Integrand size = 122, antiderivative size = 22 \[ \int \frac {1-676 x-e^{2 e^2} x-104 x^2-315 x^3-16 x^4-20 x^5+e^{e^2} \left (-52 x-4 x^2-12 x^3\right )}{-676 x^2-e^{2 e^2} x^2-52 x^3-105 x^4-4 x^5-4 x^6+e^{e^2} \left (-52 x^2-2 x^3-4 x^4\right )+x \log (x)} \, dx=\log \left (-x \left (26+e^{e^2}+x+2 x^2\right )^2+\log (x)\right ) \]
[Out]
Time = 0.38 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.05, number of steps used = 4, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.025, Rules used = {6, 6820, 6816} \[ \int \frac {1-676 x-e^{2 e^2} x-104 x^2-315 x^3-16 x^4-20 x^5+e^{e^2} \left (-52 x-4 x^2-12 x^3\right )}{-676 x^2-e^{2 e^2} x^2-52 x^3-105 x^4-4 x^5-4 x^6+e^{e^2} \left (-52 x^2-2 x^3-4 x^4\right )+x \log (x)} \, dx=\log \left (x \left (2 x^2+x+e^{e^2}+26\right )^2-\log (x)\right ) \]
[In]
[Out]
Rule 6
Rule 6816
Rule 6820
Rubi steps \begin{align*} \text {integral}& = \int \frac {1+\left (-676-e^{2 e^2}\right ) x-104 x^2-315 x^3-16 x^4-20 x^5+e^{e^2} \left (-52 x-4 x^2-12 x^3\right )}{-676 x^2-e^{2 e^2} x^2-52 x^3-105 x^4-4 x^5-4 x^6+e^{e^2} \left (-52 x^2-2 x^3-4 x^4\right )+x \log (x)} \, dx \\ & = \int \frac {1+\left (-676-e^{2 e^2}\right ) x-104 x^2-315 x^3-16 x^4-20 x^5+e^{e^2} \left (-52 x-4 x^2-12 x^3\right )}{\left (-676-e^{2 e^2}\right ) x^2-52 x^3-105 x^4-4 x^5-4 x^6+e^{e^2} \left (-52 x^2-2 x^3-4 x^4\right )+x \log (x)} \, dx \\ & = \int \frac {-1+\left (26+e^{e^2}\right )^2 x+4 \left (26+e^{e^2}\right ) x^2+3 \left (105+4 e^{e^2}\right ) x^3+16 x^4+20 x^5}{x \left (x \left (26+e^{e^2}+x+2 x^2\right )^2-\log (x)\right )} \, dx \\ & = \log \left (x \left (26+e^{e^2}+x+2 x^2\right )^2-\log (x)\right ) \\ \end{align*}
Leaf count is larger than twice the leaf count of optimal. \(66\) vs. \(2(22)=44\).
Time = 0.55 (sec) , antiderivative size = 66, normalized size of antiderivative = 3.00 \[ \int \frac {1-676 x-e^{2 e^2} x-104 x^2-315 x^3-16 x^4-20 x^5+e^{e^2} \left (-52 x-4 x^2-12 x^3\right )}{-676 x^2-e^{2 e^2} x^2-52 x^3-105 x^4-4 x^5-4 x^6+e^{e^2} \left (-52 x^2-2 x^3-4 x^4\right )+x \log (x)} \, dx=\log \left (676 x+52 e^{e^2} x+e^{2 e^2} x+52 x^2+2 e^{e^2} x^2+105 x^3+4 e^{e^2} x^3+4 x^4+4 x^5-\log (x)\right ) \]
[In]
[Out]
Leaf count of result is larger than twice the leaf count of optimal. \(54\) vs. \(2(20)=40\).
Time = 0.83 (sec) , antiderivative size = 55, normalized size of antiderivative = 2.50
method | result | size |
parallelrisch | \(\ln \left (x^{5}+x^{3} {\mathrm e}^{{\mathrm e}^{2}}+x^{4}+\frac {x \,{\mathrm e}^{2 \,{\mathrm e}^{2}}}{4}+\frac {x^{2} {\mathrm e}^{{\mathrm e}^{2}}}{2}+\frac {105 x^{3}}{4}+13 x \,{\mathrm e}^{{\mathrm e}^{2}}+13 x^{2}+169 x -\frac {\ln \left (x \right )}{4}\right )\) | \(55\) |
risch | \(\ln \left (-4 x^{5}-4 x^{3} {\mathrm e}^{{\mathrm e}^{2}}-4 x^{4}-x \,{\mathrm e}^{2 \,{\mathrm e}^{2}}-2 x^{2} {\mathrm e}^{{\mathrm e}^{2}}-105 x^{3}-52 x \,{\mathrm e}^{{\mathrm e}^{2}}-52 x^{2}+\ln \left (x \right )-676 x \right )\) | \(58\) |
default | \(\ln \left (4 x^{5}+4 x^{4}+4 x^{3} {\mathrm e}^{{\mathrm e}^{2}}+105 x^{3}+2 x^{2} {\mathrm e}^{{\mathrm e}^{2}}+x \,{\mathrm e}^{2 \,{\mathrm e}^{2}}+52 x^{2}+52 x \,{\mathrm e}^{{\mathrm e}^{2}}+676 x -\ln \left (x \right )\right )\) | \(59\) |
norman | \(\ln \left (4 x^{5}+4 x^{4}+4 x^{3} {\mathrm e}^{{\mathrm e}^{2}}+105 x^{3}+2 x^{2} {\mathrm e}^{{\mathrm e}^{2}}+x \,{\mathrm e}^{2 \,{\mathrm e}^{2}}+52 x^{2}+52 x \,{\mathrm e}^{{\mathrm e}^{2}}+676 x -\ln \left (x \right )\right )\) | \(59\) |
[In]
[Out]
Leaf count of result is larger than twice the leaf count of optimal. 52 vs. \(2 (20) = 40\).
