Optimal. Leaf size=26 \[ e \left (3 e^5-\log \left (\frac {e+x}{-\frac {3}{x^2}+x}\right )\right )^2 \]
[Out]
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Rubi [C] Result contains higher order function than in optimal. Order 4 vs. order 3 in
optimal.
time = 2.06, antiderivative size = 1214, normalized size of antiderivative = 46.69, number of
steps used = 86, number of rules used = 17, integrand size = 77, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.221, Rules used = {6820,
12, 2608, 2604, 2404, 2338, 2354, 2438, 2375, 2465, 2439, 2437, 266, 2463, 2441, 2440, 2352}
\begin {gather*} -e \log ^2\left (-x-\sqrt [3]{-3}\right )-2 e \log \left (\frac {\sqrt [3]{3}-x}{\sqrt [3]{-3}+\sqrt [3]{3}}\right ) \log \left (-x-\sqrt [3]{-3}\right )-2 e \log \left (-\frac {(-1)^{2/3} \left ((-1)^{2/3} \sqrt [3]{3}-x\right )}{\sqrt [3]{-3}+\sqrt [3]{3}}\right ) \log \left (-x-\sqrt [3]{-3}\right )+4 e \log \left (\frac {(-1)^{2/3} x}{\sqrt [3]{3}}\right ) \log \left (-x-\sqrt [3]{-3}\right )+2 e \log \left (-\frac {x+e}{\sqrt [3]{-3}-e}\right ) \log \left (-x-\sqrt [3]{-3}\right )+2 e \left (3 e^5-\log \left (-\frac {x^2 (x+e)}{3-x^3}\right )\right ) \log \left (-x-\sqrt [3]{-3}\right )-e \log ^2\left (\sqrt [3]{3}-x\right )-e \log ^2\left ((-1)^{2/3} \sqrt [3]{3}-x\right )-4 e \log ^2(x)-e \log ^2(x+e)-2 e \log \left (\frac {\sqrt [3]{3}-x}{\sqrt [3]{3} \left (1-(-1)^{2/3}\right )}\right ) \log \left ((-1)^{2/3} \sqrt [3]{3}-x\right )+\frac {4}{3} e \log (3) \log (x)-4 e \log (x)+4 e \log \left ((-1)^{2/3} \sqrt [3]{3}-x\right ) \log \left (-\sqrt [3]{-\frac {1}{3}} x\right )-2 e \log \left ((-1)^{2/3} \sqrt [3]{3}-x\right ) \log \left (-\frac {i \left (x+\sqrt [3]{-3}\right )}{3^{5/6}}\right )-2 e \log \left (\sqrt [3]{3}-x\right ) \log \left (\frac {x+\sqrt [3]{-3}}{\sqrt [3]{-3}+\sqrt [3]{3}}\right )+2 e \log \left (\frac {\sqrt [3]{3}-x}{\sqrt [3]{3}+e}\right ) \log (x+e)+2 e \log \left (\frac {x+\sqrt [3]{-3}}{\sqrt [3]{-3}-e}\right ) \log (x+e)+2 e \log \left (\sqrt [3]{3}-x\right ) \log \left (\frac {x+e}{\sqrt [3]{3}+e}\right )+2 e \log \left ((-1)^{2/3} \sqrt [3]{3}-x\right ) \log \left (\frac {x+e}{(-1)^{2/3} \sqrt [3]{3}+e}\right )-2 e \log \left (\sqrt [3]{3}-x\right ) \log \left (-\frac {(-1)^{2/3} \left (\sqrt [3]{-1} x+\sqrt [3]{3}\right )}{\sqrt [3]{3} \left (1-(-1)^{2/3}\right )}\right )+2 e \log (x+e) \log \left (\frac {(-1)^{2/3} \left (\sqrt [3]{-1} x+\sqrt [3]{3}\right )}{(-1)^{2/3} \sqrt [3]{3}+e}\right )-4 e \log (x) \log \left (\frac {x}{e}+1\right )+2 e \log \left (\sqrt [3]{3}-x\right ) \left (3 e^5-\log \left (-\frac {x^2 (x+e)}{3-x^3}\right )\right )+2 e \log \left ((-1)^{2/3} \sqrt [3]{3}-x\right ) \left (3 e^5-\log \left (-\frac {x^2 (x+e)}{3-x^3}\right )\right )-4 e \log (x) \left (3 e^5-\log \left (-\frac {x^2 (x+e)}{3-x^3}\right )\right )-2 e \log (x+e) \left (3 e^5-\log \left (-\frac {x^2 (x+e)}{3-x^3}\right )\right )+4 e \log (x) \log \left (1-\frac {x^3}{3}\right )-2 e \text {Li}_2\left (\frac {\sqrt [3]{3}-x}{\sqrt [3]{-3}+\sqrt [3]{3}}\right )-2 e \text {Li}_2\left (\frac {2 \left (\sqrt [3]{3}-x\right )}{\sqrt [3]{3} \left (3-i \sqrt {3}\right )}\right )+2 e \text {Li}_2\left (\frac {\sqrt [3]{3}-x}{\sqrt [3]{3}+e}\right )-2 e \text {Li}_2\left (\frac {i x+\sqrt [6]{-1} \sqrt [3]{3}}{3^{5/6}}\right )-2 e \text {Li}_2\left (\frac {2 i x+\sqrt [3]{3} \left (i+\sqrt {3}\right )}{\sqrt [3]{3} \left (3 i+\sqrt {3}\right )}\right )-4 e \text {Li}_2\left (\frac {x}{\sqrt [3]{3}}\right )+\frac {4}{3} e \text {Li}_2\left (\frac {x^3}{3}\right )-2 e \text {Li}_2\left (\frac {x+\sqrt [3]{-3}}{\sqrt [3]{-3}+\sqrt [3]{3}}\right )+2 e \text {Li}_2\left (\frac {x+\sqrt [3]{-3}}{\sqrt [3]{-3}-e}\right )+2 e \text {Li}_2\left (-\frac {x+e}{\sqrt [3]{-3}-e}\right )+2 e \text {Li}_2\left (\frac {x+e}{\sqrt [3]{3}+e}\right )+2 e \text {Li}_2\left (\frac {x+e}{(-1)^{2/3} \sqrt [3]{3}+e}\right )+2 e \text {Li}_2\left (\frac {(-1)^{2/3} \left (\sqrt [3]{-1} x+\sqrt [3]{3}\right )}{(-1)^{2/3} \sqrt [3]{3}+e}\right )-2 e \text {Li}_2\left (\frac {\sqrt [3]{3}-(-1)^{2/3} x}{\sqrt [3]{-3}+\sqrt [3]{3}}\right )+4 e \text {Li}_2\left (\sqrt [3]{-\frac {1}{3}} x+1\right )+4 e \text {Li}_2\left (1-\frac {(-1)^{2/3} x}{\sqrt [3]{3}}\right ) \end {gather*}
Warning: Unable to verify antiderivative.
