Integrand size = 104, antiderivative size = 15 \[ \int \frac {7040+4096 x+810 x^2+67 x^3+2 x^4+e^9 (7+2 x)+e^6 \left (210+81 x+6 x^2\right )+e^3 \left (2104+1020 x+141 x^2+6 x^3\right )}{1000+e^9+300 x+30 x^2+x^3+e^6 (30+3 x)+e^3 \left (300+60 x+3 x^2\right )} \, dx=x \left (7+x+\frac {4}{\left (10+e^3+x\right )^2}\right ) \]
[Out]
Leaf count is larger than twice the leaf count of optimal. \(32\) vs. \(2(15)=30\).
Time = 0.07 (sec) , antiderivative size = 32, normalized size of antiderivative = 2.13, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.010, Rules used = {2099} \[ \int \frac {7040+4096 x+810 x^2+67 x^3+2 x^4+e^9 (7+2 x)+e^6 \left (210+81 x+6 x^2\right )+e^3 \left (2104+1020 x+141 x^2+6 x^3\right )}{1000+e^9+300 x+30 x^2+x^3+e^6 (30+3 x)+e^3 \left (300+60 x+3 x^2\right )} \, dx=x^2+7 x+\frac {4}{x+e^3+10}-\frac {4 \left (10+e^3\right )}{\left (x+e^3+10\right )^2} \]
[In]
[Out]
Rule 2099
Rubi steps \begin{align*} \text {integral}& = \int \left (7+2 x+\frac {8 \left (10+e^3\right )}{\left (10+e^3+x\right )^3}-\frac {4}{\left (10+e^3+x\right )^2}\right ) \, dx \\ & = 7 x+x^2-\frac {4 \left (10+e^3\right )}{\left (10+e^3+x\right )^2}+\frac {4}{10+e^3+x} \\ \end{align*}
Leaf count is larger than twice the leaf count of optimal. \(48\) vs. \(2(15)=30\).
Time = 0.05 (sec) , antiderivative size = 48, normalized size of antiderivative = 3.20 \[ \int \frac {7040+4096 x+810 x^2+67 x^3+2 x^4+e^9 (7+2 x)+e^6 \left (210+81 x+6 x^2\right )+e^3 \left (2104+1020 x+141 x^2+6 x^3\right )}{1000+e^9+300 x+30 x^2+x^3+e^6 (30+3 x)+e^3 \left (300+60 x+3 x^2\right )} \, dx=-\frac {4 \left (10+e^3\right )}{\left (10+e^3+x\right )^2}+\frac {4}{10+e^3+x}+\left (-13-2 e^3\right ) \left (10+e^3+x\right )+\left (10+e^3+x\right )^2 \]
[In]
[Out]
Leaf count of result is larger than twice the leaf count of optimal. \(31\) vs. \(2(14)=28\).
Time = 0.13 (sec) , antiderivative size = 32, normalized size of antiderivative = 2.13
method | result | size |
risch | \(x^{2}+7 x +\frac {4 x}{{\mathrm e}^{6}+2 x \,{\mathrm e}^{3}+x^{2}+20 \,{\mathrm e}^{3}+20 x +100}\) | \(32\) |
norman | \(\frac {x^{4}+\left (27+2 \,{\mathrm e}^{3}\right ) x^{3}-24000+\left (-2 \,{\mathrm e}^{9}-81 \,{\mathrm e}^{6}-1020 \,{\mathrm e}^{3}-4096\right ) x -{\mathrm e}^{12}-54 \,{\mathrm e}^{9}-1020 \,{\mathrm e}^{6}-8200 \,{\mathrm e}^{3}}{\left (10+{\mathrm e}^{3}+x \right )^{2}}\) | \(66\) |
default | \(x^{2}+7 x +\frac {4 \left (\munderset {\textit {\_R} =\operatorname {RootOf}\left (\textit {\_Z}^{3}+\left (3 \,{\mathrm e}^{3}+30\right ) \textit {\_Z}^{2}+\left (60 \,{\mathrm e}^{3}+3 \,{\mathrm e}^{6}+300\right ) \textit {\_Z} +300 \,{\mathrm e}^{3}+{\mathrm e}^{9}+30 \,{\mathrm e}^{6}+1000\right )}{\sum }\frac {\left (10-\textit {\_R} +{\mathrm e}^{3}\right ) \ln \left (x -\textit {\_R} \right )}{100+{\mathrm e}^{6}+2 \textit {\_R} \,{\mathrm e}^{3}+\textit {\_R}^{2}+20 \,{\mathrm e}^{3}+20 \textit {\_R}}\right )}{3}\) | \(86\) |
gosper | \(-\frac {{\mathrm e}^{12}+2 x \,{\mathrm e}^{9}-2 x^{3} {\mathrm e}^{3}-x^{4}+54 \,{\mathrm e}^{9}+81 x \,{\mathrm e}^{6}-27 x^{3}+1020 \,{\mathrm e}^{6}+1020 x \,{\mathrm e}^{3}+8200 \,{\mathrm e}^{3}+4096 x +24000}{{\mathrm e}^{6}+2 x \,{\mathrm e}^{3}+x^{2}+20 \,{\mathrm e}^{3}+20 x +100}\) | \(87\) |
parallelrisch | \(-\frac {{\mathrm e}^{12}+2 x \,{\mathrm e}^{9}-2 x^{3} {\mathrm e}^{3}-x^{4}+54 \,{\mathrm e}^{9}+81 x \,{\mathrm e}^{6}-27 x^{3}+1020 \,{\mathrm e}^{6}+1020 x \,{\mathrm e}^{3}+8200 \,{\mathrm e}^{3}+4096 x +24000}{{\mathrm e}^{6}+2 x \,{\mathrm e}^{3}+x^{2}+20 \,{\mathrm e}^{3}+20 x +100}\) | \(87\) |
[In]
[Out]
Leaf count of result is larger than twice the leaf count of optimal. 63 vs. \(2 (14) = 28\).
