Optimal. Leaf size=28 \[ 3-\left (-x+e^5 (4+x) \log \left (\frac {5 e^x \log (x)}{x}\right )\right )^2 \]
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Rubi [F] time = 2.53, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {-2 x^2 \log (x) \log \left (\frac {5 e^x \log (x)}{x}\right )+e^{10} \log ^2\left (\frac {5 e^x \log (x)}{x}\right ) \left (-32-16 x-2 x^2+\left (32-16 x-14 x^2-2 x^3\right ) \log (x)+\left (-8 x-2 x^2\right ) \log (x) \log \left (\frac {5 e^x \log (x)}{x}\right )\right )+e^5 \log \left (\frac {5 e^x \log (x)}{x}\right ) \left (8 x+2 x^2+\left (-8 x+6 x^2+2 x^3\right ) \log (x)+\left (8 x+4 x^2\right ) \log (x) \log \left (\frac {5 e^x \log (x)}{x}\right )\right )}{x \log (x) \log \left (\frac {5 e^x \log (x)}{x}\right )} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {2 \left (x-e^5 (4+x) \log \left (\frac {5 e^x \log (x)}{x}\right )\right ) \left (e^5 (4+x)+\log (x) \left (-x+e^5 \left (-4+3 x+x^2\right )+e^5 x \log \left (\frac {5 e^x \log (x)}{x}\right )\right )\right )}{x \log (x)} \, dx\\ &=2 \int \frac {\left (x-e^5 (4+x) \log \left (\frac {5 e^x \log (x)}{x}\right )\right ) \left (e^5 (4+x)+\log (x) \left (-x+e^5 \left (-4+3 x+x^2\right )+e^5 x \log \left (\frac {5 e^x \log (x)}{x}\right )\right )\right )}{x \log (x)} \, dx\\ &=2 \int \left (\frac {4 e^5+e^5 x-4 e^5 \log (x)-\left (1-3 e^5\right ) x \log (x)+e^5 x^2 \log (x)}{\log (x)}+\frac {e^5 \left (-16 e^5-8 e^5 x-e^5 x^2+16 e^5 \log (x)+4 \left (1-2 e^5\right ) x \log (x)+2 \left (1-\frac {7 e^5}{2}\right ) x^2 \log (x)-e^5 x^3 \log (x)\right ) \log \left (\frac {5 e^x \log (x)}{x}\right )}{x \log (x)}-e^{10} (4+x) \log ^2\left (\frac {5 e^x \log (x)}{x}\right )\right ) \, dx\\ &=2 \int \frac {4 e^5+e^5 x-4 e^5 \log (x)-\left (1-3 e^5\right ) x \log (x)+e^5 x^2 \log (x)}{\log (x)} \, dx+\left (2 e^5\right ) \int \frac {\left (-16 e^5-8 e^5 x-e^5 x^2+16 e^5 \log (x)+4 \left (1-2 e^5\right ) x \log (x)+2 \left (1-\frac {7 e^5}{2}\right ) x^2 \log (x)-e^5 x^3 \log (x)\right ) \log \left (\frac {5 e^x \log (x)}{x}\right )}{x \log (x)} \, dx-\left (2 e^{10}\right ) \int (4+x) \log ^2\left (\frac {5 e^x \log (x)}{x}\right ) \, dx\\ &=2 \int \left (-x+e^5 \left (-4+3 x+x^2\right )+\frac {e^5 (4+x)}{\log (x)}\right ) \, dx+\left (2 e^5\right ) \int \frac {\left (-e^5 (4+x)^2-\left (-2 x (2+x)+e^5 (-1+x) (4+x)^2\right ) \log (x)\right ) \log \left (\frac {5 e^x \log (x)}{x}\right )}{x \log (x)} \, dx-\left (2 e^{10}\right ) \int \left (4 \log ^2\left (\frac {5 e^x \log (x)}{x}\right )+x \log ^2\left (\frac {5 e^x \log (x)}{x}\right )\right ) \, dx\\ &=-x^2+\left (2 e^5\right ) \int \left (-4+3 x+x^2\right ) \, dx+\left (2 e^5\right ) \int \frac {4+x}{\log (x)} \, dx+\left (2 e^5\right ) \int \left (4 \left (1-2 e^5\right ) \log \left (\frac {5 e^x \log (x)}{x}\right )+\frac {16 e^5 \log \left (\frac {5 e^x \log (x)}{x}\right )}{x}+2 \left (1-\frac {7 e^5}{2}\right ) x \log \left (\frac {5 e^x \log (x)}{x}\right )-e^5 x^2 \log \left (\frac {5 e^x \log (x)}{x}\right )-\frac {8 e^5 \log \left (\frac {5 e^x \log (x)}{x}\right )}{\log (x)}-\frac {16 e^5 \log \left (\frac {5 e^x \log (x)}{x}\right )}{x \log (x)}-\frac {e^5 x \log \left (\frac {5 e^x \log (x)}{x}\right )}{\log (x)}\right ) \, dx-\left (2 e^{10}\right ) \int x \log ^2\left (\frac {5 e^x \log (x)}{x}\right ) \, dx-\left (8 e^{10}\right ) \int \log ^2\left (\frac {5 e^x \log (x)}{x}\right ) \, dx\\ &=-8 e^5 x-x^2+3 e^5 x^2+\frac {2 e^5 x^3}{3}+\left (2 e^5\right ) \int \left (\frac {4}{\log (x)}+\frac {x}{\log (x)}\right ) \, dx-\left (2 e^{10}\right ) \int x^2 \log \left (\frac {5 e^x \log (x)}{x}\right ) \, dx-\left (2 e^{10}\right ) \int \frac {x \log \left (\frac {5 e^x \log (x)}{x}\right )}{\log (x)} \, dx-\left (2 e^{10}\right ) \int x \log ^2\left (\frac {5 e^x \log (x)}{x}\right ) \, dx-\left (8 e^{10}\right ) \int \log ^2\left (\frac {5 e^x \log (x)}{x}\right ) \, dx-\left (16 e^{10}\right ) \int \frac {\log \left (\frac {5 e^x \log (x)}{x}\right )}{\log (x)} \, dx+\left (32 e^{10}\right ) \int \frac {\log \left (\frac {5 e^x \log (x)}{x}\right )}{x} \, dx-\left (32 e^{10}\right ) \int \frac {\log \left (\frac {5 e^x \log (x)}{x}\right )}{x \log (x)} \, dx+\left (2 e^5 \left (2-7 e^5\right )\right ) \int x \log \left (\frac {5 e^x \log (x)}{x}\right ) \, dx+\left (8 e^5 \left (1-2 e^5\right )\right ) \int \log \left (\frac {5 e^x \log (x)}{x}\right ) \, dx\\ &=-8 e^5 x-x^2+3 e^5 x^2+\frac {2 e^5 x^3}{3}+8 e^5 \left (1-2 e^5\right ) x \log \left (\frac {5 e^x \log (x)}{x}\right )+e^5 \left (2-7 e^5\right ) x^2 \log \left (\frac {5 e^x \log (x)}{x}\right )-\frac {2}{3} e^{10} x^3 \log \left (\frac {5 e^x \log (x)}{x}\right )-16 e^{10} \log \left (\frac {5 e^x \log (x)}{x}\right ) \text {li}(x)+\left (2 e^5\right ) \int \frac {x}{\log (x)} \, dx+\left (8 e^5\right ) \int \frac {1}{\log (x)} \, dx+\left (2 e^{10}\right ) \int \frac {x^2 (1+(-1+x) \log (x))}{3 \log (x)} \, dx-\left (2 e^{10}\right ) \int \frac {x \log \left (\frac {5 e^x \log (x)}{x}\right )}{\log (x)} \, dx-\left (2 e^{10}\right ) \int x \log ^2\left (\frac {5 e^x \log (x)}{x}\right ) \, dx-\left (8 e^{10}\right ) \int \log ^2\left (\frac {5 e^x \log (x)}{x}\right ) \, dx+\left (16 e^{10}\right ) \int \frac {(1+(-1+x) \log (x)) \text {li}(x)}{x \log (x)} \, dx+\left (32 e^{10}\right ) \int \frac {\log \left (\frac {5 e^x \log (x)}{x}\right )}{x} \, dx-\left (32 e^{10}\right ) \int \frac {\log \left (\frac {5 e^x \log (x)}{x}\right )}{x \log (x)} \, dx-\left (2 e^5 \left (2-7 e^5\right )\right ) \int \frac {x (1+(-1+x) \log (x))}{2 \log (x)} \, dx-\left (8 e^5 \left (1-2 e^5\right )\right ) \int \left (-1+x+\frac {1}{\log (x)}\right ) \, dx\\ &=-8 e^5 x+8 e^5 \left (1-2 e^5\right ) x-x^2+3 e^5 x^2-4 e^5 \left (1-2 e^5\right ) x^2+\frac {2 e^5 x^3}{3}+8 e^5 \left (1-2 e^5\right ) x \log \left (\frac {5 e^x \log (x)}{x}\right )+e^5 \left (2-7 e^5\right ) x^2 \log \left (\frac {5 e^x \log (x)}{x}\right )-\frac {2}{3} e^{10} x^3 \log \left (\frac {5 e^x \log (x)}{x}\right )+8 e^5 \text {li}(x)-16 e^{10} \log \left (\frac {5 e^x \log (x)}{x}\right ) \text {li}(x)+\left (2 e^5\right ) \operatorname {Subst}\left (\int \frac {e^{2 x}}{x} \, dx,x,\log (x)\right )+\frac {1}{3} \left (2 e^{10}\right ) \int \frac {x^2 (1+(-1+x) \log (x))}{\log (x)} \, dx-\left (2 e^{10}\right ) \int \frac {x \log \left (\frac {5 e^x \log (x)}{x}\right )}{\log (x)} \, dx-\left (2 e^{10}\right ) \int x \log ^2\left (\frac {5 e^x \log (x)}{x}\right ) \, dx-\left (8 e^{10}\right ) \int \log ^2\left (\frac {5 e^x \log (x)}{x}\right ) \, dx+\left (16 e^{10}\right ) \int \left (\text {li}(x)-\frac {\text {li}(x)}{x}+\frac {\text {li}(x)}{x \log (x)}\right ) \, dx+\left (32 e^{10}\right ) \int \frac {\log \left (\frac {5 e^x \log (x)}{x}\right )}{x} \, dx-\left (32 e^{10}\right ) \int \frac {\log \left (\frac {5 e^x \log (x)}{x}\right )}{x \log (x)} \, dx-\left (e^5 \left (2-7 e^5\right )\right ) \int \frac {x (1+(-1+x) \log (x))}{\log (x)} \, dx-\left (8 e^5 \left (1-2 e^5\right )\right ) \int \frac {1}{\log (x)} \, dx\\ &=-8 e^5 x+8 e^5 \left (1-2 e^5\right ) x-x^2+3 e^5 x^2-4 e^5 \left (1-2 e^5\right ) x^2+\frac {2 e^5 x^3}{3}+2 e^5 \text {Ei}(2 \log (x))+8 e^5 \left (1-2 e^5\right ) x \log \left (\frac {5 e^x \log (x)}{x}\right )+e^5 \left (2-7 e^5\right ) x^2 \log \left (\frac {5 e^x \log (x)}{x}\right )-\frac {2}{3} e^{10} x^3 \log \left (\frac {5 e^x \log (x)}{x}\right )+8 e^5 \text {li}(x)-8 e^5 \left (1-2 e^5\right ) \text {li}(x)-16 e^{10} \log \left (\frac {5 e^x \log (x)}{x}\right ) \text {li}(x)+\frac {1}{3} \left (2 e^{10}\right ) \int \left ((-1+x) x^2+\frac {x^2}{\log (x)}\right ) \, dx-\left (2 e^{10}\right ) \int \frac {x \log \left (\frac {5 e^x \log (x)}{x}\right )}{\log (x)} \, dx-\left (2 e^{10}\right ) \int x \log ^2\left (\frac {5 e^x \log (x)}{x}\right ) \, dx-\left (8 e^{10}\right ) \int \log ^2\left (\frac {5 e^x \log (x)}{x}\right ) \, dx+\left (16 e^{10}\right ) \int \text {li}(x) \, dx-\left (16 e^{10}\right ) \int \frac {\text {li}(x)}{x} \, dx+\left (16 e^{10}\right ) \int \frac {\text {li}(x)}{x \log (x)} \, dx+\left (32 e^{10}\right ) \int \frac {\log \left (\frac {5 e^x \log (x)}{x}\right )}{x} \, dx-\left (32 e^{10}\right ) \int \frac {\log \left (\frac {5 e^x \log (x)}{x}\right )}{x \log (x)} \, dx-\left (e^5 \left (2-7 e^5\right )\right ) \int x \left (-1+x+\frac {1}{\log (x)}\right ) \, dx\\ &=-8 e^5 x+16 e^{10} x+8 e^5 \left (1-2 e^5\right ) x-x^2+3 e^5 x^2-4 e^5 \left (1-2 e^5\right ) x^2+\frac {2 e^5 x^3}{3}+2 e^5 \text {Ei}(2 \log (x))-16 e^{10} \text {Ei}(2 \log (x))+8 e^5 \left (1-2 e^5\right ) x \log \left (\frac {5 e^x \log (x)}{x}\right )+e^5 \left (2-7 e^5\right ) x^2 \log \left (\frac {5 e^x \log (x)}{x}\right )-\frac {2}{3} e^{10} x^3 \log \left (\frac {5 e^x \log (x)}{x}\right )+8 e^5 \text {li}(x)-8 e^5 \left (1-2 e^5\right ) \text {li}(x)+16 e^{10} x \text {li}(x)-16 e^{10} \log (x) \text {li}(x)-16 e^{10} \log \left (\frac {5 e^x \log (x)}{x}\right ) \text {li}(x)+\frac {1}{3} \left (2 e^{10}\right ) \int (-1+x) x^2 \, dx+\frac {1}{3} \left (2 e^{10}\right ) \int \frac {x^2}{\log (x)} \, dx-\left (2 e^{10}\right ) \int \frac {x \log \left (\frac {5 e^x \log (x)}{x}\right )}{\log (x)} \, dx-\left (2 e^{10}\right ) \int x \log ^2\left (\frac {5 e^x \log (x)}{x}\right ) \, dx-\left (8 e^{10}\right ) \int \log ^2\left (\frac {5 e^x \log (x)}{x}\right ) \, dx+\left (16 e^{10}\right ) \int \frac {\text {li}(x)}{x \log (x)} \, dx+\left (32 e^{10}\right ) \int \frac {\log \left (\frac {5 e^x \log (x)}{x}\right )}{x} \, dx-\left (32 e^{10}\right ) \int \frac {\log \left (\frac {5 e^x \log (x)}{x}\right )}{x \log (x)} \, dx-\left (e^5 \left (2-7 e^5\right )\right ) \int \left ((-1+x) x+\frac {x}{\log (x)}\right ) \, dx\\ &=-8 e^5 x+16 e^{10} x+8 e^5 \left (1-2 e^5\right ) x-x^2+3 e^5 x^2-4 e^5 \left (1-2 e^5\right ) x^2+\frac {2 e^5 x^3}{3}+2 e^5 \text {Ei}(2 \log (x))-16 e^{10} \text {Ei}(2 \log (x))+8 e^5 \left (1-2 e^5\right ) x \log \left (\frac {5 e^x \log (x)}{x}\right )+e^5 \left (2-7 e^5\right ) x^2 \log \left (\frac {5 e^x \log (x)}{x}\right )-\frac {2}{3} e^{10} x^3 \log \left (\frac {5 e^x \log (x)}{x}\right )+8 e^5 \text {li}(x)-8 e^5 \left (1-2 e^5\right ) \text {li}(x)+16 e^{10} x \text {li}(x)-16 e^{10} \log (x) \text {li}(x)-16 e^{10} \log \left (\frac {5 e^x \log (x)}{x}\right ) \text {li}(x)+\frac {1}{3} \left (2 e^{10}\right ) \int \left (-x^2+x^3\right ) \, dx+\frac {1}{3} \left (2 e^{10}\right ) \operatorname {Subst}\left (\int \frac {e^{3 x}}{x} \, dx,x,\log (x)\right )-\left (2 e^{10}\right ) \int \frac {x \log \left (\frac {5 e^x \log (x)}{x}\right )}{\log (x)} \, dx-\left (2 e^{10}\right ) \int x \log ^2\left (\frac {5 e^x \log (x)}{x}\right ) \, dx-\left (8 e^{10}\right ) \int \log ^2\left (\frac {5 e^x \log (x)}{x}\right ) \, dx+\left (16 e^{10}\right ) \int \frac {\text {li}(x)}{x \log (x)} \, dx+\left (32 e^{10}\right ) \int \frac {\log \left (\frac {5 e^x \log (x)}{x}\right )}{x} \, dx-\left (32 e^{10}\right ) \int \frac {\log \left (\frac {5 e^x \log (x)}{x}\right )}{x \log (x)} \, dx-\left (e^5 \left (2-7 e^5\right )\right ) \int (-1+x) x \, dx-\left (e^5 \left (2-7 e^5\right )\right ) \int \frac {x}{\log (x)} \, dx\\ &=-8 e^5 x+16 e^{10} x+8 e^5 \left (1-2 e^5\right ) x-x^2+3 e^5 x^2-4 e^5 \left (1-2 e^5\right ) x^2+\frac {2 e^5 x^3}{3}-\frac {2 e^{10} x^3}{9}+\frac {e^{10} x^4}{6}+2 e^5 \text {Ei}(2 \log (x))-16 e^{10} \text {Ei}(2 \log (x))+\frac {2}{3} e^{10} \text {Ei}(3 \log (x))+8 e^5 \left (1-2 e^5\right ) x \log \left (\frac {5 e^x \log (x)}{x}\right )+e^5 \left (2-7 e^5\right ) x^2 \log \left (\frac {5 e^x \log (x)}{x}\right )-\frac {2}{3} e^{10} x^3 \log \left (\frac {5 e^x \log (x)}{x}\right )+8 e^5 \text {li}(x)-8 e^5 \left (1-2 e^5\right ) \text {li}(x)+16 e^{10} x \text {li}(x)-16 e^{10} \log (x) \text {li}(x)-16 e^{10} \log \left (\frac {5 e^x \log (x)}{x}\right ) \text {li}(x)-\left (2 e^{10}\right ) \int \frac {x \log \left (\frac {5 e^x \log (x)}{x}\right )}{\log (x)} \, dx-\left (2 e^{10}\right ) \int x \log ^2\left (\frac {5 e^x \log (x)}{x}\right ) \, dx-\left (8 e^{10}\right ) \int \log ^2\left (\frac {5 e^x \log (x)}{x}\right ) \, dx+\left (16 e^{10}\right ) \int \frac {\text {li}(x)}{x \log (x)} \, dx+\left (32 e^{10}\right ) \int \frac {\log \left (\frac {5 e^x \log (x)}{x}\right )}{x} \, dx-\left (32 e^{10}\right ) \int \frac {\log \left (\frac {5 e^x \log (x)}{x}\right )}{x \log (x)} \, dx-\left (e^5 \left (2-7 e^5\right )\right ) \int \left (-x+x^2\right ) \, dx-\left (e^5 \left (2-7 e^5\right )\right ) \operatorname {Subst}\left (\int \frac {e^{2 x}}{x} \, dx,x,\log (x)\right )\\ &=-8 e^5 x+16 e^{10} x+8 e^5 \left (1-2 e^5\right ) x-x^2+3 e^5 x^2+\frac {1}{2} e^5 \left (2-7 e^5\right ) x^2-4 e^5 \left (1-2 e^5\right ) x^2+\frac {2 e^5 x^3}{3}-\frac {2 e^{10} x^3}{9}-\frac {1}{3} e^5 \left (2-7 e^5\right ) x^3+\frac {e^{10} x^4}{6}+2 e^5 \text {Ei}(2 \log (x))-16 e^{10} \text {Ei}(2 \log (x))-e^5 \left (2-7 e^5\right ) \text {Ei}(2 \log (x))+\frac {2}{3} e^{10} \text {Ei}(3 \log (x))+8 e^5 \left (1-2 e^5\right ) x \log \left (\frac {5 e^x \log (x)}{x}\right )+e^5 \left (2-7 e^5\right ) x^2 \log \left (\frac {5 e^x \log (x)}{x}\right )-\frac {2}{3} e^{10} x^3 \log \left (\frac {5 e^x \log (x)}{x}\right )+8 e^5 \text {li}(x)-8 e^5 \left (1-2 e^5\right ) \text {li}(x)+16 e^{10} x \text {li}(x)-16 e^{10} \log (x) \text {li}(x)-16 e^{10} \log \left (\frac {5 e^x \log (x)}{x}\right ) \text {li}(x)-\left (2 e^{10}\right ) \int \frac {x \log \left (\frac {5 e^x \log (x)}{x}\right )}{\log (x)} \, dx-\left (2 e^{10}\right ) \int x \log ^2\left (\frac {5 e^x \log (x)}{x}\right ) \, dx-\left (8 e^{10}\right ) \int \log ^2\left (\frac {5 e^x \log (x)}{x}\right ) \, dx+\left (16 e^{10}\right ) \int \frac {\text {li}(x)}{x \log (x)} \, dx+\left (32 e^{10}\right ) \int \frac {\log \left (\frac {5 e^x \log (x)}{x}\right )}{x} \, dx-\left (32 e^{10}\right ) \int \frac {\log \left (\frac {5 e^x \log (x)}{x}\right )}{x \log (x)} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [B] time = 0.45, size = 180, normalized size = 6.43 \begin {gather*} -x^2+16 e^{10} x^2-16 e^{10} \log ^2\left (\frac {\log (x)}{x}\right )-32 e^{10} \log (x) \left (x+\log \left (\frac {\log (x)}{x}\right )-\log \left (\frac {5 e^x \log (x)}{x}\right )\right )+32 e^{10} \log (\log (x)) \left (x+\log \left (\frac {\log (x)}{x}\right )-\log \left (\frac {5 e^x \log (x)}{x}\right )\right )+8 e^5 x \log \left (\frac {5 e^x \log (x)}{x}\right )-32 e^{10} x \log \left (\frac {5 e^x \log (x)}{x}\right )+2 e^5 x^2 \log \left (\frac {5 e^x \log (x)}{x}\right )-8 e^{10} x \log ^2\left (\frac {5 e^x \log (x)}{x}\right )-e^{10} x^2 \log ^2\left (\frac {5 e^x \log (x)}{x}\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.73, size = 51, normalized size = 1.82 \begin {gather*} -{\left (x^{2} + 8 \, x + 16\right )} e^{10} \log \left (\frac {5 \, e^{x} \log \relax (x)}{x}\right )^{2} + 2 \, {\left (x^{2} + 4 \, x\right )} e^{5} \log \left (\frac {5 \, e^{x} \log \relax (x)}{x}\right ) - x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.38, size = 338, normalized size = 12.07 \begin {gather*} -x^{4} e^{10} - 2 \, x^{3} e^{10} \log \relax (5) - x^{2} e^{10} \log \relax (5)^{2} + 2 \, x^{3} e^{10} \log \relax (x) + 2 \, x^{2} e^{10} \log \relax (5) \log \relax (x) - x^{2} e^{10} \log \relax (x)^{2} - 2 \, x^{3} e^{10} \log \left (\log \relax (x)\right ) - 2 \, x^{2} e^{10} \log \relax (5) \log \left (\log \relax (x)\right ) + 2 \, x^{2} e^{10} \log \relax (x) \log \left (\log \relax (x)\right ) - x^{2} e^{10} \log \left (\log \relax (x)\right )^{2} - 8 \, x^{3} e^{10} + 2 \, x^{3} e^{5} - 16 \, x^{2} e^{10} \log \relax (5) + 2 \, x^{2} e^{5} \log \relax (5) - 8 \, x e^{10} \log \relax (5)^{2} + 16 \, x^{2} e^{10} \log \relax (x) - 2 \, x^{2} e^{5} \log \relax (x) + 16 \, x e^{10} \log \relax (5) \log \relax (x) - 8 \, x e^{10} \log \relax (x)^{2} - 16 \, x^{2} e^{10} \log \left (\log \relax (x)\right ) + 2 \, x^{2} e^{5} \log \left (\log \relax (x)\right ) - 16 \, x e^{10} \log \relax (5) \log \left (\log \relax (x)\right ) + 16 \, x e^{10} \log \relax (x) \log \left (\log \relax (x)\right ) - 8 \, x e^{10} \log \left (\log \relax (x)\right )^{2} - 16 \, x^{2} e^{10} + 8 \, x^{2} e^{5} - 32 \, x e^{10} \log \relax (5) + 8 \, x e^{5} \log \relax (5) + 32 \, x e^{10} \log \relax (x) - 8 \, x e^{5} \log \relax (x) + 32 \, e^{10} \log \relax (5) \log \relax (x) - 16 \, e^{10} \log \relax (x)^{2} - 32 \, x e^{10} \log \left (\log \relax (x)\right ) + 8 \, x e^{5} \log \left (\log \relax (x)\right ) - 32 \, e^{10} \log \relax (5) \log \left (\log \relax (x)\right ) + 32 \, e^{10} \log \relax (x) \log \left (\log \relax (x)\right ) - 16 \, e^{10} \log \left (\log \relax (x)\right )^{2} - x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [C] time = 1.56, size = 5540, normalized size = 197.86
method | result | size |
risch | \(\text {Expression too large to display}\) | \(5540\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} -x^{4} e^{10} - \frac {2}{3} \, {\left (3 \, {\left (\log \relax (5) + 4\right )} e^{10} - 2 \, e^{5}\right )} x^{3} + \frac {2}{3} \, x^{3} e^{5} - {\left ({\left (\log \relax (5)^{2} + 16 \, \log \relax (5) + 16\right )} e^{10} - {\left (2 \, \log \relax (5) + 5\right )} e^{5}\right )} x^{2} + 3 \, x^{2} e^{5} - {\left (x^{2} e^{10} + 8 \, x e^{10} + 16 \, e^{10}\right )} \log \relax (x)^{2} - {\left (x^{2} e^{10} + 8 \, x e^{10} + 16 \, e^{10}\right )} \log \left (\log \relax (x)\right )^{2} - 8 \, {\left ({\left (\log \relax (5)^{2} + 4 \, \log \relax (5)\right )} e^{10} - {\left (\log \relax (5) + 1\right )} e^{5}\right )} x - x^{2} - 8 \, x e^{5} + 2 \, {\rm Ei}\left (2 \, \log \relax (x)\right ) e^{5} + 8 \, {\rm Ei}\left (\log \relax (x)\right ) e^{5} + 2 \, {\left (x^{3} e^{10} + {\left ({\left (\log \relax (5) + 8\right )} e^{10} - e^{5}\right )} x^{2} + 4 \, {\left (2 \, {\left (\log \relax (5) + 2\right )} e^{10} - e^{5}\right )} x + 16 \, e^{10} \log \relax (5)\right )} \log \relax (x) - 2 \, {\left (x^{3} e^{10} + {\left ({\left (\log \relax (5) + 8\right )} e^{10} - e^{5}\right )} x^{2} + 4 \, {\left (2 \, {\left (\log \relax (5) + 2\right )} e^{10} - e^{5}\right )} x - {\left (x^{2} e^{10} + 8 \, x e^{10} + 16 \, e^{10}\right )} \log \relax (x)\right )} \log \left (\log \relax (x)\right ) - 2 \, \int \frac {x^{2} e^{5} + 4 \, x e^{5} + 16 \, e^{10} \log \relax (5)}{x \log \relax (x)}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.59, size = 36, normalized size = 1.29 \begin {gather*} -{\left (4\,\ln \left (\frac {5\,{\mathrm {e}}^x\,\ln \relax (x)}{x}\right )\,{\mathrm {e}}^5-x+x\,\ln \left (\frac {5\,{\mathrm {e}}^x\,\ln \relax (x)}{x}\right )\,{\mathrm {e}}^5\right )}^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.78, size = 63, normalized size = 2.25 \begin {gather*} - x^{2} + \left (2 x^{2} e^{5} + 8 x e^{5}\right ) \log {\left (\frac {5 e^{x} \log {\relax (x )}}{x} \right )} + \left (- x^{2} e^{10} - 8 x e^{10} - 16 e^{10}\right ) \log {\left (\frac {5 e^{x} \log {\relax (x )}}{x} \right )}^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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