[In]
[Out]
Rule 12
Rule 266
Rule 2338
Rule 2352
Rule 2354
Rule 2375
Rule 2404
Rule 2437
Rule 2438
Rule 2439
Rule 2440
Rule 2441
Rule 2463
Rule 2465
Rule 2604
Rule 2608
Rule 6820
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {2 e \left (6 e+9 x+e x^3\right ) \left (-3 e^5+\log \left (\frac {x^2 (e+x)}{-3+x^3}\right )\right )}{x (e+x) \left (3-x^3\right )} \, dx\\ &=(2 e) \int \frac {\left (6 e+9 x+e x^3\right ) \left (-3 e^5+\log \left (\frac {x^2 (e+x)}{-3+x^3}\right )\right )}{x (e+x) \left (3-x^3\right )} \, dx\\ &=(2 e) \int \left (\frac {2 \left (-3 e^5+\log \left (\frac {x^2 (e+x)}{-3+x^3}\right )\right )}{x}+\frac {-3 e^5+\log \left (\frac {x^2 (e+x)}{-3+x^3}\right )}{e+x}-\frac {3 x^2 \left (-3 e^5+\log \left (\frac {x^2 (e+x)}{-3+x^3}\right )\right )}{-3+x^3}\right ) \, dx\\ &=(2 e) \int \frac {-3 e^5+\log \left (\frac {x^2 (e+x)}{-3+x^3}\right )}{e+x} \, dx+(4 e) \int \frac {-3 e^5+\log \left (\frac {x^2 (e+x)}{-3+x^3}\right )}{x} \, dx-(6 e) \int \frac {x^2 \left (-3 e^5+\log \left (\frac {x^2 (e+x)}{-3+x^3}\right )\right )}{-3+x^3} \, dx\\ &=-4 e \log (x) \left (3 e^5-\log \left (-\frac {x^2 (e+x)}{3-x^3}\right )\right )-2 e \log (e+x) \left (3 e^5-\log \left (-\frac {x^2 (e+x)}{3-x^3}\right )\right )-(2 e) \int \frac {\left (-3+x^3\right ) \left (-\frac {3 x^4 (e+x)}{\left (-3+x^3\right )^2}+\frac {x^2}{-3+x^3}+\frac {2 x (e+x)}{-3+x^3}\right ) \log (e+x)}{x^2 (e+x)} \, dx-(4 e) \int \frac {\left (-3+x^3\right ) \left (-\frac {3 x^4 (e+x)}{\left (-3+x^3\right )^2}+\frac {x^2}{-3+x^3}+\frac {2 x (e+x)}{-3+x^3}\right ) \log (x)}{x^2 (e+x)} \, dx-(6 e) \int \left (-\frac {-3 e^5+\log \left (\frac {x^2 (e+x)}{-3+x^3}\right )}{3 \left (-\sqrt [3]{-3}-x\right )}-\frac {-3 e^5+\log \left (\frac {x^2 (e+x)}{-3+x^3}\right )}{3 \left (\sqrt [3]{3}-x\right )}-\frac {-3 e^5+\log \left (\frac {x^2 (e+x)}{-3+x^3}\right )}{3 \left ((-1)^{2/3} \sqrt [3]{3}-x\right )}\right ) \, dx\\ &=-4 e \log (x) \left (3 e^5-\log \left (-\frac {x^2 (e+x)}{3-x^3}\right )\right )-2 e \log (e+x) \left (3 e^5-\log \left (-\frac {x^2 (e+x)}{3-x^3}\right )\right )-(2 e) \int \left (\frac {2 \log (e+x)}{x}+\frac {\log (e+x)}{e+x}-\frac {3 x^2 \log (e+x)}{-3+x^3}\right ) \, dx+(2 e) \int \frac {-3 e^5+\log \left (\frac {x^2 (e+x)}{-3+x^3}\right )}{-\sqrt [3]{-3}-x} \, dx+(2 e) \int \frac {-3 e^5+\log \left (\frac {x^2 (e+x)}{-3+x^3}\right )}{\sqrt [3]{3}-x} \, dx+(2 e) \int \frac {-3 