Time = 0.26 (sec) , antiderivative size = 52, normalized size of antiderivative = 2.36 \[ \int \frac {1-676 x-e^{2 e^2} x-104 x^2-315 x^3-16 x^4-20 x^5+e^{e^2} \left (-52 x-4 x^2-12 x^3\right )}{-676 x^2-e^{2 e^2} x^2-52 x^3-105 x^4-4 x^5-4 x^6+e^{e^2} \left (-52 x^2-2 x^3-4 x^4\right )+x \log (x)} \, dx=\log \left (-4 \, x^{5} - 4 \, x^{4} - 105 \, x^{3} - 52 \, x^{2} - x e^{\left (2 \, e^{2}\right )} - 2 \, {\left (2 \, x^{3} + x^{2} + 26 \, x\right )} e^{\left (e^{2}\right )} - 676 \, x + \log \left (x\right )\right ) \]
[In]
[Out]
Leaf count of result is larger than twice the leaf count of optimal. 65 vs. \(2 (20) = 40\).
Time = 0.15 (sec) , antiderivative size = 65, normalized size of antiderivative = 2.95 \[ \int \frac {1-676 x-e^{2 e^2} x-104 x^2-315 x^3-16 x^4-20 x^5+e^{e^2} \left (-52 x-4 x^2-12 x^3\right )}{-676 x^2-e^{2 e^2} x^2-52 x^3-105 x^4-4 x^5-4 x^6+e^{e^2} \left (-52 x^2-2 x^3-4 x^4\right )+x \log (x)} \, dx=\log {\left (- 4 x^{5} - 4 x^{4} - 4 x^{3} e^{e^{2}} - 105 x^{3} - 2 x^{2} e^{e^{2}} - 52 x^{2} - x e^{2 e^{2}} - 52 x e^{e^{2}} - 676 x + \log {\left (x \right )} \right )} \]
[In]
[Out]
Leaf count of result is larger than twice the leaf count of optimal. 51 vs. \(2 (20) = 40\).
Time = 0.25 (sec) , antiderivative size = 51, normalized size of antiderivative = 2.32 \[ \int \frac {1-676 x-e^{2 e^2} x-104 x^2-315 x^3-16 x^4-20 x^5+e^{e^2} \left (-52 x-4 x^2-12 x^3\right )}{-676 x^2-e^{2 e^2} x^2-52 x^3-105 x^4-4 x^5-4 x^6+e^{e^2} \left (-52 x^2-2 x^3-4 x^4\right )+x \log (x)} \, dx=\log \left (-4 \, x^{5} - 4 \, x^{4} - x^{3} {\left (4 \, e^{\left (e^{2}\right )} + 105\right )} - 2 \, x^{2} {\left (e^{\left (e^{2}\right )} + 26\right )} - x {\left (e^{\left (2 \, e^{2}\right )} + 52 \, e^{\left (e^{2}\right )} + 676\right )} + \log \left (x\right )\right ) \]
[In]
[Out]
Leaf count of result is larger than twice the leaf count of optimal. 57 vs. \(2 (20) = 40\).
Time = 0.27 (sec) , antiderivative size = 57, normalized size of antiderivative = 2.59 \[ \int \frac {1-676 x-e^{2 e^2} x-104 x^2-315 x^3-16 x^4-20 x^5+e^{e^2} \left (-52 x-4 x^2-12 x^3\right )}{-676 x^2-e^{2 e^2} x^2-52 x^3-105 x^4-4 x^5-4 x^6+e^{e^2} \left (-52 x^2-2 x^3-4 x^4\right )+x \log (x)} \, dx=\log \left (-4 \, x^{5} - 4 \, x^{4} - 4 \, x^{3} e^{\left (e^{2}\right )} - 105 \, x^{3} - 2 \, x^{2} e^{\left (e^{2}\right )} - 52 \, x^{2} - x e^{\left (2 \, e^{2}\right )} - 52 \, x e^{\left (e^{2}\right )} - 676 \, x + \log \left (x\right )\right ) \]
[In]
[Out]
Timed out. \[ \int \frac {1-676 x-e^{2 e^2} x-104 x^2-315 x^3-16 x^4-20 x^5+e^{e^2} \left (-52 x-4 x^2-12 x^3\right )}{-676 x^2-e^{2 e^2} x^2-52 x^3-105 x^4-4 x^5-4 x^6+e^{e^2} \left (-52 x^2-2 x^3-4 x^4\right )+x \log (x)} \, dx=\int \frac {676\,x+x\,{\mathrm {e}}^{2\,{\mathrm {e}}^2}+{\mathrm {e}}^{{\mathrm {e}}^2}\,\left (12\,x^3+4\,x^2+52\,x\right )+104\,x^2+315\,x^3+16\,x^4+20\,x^5-1}{{\mathrm {e}}^{{\mathrm {e}}^2}\,\left (4\,x^4+2\,x^3+52\,x^2\right )+x^2\,{\mathrm {e}}^{2\,{\mathrm {e}}^2}-x\,\ln \left (x\right )+676\,x^2+52\,x^3+105\,x^4+4\,x^5+4\,x^6} \,d x \]
[In]
[Out]