Optimal. Leaf size=26 \[ \left (10-\frac {e^x x^2}{2+x}\right ) \log (2 x) \log ^2\left (x^2\right ) \]
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Rubi [F] time = 38.95, 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 {\left (160+160 x+40 x^2+e^x \left (-8 x^2-4 x^3\right )\right ) \log (2 x) \log \left (x^2\right )+\left (40+40 x+10 x^2+e^x \left (-2 x^2-x^3\right )+e^x \left (-4 x^2-3 x^3-x^4\right ) \log (2 x)\right ) \log ^2\left (x^2\right )}{4 x+4 x^2+x^3} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {\left (160+160 x+40 x^2+e^x \left (-8 x^2-4 x^3\right )\right ) \log (2 x) \log \left (x^2\right )+\left (40+40 x+10 x^2+e^x \left (-2 x^2-x^3\right )+e^x \left (-4 x^2-3 x^3-x^4\right ) \log (2 x)\right ) \log ^2\left (x^2\right )}{x \left (4+4 x+x^2\right )} \, dx\\ &=\int \frac {\left (160+160 x+40 x^2+e^x \left (-8 x^2-4 x^3\right )\right ) \log (2 x) \log \left (x^2\right )+\left (40+40 x+10 x^2+e^x \left (-2 x^2-x^3\right )+e^x \left (-4 x^2-3 x^3-x^4\right ) \log (2 x)\right ) \log ^2\left (x^2\right )}{x (2+x)^2} \, dx\\ &=\int \left (\frac {160 \log (2 x) \log \left (x^2\right )}{(2+x)^2}+\frac {160 \log (2 x) \log \left (x^2\right )}{x (2+x)^2}+\frac {40 x \log (2 x) \log \left (x^2\right )}{(2+x)^2}+\frac {40 \log ^2\left (x^2\right )}{(2+x)^2}+\frac {40 \log ^2\left (x^2\right )}{x (2+x)^2}+\frac {10 x \log ^2\left (x^2\right )}{(2+x)^2}-\frac {e^x x \log \left (x^2\right ) \left (8 \log (2 x)+4 x \log (2 x)+2 \log \left (x^2\right )+x \log \left (x^2\right )+4 \log (2 x) \log \left (x^2\right )+3 x \log (2 x) \log \left (x^2\right )+x^2 \log (2 x) \log \left (x^2\right )\right )}{(2+x)^2}\right ) \, dx\\ &=10 \int \frac {x \log ^2\left (x^2\right )}{(2+x)^2} \, dx+40 \int \frac {x \log (2 x) \log \left (x^2\right )}{(2+x)^2} \, dx+40 \int \frac {\log ^2\left (x^2\right )}{(2+x)^2} \, dx+40 \int \frac {\log ^2\left (x^2\right )}{x (2+x)^2} \, dx+160 \int \frac {\log (2 x) \log \left (x^2\right )}{(2+x)^2} \, dx+160 \int \frac {\log (2 x) \log \left (x^2\right )}{x (2+x)^2} \, dx-\int \frac {e^x x \log \left (x^2\right ) \left (8 \log (2 x)+4 x \log (2 x)+2 \log \left (x^2\right )+x \log \left (x^2\right )+4 \log (2 x) \log \left (x^2\right )+3 x \log (2 x) \log \left (x^2\right )+x^2 \log (2 x) \log \left (x^2\right )\right )}{(2+x)^2} \, dx\\ &=-\frac {160 \log (2 x) \log \left (x^2\right )}{2+x}+\frac {20 x \log ^2\left (x^2\right )}{2+x}+10 \int \left (-\frac {2 \log ^2\left (x^2\right )}{(2+x)^2}+\frac {\log ^2\left (x^2\right )}{2+x}\right ) \, dx-20 \int \frac {\log ^2\left (x^2\right )}{(2+x)^2} \, dx+20 \int \frac {\log ^2\left (x^2\right )}{x (2+x)} \, dx+40 \int \left (-\frac {2 \log (2 x) \log \left (x^2\right )}{(2+x)^2}+\frac {\log (2 x) \log \left (x^2\right )}{2+x}\right ) \, dx-80 \int \frac {\log \left (x^2\right )}{2+x} \, dx-160 \int -\frac {2 \log (2 