e^5+\log \left (\frac {x^2 (e+x)}{-3+x^3}\right )}{(-1)^{2/3} \sqrt [3]{3}-x} \, dx-(4 e) \int \left (\frac {2 \log (x)}{x}+\frac {\log (x)}{e+x}-\frac {3 x^2 \log (x)}{-3+x^3}\right ) \, dx\\ &=2 e \log \left (-\sqrt [3]{-3}-x\right ) \left (3 e^5-\log \left (-\frac {x^2 (e+x)}{3-x^3}\right )\right )+2 e \log \left (\sqrt [3]{3}-x\right ) \left (3 e^5-\log \left (-\frac {x^2 (e+x)}{3-x^3}\right )\right )+2 e \log \left ((-1)^{2/3} \sqrt [3]{3}-x\right ) \left (3 e^5-\log \left (-\frac {x^2 (e+x)}{3-x^3}\right )\right )-4 e \log (x) \left (3 e^5-\log \left (-\frac {x^2 (e+x)}{3-x^3}\right )\right )-2 e \log (e+x) \left (3 e^5-\log \left (-\frac {x^2 (e+x)}{3-x^3}\right )\right )+(2 e) \int \frac {\left (-3+x^3\right ) \left (-\frac {3 x^4 (e+x)}{\left (-3+x^3\right )^2}+\frac {x^2}{-3+x^3}+\frac {2 x (e+x)}{-3+x^3}\right ) \log \left (-\sqrt [3]{-3}-x\right )}{x^2 (e+x)} \, dx+(2 e) \int \frac {\left (-3+x^3\right ) \left (-\frac {3 x^4 (e+x)}{\left (-3+x^3\right )^2}+\frac {x^2}{-3+x^3}+\frac {2 x (e+x)}{-3+x^3}\right ) \log \left (\sqrt [3]{3}-x\right )}{x^2 (e+x)} \, dx+(2 e) \int \frac {\left (-3+x^3\right ) \left (-\frac {3 x^4 (e+x)}{\left (-3+x^3\right )^2}+\frac {x^2}{-3+x^3}+\frac {2 x (e+x)}{-3+x^3}\right ) \log \left ((-1)^{2/3} \sqrt [3]{3}-x\right )}{x^2 (e+x)} \, dx-(2 e) \int \frac {\log (e+x)}{e+x} \, dx-(4 e) \int \frac {\log (x)}{e+x} \, dx-(4 e) \int \frac {\log (e+x)}{x} \, dx+(6 e) \int \frac {x^2 \log (e+x)}{-3+x^3} \, dx-(8 e) \int \frac {\log (x)}{x} \, dx+(12 e) \int \frac {x^2 \log (x)}{-3+x^3} \, dx\\ &=-4 e \log (x)-4 e \log ^2(x)-4 e \log (x) \log \left (1+\frac {x}{e}\right )+2 e \log \left (-\sqrt [3]{-3}-x\right ) \left (3 e^5-\log \left (-\frac {x^2 (e+x)}{3-x^3}\right )\right )+2 e \log \left (\sqrt [3]{3}-x\right ) \left (3 e^5-\log \left (-\frac {x^2 (e+x)}{3-x^3}\right )\right )+2 e \log \left ((-1)^{2/3} \sqrt [3]{3}-x\right ) \left (3 e^5-\log \left (-\frac {x^2 (e+x)}{3-x^3}\right )\right )-4 e \log (x) \left (3 e^5-\log \left (-\frac {x^2 (e+x)}{3-x^3}\right )\right )-2 e \log (e+x) \left (3 e^5-\log \left (-\frac {x^2 (e+x)}{3-x^3}\right )\right )+4 e \log (x) \log \left (1-\frac {x^3}{3}\right )+(2 e) \int \left (\frac {2 \log \left (-\sqrt [3]{-3}-x\right )}{x}+\frac {\log \left (-\sqrt [3]{-3}-x\right )}{e+x}-\frac {3 x^2 \log \left (-\sqrt [3]{-3}-x\right )}{-3+x^3}\right ) \, dx+(2 e) \int \left (\frac {2 \log \left (\sqrt [3]{3}-x\right )}{x}+\frac {\log \left (\sqrt [3]{3}-x\right )}{e+x}-\frac {3 x^2 \log \left (\sqrt [3]{3}-x\right )}{-3+x^3}\right ) \, dx+(2 e) \int \left (\frac {2 \log \left ((-1)^{2/3} \sqrt [3]{3}-x\right )}{x}+\frac {\log \left ((-1)^{2/3} \sqrt [3]{3}-x\right )}{e+x}-\frac {3 x^2 \log \left ((-1)^{2/3} \sqrt [3]{3}-x\right )}{-3+x^3}\right ) \, dx-(2 e) \text {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,e+x\right )-(4 e) \int \frac {\log \left (1-\frac {x^3}{3}\right )}{x} \, dx+(6 e) \int \left (-\frac {\log (e+x)}{3 \left (-\sqrt [3]{-3}-x\right )}-\frac {\log (e+x)}{3 \left (\sqrt [3]{3}-x\right )}-\frac {\log (e+x)}{3 \left ((-1)^{2/3} \sqrt [3]{3}-x\right )}\right ) \, dx\\ &=-4 e \log (x)-4 e \log ^2(x)-e \log ^2(e+x)-4 e \log (x) \log \left (1+\frac {x}{e}\right )+2 e \log \left (-\sqrt [3]{-3}-x\right ) \left (3 e^5-\log \left (-\frac {x^2 (e+x)}{3-x^3}\right )\right )+2 e \log \left (\sqrt [3]{3}-x\right ) \left (3 e^5-\log \left (-\frac {x^2 (e+x)}{3-x^3}\right )\right )+2 e \log \left ((-1)^{2/3} \sqrt [3]{3}-x\right ) \left (3 e^5-\log \left (-\frac {x^2 (e+x)}{3-x^3}\right )\right )-4 e \log (x) \left (3 e^5-\log \left (-\frac {x^2 (e+x)}{3-x^3}\right )\right )-2 e \log (e+x) \left (3 e^5-\log \left (-\frac {x^2 (e+x)}{3-x^3}\right )\right )+4 e \log (x) \log \left (1-\frac {x^3}{3}\right )+\frac {4}{3} e \text {Li}_2\left (\frac {x^3}{3}\right )+(2 e) \int \frac {\log \left (-\sqrt [3]{-3}-x\right )}{e+x} \, dx+(2 e) \int \frac {\log \left (\sqrt [3]{3}-x\right )}{e+x} \, dx+(2 e) \int \frac {\log \left ((-1)^{2/3} \sqrt [3]{3}-x\right )}{e+x} \, dx-(2 e) \int \frac {\log (e+x)}{-\sqrt [3]{-3}-x} \, dx-(2 e) \int \frac {\log (e+x)}{\sqrt [3]{3}-x} \, dx-(2 e) \int \frac {\log (e+x)}{(-1)^{2/3} \sqrt [3]{3}-x} \, dx+(4 e) \int \frac {\log \left (-\sqrt [3]{-3}-x\right )}{x} \, dx+(4 e) \int \frac {\log \left (\sqrt [3]{3}-x\right )}{x} \, dx+(4 e) \int \frac {\log \left ((-1)^{2/3} \sqrt [3]{3}-x\right )}{x} \, dx-(6 e) \int \frac {x^2 \log \left (-\sqrt [3]{-3}-x\right )}{-3+x^3} \, dx-(6 e) \int \frac {x^2 \log \left (\sqrt [3]{3}-x\right )}{-3+x^3} \, dx-(6 e) \int \frac {x^2 \log \left ((-1)^{2/3} \sqrt [3]{3}-x\right )}{-3+x^3} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}
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Mathematica [C] Result contains higher order function than in optimal. Order 4 vs. order 3 in
optimal.
