+\left (-16+8 x+7 x^2-2 x^3-x^4\right ) \log (3)}{16-8 x-7 x^2+2 x^3+x^4} \, dx=\frac {4 (x+400)}{17-4 \left (x+\frac {1}{2}\right )^2}+x (2-\log (3)) \]
[In]
[Out]
Rule 8
Rule 21
Rule 1694
Rule 1828
Rubi steps \begin{align*} \text {integral}& = \text {Subst}\left (\int \frac {12784 x-8 x^2 (32-17 \log (3))+17 (38-17 \log (3))+16 x^4 (2-\log (3))}{\left (17-4 x^2\right )^2} \, dx,x,\frac {1}{2}+x\right ) \\ & = \frac {4 (400+x)}{17-4 \left (\frac {1}{2}+x\right )^2}-\frac {1}{34} \text {Subst}\left (\int \frac {-578 (2-\log (3))+136 x^2 (2-\log (3))}{17-4 x^2} \, dx,x,\frac {1}{2}+x\right ) \\ & = \frac {4 (400+x)}{17-4 \left (\frac {1}{2}+x\right )^2}-(-2+\log (3)) \text {Subst}\left (\int 1 \, dx,x,\frac {1}{2}+x\right ) \\ & = \frac {4 (400+x)}{17-4 \left (\frac {1}{2}+x\right )^2}+x (2-\log (3)) \\ \end{align*}
Time = 0.03 (sec) , antiderivative size = 23, normalized size of antiderivative = 0.92 \[ \int \frac {436+784 x-13 x^2+4 x^3+2 x^4+\left (-16+8 x+7 x^2-2 x^3-x^4\right ) \log (3)}{16-8 x-7 x^2+2 x^3+x^4} \, dx=\frac {-400-x}{-4+x+x^2}+x (2-\log (3)) \]
[In]
[Out]
Time = 0.06 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.96
method | result | size |
default | \(2 x -x \ln \left (3\right )+\frac {-x -400}{x^{2}+x -4}\) | \(24\) |
risch | \(2 x -x \ln \left (3\right )+\frac {-x -400}{x^{2}+x -4}\) | \(24\) |
norman | \(\frac {\left (2-\ln \left (3\right )\right ) x^{3}+\left (5 \ln \left (3\right )-11\right ) x -392-4 \ln \left (3\right )}{x^{2}+x -4}\) | \(34\) |
gosper | \(-\frac {x^{3} \ln \left (3\right )-2 x^{3}-5 x \ln \left (3\right )+4 \ln \left (3\right )+11 x +392}{x^{2}+x -4}\) | \(36\) |
parallelrisch | \(-\frac {x^{3} \ln \left (3\right )-2 x^{3}-5 x \ln \left (3\right )+4 \ln \left (3\right )+11 x +392}{x^{2}+x -4}\) | \(36\) |
[In]
[Out]
none
Time = 0.31 (sec) , antiderivative size = 38, normalized size of antiderivative = 1.52 \[ \int \frac {436+784 x-13 x^2+4 x^3+2 x^4+\left (-16+8 x+7 x^2-2 x^3-x^4\right ) \log (3)}{16-8 x-7 x^2+2 x^3+x^4} \, dx=\frac {2 \, x^{3} + 2 \, x^{2} - {\left (x^{3} + x^{2} - 4 \, x\right )} \log \left (3\right ) - 9 \, x - 400}{x^{2} + x - 4} \]
[In]
[Out]
Time = 0.09 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.68 \[ \int \frac {436+784 x-13 x^2+4 x^3+2 x^4+\left (-16+8 x+7 x^2-2 x^3-x^4\right ) \log (3)}{16-8 x-7 x^2+2 x^3+x^4} \, dx=x \left (2 - \log {\left (3 \right )}\right ) + \frac {- x - 400}{x^{2} + x - 4} \]
[In]
[Out]
none
Time = 0.19 (sec) , antiderivative size = 21, normalized size of antiderivative = 0.84 \[ \int \frac {436+784 x-13 x^2+4 x^3+2 x^4+\left (-16+8 x+7 x^2-2 x^3-x^4\right ) \log (3)}{16-8 x-7 x^2+2 x^3+x^4} \, dx=-x {\left (\log \left (3\right ) - 2\right )} - \frac {x + 400}{x^{2} + x - 4} \]
[In]
[Out]
none
Time = 0.28 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.88 \[ \int \frac {436+784 x-13 x^2+4 x^3+2 x^4+\left (-16+8 x+7 x^2-2 x^3-x^4\right ) \log (3)}{16-8 x-7 x^2+2 x^3+x^4} \, dx=-x \log \left (3\right ) + 2 \, x - \frac {x + 400}{x^{2} + x - 4} \]
[In]
[Out]
Time = 12.95 (sec) , antiderivative size = 21, normalized size of antiderivative = 0.84 \[ \int \frac {436+784 x-13 x^2+4 x^3+2 x^4+\left (-16+8 x+7 x^2-2 x^3-x^4\right ) \log (3)}{16-8 x-7 x^2+2 x^3+x^4} \, dx=-\frac {x+400}{x^2+x-4}-x\,\left (\ln \left (3\right )-2\right ) \]
[In]
[Out]