x)}{x (2+x)} \, dx+160 \int \frac {\log \left (x^2\right )}{x (2+x)} \, dx+160 \int \left (\frac {\log (2 x) \log \left (x^2\right )}{4 x}-\frac {\log (2 x) \log \left (x^2\right )}{2 (2+x)^2}-\frac {\log (2 x) \log \left (x^2\right )}{4 (2+x)}\right ) \, dx-\int \frac {e^x x \log \left (x^2\right ) \left ((2+x) \log \left (x^2\right )+\log (2 x) \left (4 (2+x)+\left (4+3 x+x^2\right ) \log \left (x^2\right )\right )\right )}{(2+x)^2} \, dx\\ &=-80 \log \left (1+\frac {x}{2}\right ) \log \left (x^2\right )-\frac {160 \log (2 x) \log \left (x^2\right )}{2+x}+\frac {10 x \log ^2\left (x^2\right )}{2+x}+10 \int \frac {\log ^2\left (x^2\right )}{x} \, dx-20 \int \frac {\log ^2\left (x^2\right )}{(2+x)^2} \, dx+40 \int \frac {\log \left (x^2\right )}{2+x} \, dx+40 \int \frac {\log (2 x) \log \left (x^2\right )}{x} \, dx+80 \int \frac {\log \left (x^2\right )}{x} \, dx-80 \int \frac {\log \left (x^2\right )}{2+x} \, dx-2 \left (80 \int \frac {\log (2 x) \log \left (x^2\right )}{(2+x)^2} \, dx\right )+160 \int \frac {\log \left (1+\frac {x}{2}\right )}{x} \, dx+320 \int \frac {\log (2 x)}{x (2+x)} \, dx-\int \left (\frac {4 e^x x \log (2 x) \log \left (x^2\right )}{2+x}+\frac {e^x x \left (2+x+4 \log (2 x)+3 x \log (2 x)+x^2 \log (2 x)\right ) \log ^2\left (x^2\right )}{(2+x)^2}\right ) \, dx\\ &=-120 \log \left (1+\frac {x}{2}\right ) \log \left (x^2\right )-\frac {160 \log (2 x) \log \left (x^2\right )}{2+x}+20 \log ^2(2 x) \log \left (x^2\right )+20 \log ^2\left (x^2\right )-160 \text {Li}_2\left (-\frac {x}{2}\right )-4 \int \frac {e^x x \log (2 x) \log \left (x^2\right )}{2+x} \, dx+5 \operatorname {Subst}\left (\int x^2 \, dx,x,\log \left (x^2\right )\right )+40 \int \frac {\log \left (x^2\right )}{2+x} \, dx-80 \int \frac {\log \left (1+\frac {x}{2}\right )}{x} \, dx-80 \int \frac {\log ^2(2 x)}{2 x} \, dx-2 \left (-\frac {80 \log (2 x) \log \left (x^2\right )}{2+x}-80 \int -\frac {2 \log (2 x)}{x (2+x)} \, dx+80 \int \frac {\log \left (x^2\right )}{x (2+x)} \, dx\right )+160 \int \frac {\log \left (1+\frac {x}{2}\right )}{x} \, dx+160 \int \frac {\log (2 x)}{x} \, dx-160 \int \frac {\log (2 x)}{2+x} \, dx-\int \frac {e^x x \left (2+x+4 \log (2 x)+3 x \log (2 x)+x^2 \log (2 x)\right ) \log ^2\left (x^2\right )}{(2+x)^2} \, dx\\ &=-160 \log \left (1+\frac {x}{2}\right ) \log (2 x)+80 \log ^2(2 x)-80 \log \left (1+\frac {x}{2}\right ) \log \left (x^2\right )-4 e^x \log (2 x) \log \left (x^2\right )-\frac {160 \log (2 x) \log \left (x^2\right )}{2+x}+\frac {8 \text {Ei}(2+x) \log (2 x) \log \left (x^2\right )}{e^2}+20 \log ^2(2 x) \log \left (x^2\right )+20 \log ^2\left (x^2\right )+\frac {5}{3} \log ^3\left (x^2\right )-240 \text {Li}_2\left (-\frac {x}{2}\right )+4 \int \frac {2 \left (e^x-\frac {2 \text {Ei}(2+x)}{e^2}\right ) \log (2 x)}{x} \, dx+4 \int \frac {\left (e^x-\frac {2 \text {Ei}(2+x)}{e^2}\right ) \log \left (x^2\right )}{x} \, dx-40 \int \frac {\log ^2(2 x)}{x} \, dx-80 \int \frac {\log \left (1+\frac {x}{2}\right )}{x} \, dx+160 \int \frac {\log \left (1+\frac {x}{2}\right )}{x} \, dx-2 \left (-\frac {80 \log (2 x) \log \left (x^2\right )}{2+x}+40 \int \frac {\log \left (x^2\right )}{x} \, dx-40 \int \frac {\log \left (x^2\right )}{2+x} \, dx+160 \int \frac {\log (2 x)}{x (2+x)} \, dx\right )-\int \frac {e^x x \left (2+x+\left (4+3 x+x^2\right ) \log (2 x)\right ) \log ^2\left (x^2\right )}{(2+x)^2} \, dx\\ &=-160 \log \left (1+\frac {x}{2}\right ) \log (2 x)+80 \log ^2(2 x)+4 \text {Ei}(x) \log \left (x^2\right )-80 \log \left (1+\frac {x}{2}\right ) \log \left (x^2\right )-4 e^x \log (2 x) \log \left (x^2\right )-\frac {160 \log (2 x) \log \left (x^2\right )}{2+x}+\frac {8 \text {Ei}(2+x) \log (2 x) \log \left (x^2\right )}{e^2}+20 \log ^2(2 x) \log \left (x^2\right )+20 \log ^2\left (x^2\right )+\frac {5}{3} \log ^3\left (x^2\right )-320 \text {Li}_2\left (-\frac {x}{2}\right )-4 \int \frac {2 \left (\text {Ei}(x)-\frac {2 \int \frac {\text {Ei}(2+x)}{x} \, dx}{e^2}\right )}{x} \, dx+8 \int \frac {\left (e^x-\frac {2 \text {Ei}(2+x)}{e^2}\right ) \log (2 x)}{x} \, dx-40 \operatorname {Subst}\left (\int x^2 \, dx,x,\log (2 x)\right )-2 \left (-40 \log \left (1+\frac {x}{2}\right ) \log \left (x^2\right )-\frac {80 \log (2 x) \log \left (x^2\right )}{2+x}+10 \log ^2\left (x^2\right )+80 \int \frac {\log \left (1+\frac {x}{2}\right )}{x} \, dx+80 \int \frac {\log (2 x)}{x} \, dx-80 \int \frac {\log (2 x)}{2+x} \, dx\right )-\frac {\left (8 \log \left (x^2\right )\right ) \int \frac {\text {Ei}(2+x)}{x} \, dx}{e^2}-\int \left (-\frac {2 e^x \left (2+x+4 \log (2 x)+3 x \log (2 x)+x^2 \log (2 x)\right ) \log ^2\left (x^2\right )}{(2+x)^2}+\frac {e^x \left (2+x+4 \log (2 x)+3 x \log (2 x)+x^2 \log (2 x)\right ) \log ^2\left (x^2\right )}{2+x}\right ) \, dx\\ &=8 \text {Ei}(x) \log (2 x)-160 \log \left (1+\frac {x}{2}\right ) \log (2 x)+80 \log ^2(2 x)-\frac {40}{3} \log ^3(2 x)+4 \text {Ei}(x) \log \left (x^2\right )-80 \log \left (1+\frac {x}{2}\right ) \log \left (x^2\right )-4 e^x \log (2 x) \log \left (x^2\right )-\frac {160 \log (2 x) \log \left (x^2\right )}{2+x}+\frac {8 \text {Ei}(2+x) \log (2 x) \log \left (x^2\right )}{e^2}+20 \log ^2(2 x) \log \left (x^2\right )+20 \log ^2\left (x^2\right )+\frac {5}{3} \log ^3\left (x^2\right )-320 \text {Li}_2\left (-\frac {x}{2}\right )+2 \int \frac {e^x \left (2+x+4 \log (2 x)+3 x \log (2 x)+x^2 \log (2 x)\right ) \log ^2\left (x^2\right )}{(2+x)^2} \, dx-2 \left (8 \int \frac {\text {Ei}(x)-\frac {2 \int \frac {\text {Ei}(2+x)}{x} \, dx}{e^2}}{x} \, dx\right )-2 \left (-80 \log \left (1+\frac {x}{2}\right ) \log (2 x)+40 \log ^2(2 x)-40 \log \left (1+\frac {x}{2}\right ) \log \left (x^2\right )-\frac {80 \log (2 x) \log \left (x^2\right )}{2+x}+10 \log ^2\left (x^2\right )-80 \text {Li}_2\left (-\frac {x}{2}\right )+80 \int \frac {\log \left (1+\frac {x}{2}\right )}{x} \, dx\right )-\frac {(16 \log (2 x)) \int \frac {\text {Ei}(2+x)}{x} \, dx}{e^2}-\frac {\left (8 \log \left (x^2\right )\right ) \int \frac {\text {Ei}(2+x)}{x} \, dx}{e^2}-\int \frac {e^x \left (2+x+4 \log (2 x)+3 x \log (2 x)+x^2 \log (2 x)\right ) \log ^2\left (x^2\right )}{2+x} \, dx\\ &=8 \text {Ei}(x) \log (2 x)-160 \log \left (1+\frac {x}{2}\right ) \log (2 x)+80 \log ^2(2 x)-\frac {40}{3} \log ^3(2 x)+4 \text {Ei}(x) \log \left (x^2\right )-80 \log \left (1+\frac {x}{2}\right ) \log \left (x^2\right )-4 e^x \log (2 x) \log \left (x^2\right )-\frac {160 \log (2 x) \log \left (x^2\right )}{2+x}+\frac {8 \text {Ei}(2+x) \log (2 x) \log \left (x^2\right )}{e^2}+20 \log ^2(2 x) \log \left (x^2\right )+20 \log ^2\left (x^2\right )+\frac {5}{3} \log ^3\left (x^2\right )-2 \left (-80 \log \left (1+\frac {x}{2}\right ) \log (2 x)+40 \log ^2(2 x)-40 \log \left (1+\frac {x}{2}\right ) \log \left (x^2\right )-\frac {80 \log (2 x) \log \left (x^2\right )}{2+x}+10 \log ^2\left (x^2\right )-160 \text {Li}_2\left (-\frac {x}{2}\right )\right )-320 \text {Li}_2\left (-\frac {x}{2}\right )+2 \int \frac {e^x \left (2+x+\left (4+3 x+x^2\right ) \log (2 x)\right ) \log ^2\left (x^2\right )}{(2+x)^2} \, dx-2 \left (8 \int \left (\frac {\text {Ei}(x)}{x}-\frac {2 \int \frac {\text {Ei}(2+x)}{x} \, dx}{e^2 x}\right ) \, dx\right )-\frac {(16 \log (2 x)) \int \frac {\text {Ei}(2+x)}{x} \, dx}{e^2}-\frac {\left (8 \log \left (x^2\right )\right ) \int \frac {\text {Ei}(2+x)}{x} \, dx}{e^2}-\int \frac {e^x \left (2+x+\left (4+3 x+x^2\right ) \log (2 x)\right ) \log ^2\left (x^2\right )}{2+x} \, dx\\ &=8 \text {Ei}(x) \log (2 x)-160 \log \left (1+\frac {x}{2}\right ) \log (2 x)+80 \log ^2(2 x)-\frac {40}{3} \log ^3(2 x)+4 \text {Ei}(x) \log \left (x^2\right )-80 \log \left (1+\frac {x}{2}\right ) \log \left (x^2\right )-4 e^x \log (2 x) \log \left (x^2\right )-\frac {160 \log (2 x) \log \left (x^2\right )}{2+x}+\frac {8 \text {Ei}(2+x) \log (2 x) \log \left (x^2\right )}{e^2}+20 \log ^2(2 x) \log \left (x^2\right )+20 \log ^2\left (x^2\right )+\frac {5}{3} \log ^3\left (x^2\right )-2 \left (-80 \log \left (1+\frac {x}{2}\right ) \log (2 x)+40 \log ^2(2 x)-40 \log \left (1+\frac {x}{2}\right ) \log \left (x^2\right )-\frac {80 \log (2 x) \log \left (x^2\right )}{2+x}+10 \log ^2\left (x^2\right )-160 \text {Li}_2\left (-\frac {x}{2}\right )\right )-320 \text {Li}_2\left (-\frac {x}{2}\right )+2 \int \left (\frac {2 e^x \log ^2\left (x^2\right )}{(2+x)^2}+\frac {e^x x \log ^2\left (x^2\right )}{(2+x)^2}+\frac {4 e^x \log (2 x) \log ^2\left (x^2\right )}{(2+x)^2}+\frac {3 e^x x \log (2 x) \log ^2\left (x^2\right )}{(2+x)^2}+\frac {e^x x^2 \log (2 x) \log ^2\left (x^2\right )}{(2+x)^2}\right ) \, dx-2 \left (8 \int \frac {\text {Ei}(x)}{x} \, dx-\frac {16 \int \frac {\int \frac {\text {Ei}(2+x)}{x} \, dx}{x} \, dx}{e^2}\right )-\frac {(16 \log (2 x)) \int \frac {\text {Ei}(2+x)}{x} \, dx}{e^2}-\frac {\left (8 \log \left (x^2\right )\right ) \int \frac {\text {Ei}(2+x)}{x} \, dx}{e^2}-\int \left (\frac {2 e^x \log ^2\left (x^2\right )}{2+x}+\frac {e^x x \log ^2\left (x^2\right )}{2+x}+\frac {4 e^x \log (2 x) \log ^2\left (x^2\right )}{2+x}+\frac {3 e^x x \log (2 x) \log ^2\left (x^2\right )}{2+x}+\frac {e^x x^2 \log (2 x) \log ^2\left (x^2\right )}{2+x}\right ) \, dx\\ &=8 \text {Ei}(x) \log (2 x)-160 \log \left (1+\frac {x}{2}\right ) \log (2 x)+80 \log ^2(2 x)-\frac {40}{3} \log ^3(2 x)+4 \text {Ei}(x) \log \left (x^2\right )-80 \log \left (1+\frac {x}{2}\right ) \log \left (x^2\right )-4 e^x \log (2 x) \log \left (x^2\right )-\frac {160 \log (2 x) \log \left (x^2\right )}{2+x}+\frac {8 \text {Ei}(2+x) \log (2 x) \log \left (x^2\right )}{e^2}+20 \log ^2(2 x) \log \left (x^2\right )+20 \log ^2\left (x^2\right )+\frac {5}{3} \log ^3\left (x^2\right )-2 \left (-80 \log \left (1+\frac {x}{2}\right ) \log (2 x)+40 \log ^2(2 x)-40 \log \left (1+\frac {x}{2}\right ) \log \left (x^2\right )-\frac {80 \log (2 x) \log \left (x^2\right )}{2+x}+10 \log ^2\left (x^2\right )-160 \text {Li}_2\left (-\frac {x}{2}\right )\right )-320 \text {Li}_2\left (-\frac {x}{2}\right )+2 \int \frac {e^x x \log ^2\left (x^2\right )}{(2+x)^2} \, dx-2 \int \frac {e^x \log ^2\left (x^2\right )}{2+x} \, dx+2 \int \frac {e^x x^2 \log (2 x) \log ^2\left (x^2\right )}{(2+x)^2} \, dx-3 \int \frac {e^x x \log (2 x) \log ^2\left (x^2\right )}{2+x} \, dx+4 \int \frac {e^x \log ^2\left (x^2\right )}{(2+x)^2} \, dx-4 \int \frac {e^x \log (2 x) \log ^2\left (x^2\right )}{2+x} \, dx+6 \int \frac {e^x x \log (2 x) \log ^2\left (x^2\right )}{(2+x)^2} \, dx+8 \int \frac {e^x \log (2 x) \log ^2\left (x^2\right )}{(2+x)^2} \, dx-2 \left (8 (E_1(-x)+\text {Ei}(x)) \log (x)-8 \int \frac {E_1(-x)}{x} \, dx-\frac {16 \int \frac {\int \frac {\text {Ei}(2+x)}{x} \, dx}{x} \, dx}{e^2}\right )-\frac {(16 \log (2 x)) \int \frac {\text {Ei}(2+x)}{x} \, dx}{e^2}-\frac {\left (8 \log \left (x^2\right )\right ) \int \frac {\text {Ei}(2+x)}{x} \, dx}{e^2}-\int \frac {e^x x \log ^2\left (x^2\right )}{2+x} \, dx-\int \frac {e^x x^2 \log (2 x) \log ^2\left (x^2\right )}{2+x} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}
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Mathematica [A] time = 1.84, size = 29, normalized size = 1.12 \begin {gather*} -\frac {\left (-20-10 x+e^x x^2\right ) \log (2 x) \log ^2\left (x^2\right )}{2+x} \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 2.23, size = 75, normalized size = 2.88 \begin {gather*} -\frac {4 \, {\left ({\left (x^{2} e^{x} - 10 \, x - 20\right )} \log \left (2 \, x\right )^{3} - 2 \, {\left (x^{2} e^{x} \log \relax (2) - 10 \, {\left (x + 2\right )} \log \relax (2)\right )} \log \left (2 \, x\right )^{2} + {\left (x^{2} e^{x} \log \relax (2)^{2} - 10 \, {\left (x + 2\right )} \log \relax (2)^{2}\right )} \log \left (2 \, x\right )\right )}}{x + 2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.44, size = 60, normalized size = 2.31 \begin {gather*} -\frac {4 \, {\left (x^{2} e^{x} \log \relax (2) \log \relax (x)^{2} + x^{2} e^{x} \log \relax (x)^{3} - 10 \, x \log \relax (2) \log \relax (x)^{2} - 10 \, x \log \relax (x)^{3} - 20 \, \log \relax (2) \log \relax (x)^{2} - 20 \, \log \relax (x)^{3}\right )}}{x + 2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [C] time = 0.60, size = 806, normalized size = 31.00
method | result | size |
risch | \(-\frac {4 \left ({\mathrm e}^{x} x^{2}-10 x -20\right ) \ln \relax (x )^{3}}{2+x}-\frac {2 \left (-i \pi \,x^{2} \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right ) {\mathrm e}^{x}+10 i \pi x \mathrm {csgn}\left (i x^{2}\right )^{3}+10 i \pi x \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )-40 i \pi \mathrm {csgn}\left (i x^{2}\right )^{2} \mathrm {csgn}\left (i x \right )+20 i \pi \mathrm {csgn}\left (i x^{2}\right )^{3}-20 i \pi x \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}-i \pi \,x^{2} \mathrm {csgn}\left (i x^{2}\right )^{3} {\mathrm e}^{x}+20 i \pi \,\mathrm {csgn}\left (i x^{2}\right ) \mathrm {csgn}\left (i x \right )^{2}+2 i \pi \,x^{2} \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2} {\mathrm e}^{x}+2 x^{2} \ln \relax (2) {\mathrm e}^{x}-20 x \ln \relax (2)-40 \ln \relax (2)\right ) \ln \relax (x )^{2}}{2+x}+\frac {\pi \,\mathrm {csgn}\left (i x^{2}\right ) \left (\mathrm {csgn}\left (i x^{2}\right ) \pi \mathrm {csgn}\left (i x \right )^{4}-4 \mathrm {csgn}\left (i x^{2}\right )^{2} \pi \mathrm {csgn}\left (i x \right )^{3}+6 \mathrm {csgn}\left (i x^{2}\right )^{3} \pi \mathrm {csgn}\left (i x \right )^{2}-4 \mathrm {csgn}\left (i x^{2}\right )^{4} \pi \,\mathrm {csgn}\left (i x \right )+\mathrm {csgn}\left (i x^{2}\right )^{5} \pi -16 i \ln \relax (2) \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )+8 i \ln \relax (2) \mathrm {csgn}\left (i x \right )^{2}+8 i \ln \relax (2) \mathrm {csgn}\left (i x^{2}\right )^{2}\right ) x^{2} {\mathrm e}^{x} \ln \relax (x )}{4 x +8}+\frac {i \pi \,\mathrm {csgn}\left (i x^{2}\right ) \left (-160 \ln \relax (x ) \ln \relax (2) \mathrm {csgn}\left (i x \right )^{2} x -160 \ln \relax (x ) \ln \relax (2) \mathrm {csgn}\left (i x^{2}\right )^{2} x +640 \ln \relax (x ) \ln \relax (2) \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )+120 i \pi \ln \relax (x ) x \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )^{3}+240 i \pi \ln \relax (x ) \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )^{3}-2 i \pi \ln \relax (2) x^{2} \mathrm {csgn}\left (i x^{2}\right )^{5} {\mathrm e}^{x}+8 