time = 0.66, size = 1185, normalized size = 45.58 \begin {gather*} 2 e \left (-\frac {1}{2} \log ^2\left (-\sqrt [3]{-3}-x\right )+\frac {2}{3} \log (3) \log \left (\sqrt [3]{3}-x\right )-\frac {1}{2} \log ^2\left (\sqrt [3]{3}-x\right )-\log \left (-\sqrt [3]{-3}-x\right ) \log \left (\frac {\sqrt [3]{3}-x}{\sqrt [3]{-3}+\sqrt [3]{3}}\right )-\frac {1}{2} \log ^2\left ((-1)^{2/3} \sqrt [3]{3}-x\right )+\log \left (\frac {\sqrt [3]{3}-x}{\sqrt [3]{3}+e}\right ) \log (-e-x)+\log \left (\frac {(-1)^{2/3} \sqrt [3]{3}-x}{(-1)^{2/3} \sqrt [3]{3}+e}\right ) \log (-e-x)-\frac {1}{2} \log ^2(-e-x)-2 \log (-e-x) (-1+\log (-x))+\frac {2}{3} \log (3) \log (x)-2 \log ^2(x)+2 \log \left ((-1)^{2/3} \sqrt [3]{3}-x\right ) \log \left (-\sqrt [3]{-\frac {1}{3}} x\right )+2 \log \left (-\sqrt [3]{-3}-x\right ) \log \left (\frac {(-1)^{2/3} x}{\sqrt [3]{3}}\right )-\log \left ((-1)^{2/3} \sqrt [3]{3}-x\right ) \log \left (-\frac {i \left (\sqrt [3]{-3}+x\right )}{3^{5/6}}\right )-\log \left (\sqrt [3]{3}-x\right ) \log \left (\frac {\sqrt [3]{-3}+x}{\sqrt [3]{-3}+\sqrt [3]{3}}\right )+\log (-e-x) \log \left (\frac {\sqrt [3]{-3}+x}{\sqrt [3]{-3}-e}\right )-2 \log (x) (-1+\log (e+x))+\log \left (\sqrt [3]{3}+e\right ) \log (e+x)+\log \left (-\sqrt [3]{-3}-x\right ) \log \left (-\frac {e+x}{\sqrt [3]{-3}-e}\right )+\log \left ((-1)^{2/3} \sqrt [3]{3}-x\right ) \log \left (\frac {e+x}{(-1)^{2/3} \sqrt [3]{3}+e}\right )+2 \log (x) \log \left (\frac {1}{3} \left (3-(-3)^{2/3} x\right )\right )-\log \left (-\sqrt [3]{-3}-x\right ) \log \left (\frac {\sqrt [3]{-3}+(-1)^{2/3} x}{\sqrt [3]{-3}+\sqrt [3]{3}}\right )+2 \log (x) \log \left (1+\sqrt [3]{-\frac {1}{3}} x\right )-\log \left (\sqrt [3]{3}-x\right ) \log \left (\frac {i+\sqrt {3}+\frac {2 i x}{\sqrt [3]{3}}}{3 i+\sqrt {3}}\right )-\log \left ((-1)^{2/3} \sqrt [3]{3}-x\right ) \log \left (-\frac {2 i \left (-3+3^{2/3} x\right )}{3 \left (3 i+\sqrt {3}\right )}\right )+\log \left (-\sqrt [3]{-3}-x\right ) \left (3 e^5-\log \left (\frac {x^2 (e+x)}{-3+x^3}\right )\right )+\log \left (\sqrt [3]{3}-x\right ) \left (3 e^5-\log \left (\frac {x^2 (e+x)}{-3+x^3}\right )\right )+\log \left ((-1)^{2/3} \sqrt [3]{3}-x\right ) \left (3 e^5-\log \left (\frac {x^2 (e+x)}{-3+x^3}\right )\right )+\log (-e-x) \left (-3 e^5+\log \left (\frac {x^2 (e+x)}{-3+x^3}\right )\right )+2 \log (x) \left (-3 e^5+\log \left (\frac {x^2 (e+x)}{-3+x^3}\right )\right )-\text {PolyLog}\left (2,\frac {\sqrt [3]{3}-x}{\sqrt [3]{-3}+\sqrt [3]{3}}\right )+\text {PolyLog}\left (2,\frac {(-1)^{2/3} \sqrt [3]{3}-x}{(-1)^{2/3} \sqrt [3]{3}+e}\right )+2 \text {PolyLog}\left (2,-\sqrt [3]{-\frac {1}{3}} x\right )-2 \text {PolyLog}\left (2,\frac {x}{\sqrt [3]{3}}\right )+2 \text {PolyLog}\left (2,\frac {(-1)^{2/3} x}{\sqrt [3]{3}}\right )-2 \text {PolyLog}\left (2,-\frac {x}{e}\right )-\text {PolyLog}\left (2,\frac {\sqrt [3]{-3}+x}{\sqrt [3]{-3}+\sqrt [3]{3}}\right )+\text {PolyLog}\left (2,\frac {\sqrt [3]{-3}+x}{\sqrt [3]{-3}-e}\right )+\text {PolyLog}\left (2,-\frac {e+x}{\sqrt [3]{-3}-e}\right )-2 \text {PolyLog}\left (2,\frac {e+x}{e}\right )+\text {PolyLog}\left (2,\frac {e+x}{(-1)^{2/3} \sqrt [3]{3}+e}\right )+2 \text {PolyLog}\left (2,\frac {1}{3} \left (3-(-3)^{2/3} x\right )\right )-\text {PolyLog}\left (2,\frac {\sqrt [3]{3}-(-1)^{2/3} x}{\sqrt [3]{-3}+\sqrt [3]{3}}\right )-\text {PolyLog}\left (2,\frac {\sqrt [3]{-3}+(-1)^{2/3} x}{\sqrt [3]{-3}+\sqrt [3]{3}}\right )+2 \text {PolyLog}\left (2,1+\sqrt [3]{-\frac {1}{3}} x\right )-2 \text {PolyLog}\left (2,1-\frac {x}{\sqrt [3]{3}}\right )-\text {PolyLog}\left (2,\frac {i+\sqrt {3}+\frac {2 i x}{\sqrt [3]{3}}}{3 i+\sqrt {3}}\right )-\text {PolyLog}\left (2,-\frac {2 i \left (-3+3^{2/3} x\right )}{3 \left (3 i+\sqrt {3}\right )}\right )\right ) \end {gather*}
Warning: Unable to verify antiderivative.
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Maple [C] Result contains higher order function than in optimal. Order 9 vs. order
3.
time = 0.60, size = 6712, normalized size = 258.15
method | result | size |
norman | \(-6 \,{\mathrm e} \,{\mathrm e}^{5} \ln \left (\frac {x^{2} {\mathrm e}+x^{3}}{x^{3}-3}\right )+{\mathrm e} \ln \left (\frac {x^{2} {\mathrm e}+x^{3}}{x^{3}-3}\right )^{2}\) | \(51\) |
risch | \(\text {Expression too large to display}\) | \(1571\) |
default | \(\text {Expression too large to display}\) | \(6712\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 513 vs.
\(2 (27) = 54\).
time = 2.91, size = 513, normalized size = 19.73 \begin {gather*} e \log \left (x^{3} - 3\right )^{2} + e \log \left (x + e\right )^{2} + 4 \, e \log \left (x + e\right ) \log \left (x\right ) + 4 \, e \log \left (x\right )^{2} - 2 \, {\left (6 \, e^{\left (-1\right )} \log \left (x\right ) - \frac {6 \cdot 3^{\frac {1}{6}} {\left (3^{\frac {1}{3}} e + 3^{\frac {2}{3}}\right )} \arctan \left (\frac {1}{3} \cdot 3^{\frac {1}{6}} {\left (2 \, x + 3^{\frac {1}{3}}\right )}\right )}{3^{\frac {2}{3}} e^{3} + 3 \cdot 3^{\frac {2}{3}}} - \frac {{\left (2 \cdot 3^{\frac {2}{3}} e^{2} - 3 \cdot 3^{\frac {1}{3}} + 3 \, e\right )} \log \left (x^{2} + 3^{\frac {1}{3}} x + 3^{\frac {2}{3}}\right )}{3^{\frac {2}{3}} e^{3} + 3 \cdot 3^{\frac {2}{3}}} - \frac {2 \, {\left (3^{\frac {2}{3}} e^{2} + 3 \cdot 3^{\frac {1}{3}} - 3 \, e\right )} \log \left (x - 3^{\frac {1}{3}}\right )}{3^{\frac {2}{3}} e^{3} + 3 \cdot 3^{\frac {2}{3}}} - \frac {18 \, \log \left (x + e\right )}{e^{4} + 3 \, e}\right )} e^{7} + {\left (\frac {6 \cdot 3^{\frac {1}{6}} {\left (3^{\frac {1}{3}} e + 3^{\frac {2}{3}}\right )} \arctan \left (\frac {1}{3} \cdot 3^{\frac {1}{6}} {\left (2 \, x + 3^{\frac {1}{3}}\right )}\right )}{3^{\frac {2}{3}} e^{3} + 3 \cdot 3^{\frac {2}{3}}} + \frac {{\left (2 \cdot 3^{\frac {2}{3}} e^{2} - 3 \cdot 3^{\frac {1}{3}} + 3 \, e\right )} \log \left (x^{2} + 3^{\frac {1}{3}} x + 3^{\frac {2}{3}}\right )}{3^{\frac {2}{3}} e^{3} + 3 \cdot 3^{\frac {2}{3}}} + \frac {2 \, {\left (3^{\frac {2}{3}} e^{2} + 3 \cdot 3^{\frac {1}{3}} - 3 \, e\right )} \log \left (x - 3^{\frac {1}{3}}\right )}{3^{\frac {2}{3}} e^{3} + 3 \cdot 3^{\frac {2}{3}}} - \frac {6 \, e^{2} \log \left (x + e\right )}{e^{3} + 3}\right )} e^{7} - 9 \, {\left (\frac {2 \cdot 3^{\frac {1}{6}} {\left (3^{\frac {2}{3}} e + 3^{\frac {1}{3}} e^{2}\right )} \arctan \left (\frac {1}{3} \cdot 3^{\frac {1}{6}} {\left (2 \, x + 3^{\frac {1}{3}}\right )}\right )}{3^{\frac {2}{3}} e^{3} + 3 \cdot 3^{\frac {2}{3}}} - \frac {{\left (3^{\frac {1}{3}} e + 2 \cdot 3^{\frac {2}{3}} - e^{2}\right )} \log \left (x^{2} + 3^{\frac {1}{3}} x + 3^{\frac {2}{3}}\right )}{3^{\frac {2}{3}} e^{3} + 3 \cdot 3^{\frac {2}{3}}} + \frac {2 \, {\left (3^{\frac {1}{3}} e - 3^{\frac {2}{3}} - e^{2}\right )} \log \left (x - 3^{\frac {1}{3}}\right )}{3^{\frac {2}{3}} e^{3} + 3 \cdot 3^{\frac {2}{3}}} + \frac {6 \, \log \left (x + e\right )}{e^{3} + 3}\right )} e^{6} - 2 \, {\left (e \log \left (x + e\right ) + 2 \, e \log \left (x\right )\right )} \log \left (x^{3} - 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.47, size = 48, normalized size = 1.85 \begin {gather*} e \log \left (\frac {x^{3} + x^{2} e}{x^{3} - 3}\right )^{2} - 6 \, e^{6} \log \left (\frac {x^{3} + x^{2} e}{x^{3} - 3}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 53 vs.
\(2 (22) = 44\).
time = 1.29, size = 53, normalized size = 2.04 \begin {gather*} - 12 e^{6} \log {\left (x \right )} + e \log {\left (\frac {x^{3} + e x^{2}}{x^{3} - 3} \right )}^{2} - 6 e^{6} \log {\left (x + e \right )} + 6 e^{6} \log {\left (x^{3} - 3 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.54, size = 50, normalized size = 1.92 \begin {gather*} \mathrm {e}\,{\ln \left (\frac {x^3+\mathrm {e}\,x^2}{x^3-3}\right )}^2+6\,{\mathrm {e}}^6\,\ln \left (x^3-3\right )-6\,{\mathrm {e}}^6\,\ln \left (x+\mathrm {e}\right )-12\,{\mathrm {e}}^6\,\ln \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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