Time = 0.27 (sec) , antiderivative size = 63, normalized size of antiderivative = 4.20 \[ \int \frac {7040+4096 x+810 x^2+67 x^3+2 x^4+e^9 (7+2 x)+e^6 \left (210+81 x+6 x^2\right )+e^3 \left (2104+1020 x+141 x^2+6 x^3\right )}{1000+e^9+300 x+30 x^2+x^3+e^6 (30+3 x)+e^3 \left (300+60 x+3 x^2\right )} \, dx=\frac {x^{4} + 27 \, x^{3} + 240 \, x^{2} + {\left (x^{2} + 7 \, x\right )} e^{6} + 2 \, {\left (x^{3} + 17 \, x^{2} + 70 \, x\right )} e^{3} + 704 \, x}{x^{2} + 2 \, {\left (x + 10\right )} e^{3} + 20 \, x + e^{6} + 100} \]
[In]
[Out]
Leaf count of result is larger than twice the leaf count of optimal. 31 vs. \(2 (14) = 28\).
Time = 0.22 (sec) , antiderivative size = 31, normalized size of antiderivative = 2.07 \[ \int \frac {7040+4096 x+810 x^2+67 x^3+2 x^4+e^9 (7+2 x)+e^6 \left (210+81 x+6 x^2\right )+e^3 \left (2104+1020 x+141 x^2+6 x^3\right )}{1000+e^9+300 x+30 x^2+x^3+e^6 (30+3 x)+e^3 \left (300+60 x+3 x^2\right )} \, dx=x^{2} + 7 x + \frac {4 x}{x^{2} + x \left (20 + 2 e^{3}\right ) + 100 + 20 e^{3} + e^{6}} \]
[In]
[Out]
Leaf count of result is larger than twice the leaf count of optimal. 30 vs. \(2 (14) = 28\).
Time = 0.18 (sec) , antiderivative size = 30, normalized size of antiderivative = 2.00 \[ \int \frac {7040+4096 x+810 x^2+67 x^3+2 x^4+e^9 (7+2 x)+e^6 \left (210+81 x+6 x^2\right )+e^3 \left (2104+1020 x+141 x^2+6 x^3\right )}{1000+e^9+300 x+30 x^2+x^3+e^6 (30+3 x)+e^3 \left (300+60 x+3 x^2\right )} \, dx=x^{2} + 7 \, x + \frac {4 \, x}{x^{2} + 2 \, x {\left (e^{3} + 10\right )} + e^{6} + 20 \, e^{3} + 100} \]
[In]
[Out]
none
Time = 0.26 (sec) , antiderivative size = 17, normalized size of antiderivative = 1.13 \[ \int \frac {7040+4096 x+810 x^2+67 x^3+2 x^4+e^9 (7+2 x)+e^6 \left (210+81 x+6 x^2\right )+e^3 \left (2104+1020 x+141 x^2+6 x^3\right )}{1000+e^9+300 x+30 x^2+x^3+e^6 (30+3 x)+e^3 \left (300+60 x+3 x^2\right )} \, dx=x^{2} + 7 \, x + \frac {4 \, x}{{\left (x + e^{3} + 10\right )}^{2}} \]
[In]
[Out]
Time = 11.28 (sec) , antiderivative size = 31, normalized size of antiderivative = 2.07 \[ \int \frac {7040+4096 x+810 x^2+67 x^3+2 x^4+e^9 (7+2 x)+e^6 \left (210+81 x+6 x^2\right )+e^3 \left (2104+1020 x+141 x^2+6 x^3\right )}{1000+e^9+300 x+30 x^2+x^3+e^6 (30+3 x)+e^3 \left (300+60 x+3 x^2\right )} \, dx=7\,x+\frac {4\,x}{x^2+\left (2\,{\mathrm {e}}^3+20\right )\,x+20\,{\mathrm {e}}^3+{\mathrm {e}}^6+100}+x^2 \]
[In]
[Out]