i \pi \ln \relax (2) x^{2} \mathrm {csgn}\left (i x \right )^{3} \mathrm {csgn}\left (i x^{2}\right )^{2} {\mathrm e}^{x}+40 i \pi \ln \relax (x ) \mathrm {csgn}\left (i x^{2}\right )^{5}-320 \ln \relax (x ) \ln \relax (2) \mathrm {csgn}\left (i x \right )^{2}-320 \ln \relax (x ) \ln \relax (2) \mathrm {csgn}\left (i x^{2}\right )^{2}-2 i \pi \ln \relax (2) x^{2} \mathrm {csgn}\left (i x \right )^{4} \mathrm {csgn}\left (i x^{2}\right ) {\mathrm e}^{x}-160 i \pi \ln \relax (x ) \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{4}+20 i \pi \ln \relax (x ) x \mathrm {csgn}\left (i x \right )^{4} \mathrm {csgn}\left (i x^{2}\right )-12 i \pi \ln \relax (2) x^{2} \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )^{3} {\mathrm e}^{x}+20 i \pi \ln \relax (x ) x \mathrm {csgn}\left (i x^{2}\right )^{5}-80 i \pi \ln \relax (x ) x \mathrm {csgn}\left (i x \right )^{3} \mathrm {csgn}\left (i x^{2}\right )^{2}+320 \ln \relax (x ) \ln \relax (2) \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right ) x +8 i \pi \ln \relax (2) x^{2} \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{4} {\mathrm e}^{x}+40 i \pi \ln \relax (x ) \mathrm {csgn}\left (i x \right )^{4} \mathrm {csgn}\left (i x^{2}\right )-160 i \pi \ln \relax (x ) \mathrm {csgn}\left (i x \right )^{3} \mathrm {csgn}\left (i x^{2}\right )^{2}-80 i \pi \ln \relax (x ) x \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{4}\right )}{8 x +16}\) | \(806\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.54, size = 55, normalized size = 2.12 \begin {gather*} \frac {4 \, {\left (10 \, {\left (x + 2\right )} \log \relax (x)^{3} + 10 \, {\left (x \log \relax (2) + 2 \, \log \relax (2)\right )} \log \relax (x)^{2} - {\left (x^{2} \log \relax (2) \log \relax (x)^{2} + x^{2} \log \relax (x)^{3}\right )} e^{x}\right )}}{x + 2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.15, size = 87, normalized size = 3.35 \begin {gather*} 40\,\ln \left (x^2\right )\,{\ln \relax (2)}^2-80\,{\ln \relax (2)}^2\,\ln \relax (x)-40\,\ln \relax (2)\,{\ln \relax (x)}^2+10\,{\ln \left (x^2\right )}^2\,\ln \relax (x)+40\,\ln \left (x^2\right )\,\ln \relax (2)\,\ln \relax (x)-\frac {x^2\,{\ln \left (x^2\right )}^2\,{\mathrm {e}}^x\,\ln \relax (2)}{x+2}-\frac {x^2\,{\ln \left (x^2\right )}^2\,{\mathrm {e}}^x\,\ln \relax (x)}{x+2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.52, size = 78, normalized size = 3.00 \begin {gather*} 40 \log {\relax (2 )}^{2} \log {\relax (x )} + 40 \log {\left (2 x \right )}^{3} - 80 \log {\relax (2 )} \log {\left (2 x \right )}^{2} + \frac {\left (- 4 x^{2} \log {\left (2 x \right )}^{3} + 8 x^{2} \log {\relax (2 )} \log {\left (2 x \right )}^{2} - 4 x^{2} \log {\relax (2 )}^{2} \log {\left (2 x \right )}\right ) e^{x}}{x + 2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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