3.101.6 \(\int \frac {10 e^{-2-6 x+x^2}+e^{-4-12 x+2 x^2} (-59 x+20 x^2)+(-10+e^{-2-6 x+x^2} (58 x-20 x^2)) \log (\frac {3}{x})+x \log ^2(\frac {3}{x})+(2 e^{-2-6 x+x^2} x+e^{-4-12 x+2 x^2} (x-12 x^2+4 x^3)+(-2 x+e^{-2-6 x+x^2} (-2 x+12 x^2-4 x^3)) \log (\frac {3}{x})+x \log ^2(\frac {3}{x})) \log (x)}{x} \, dx\)

Optimal. Leaf size=31 \[ x \left (e^{-2-6 x+x^2}-\log \left (\frac {3}{x}\right )\right )^2 \left (\frac {5}{x}+\log (x)\right ) \]

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Rubi [F]  time = 7.31, 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 {10 e^{-2-6 x+x^2}+e^{-4-12 x+2 x^2} \left (-59 x+20 x^2\right )+\left (-10+e^{-2-6 x+x^2} \left (58 x-20 x^2\right )\right ) \log \left (\frac {3}{x}\right )+x \log ^2\left (\frac {3}{x}\right )+\left (2 e^{-2-6 x+x^2} x+e^{-4-12 x+2 x^2} \left (x-12 x^2+4 x^3\right )+\left (-2 x+e^{-2-6 x+x^2} \left (-2 x+12 x^2-4 x^3\right )\right ) \log \left (\frac {3}{x}\right )+x \log ^2\left (\frac {3}{x}\right )\right ) \log (x)}{x} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(10*E^(-2 - 6*x + x^2) + E^(-4 - 12*x + 2*x^2)*(-59*x + 20*x^2) + (-10 + E^(-2 - 6*x + x^2)*(58*x - 20*x^2
))*Log[3/x] + x*Log[3/x]^2 + (2*E^(-2 - 6*x + x^2)*x + E^(-4 - 12*x + 2*x^2)*(x - 12*x^2 + 4*x^3) + (-2*x + E^
(-2 - 6*x + x^2)*(-2*x + 12*x^2 - 4*x^3))*Log[3/x] + x*Log[3/x]^2)*Log[x])/x,x]

[Out]

5*E^(-4 - 12*x + 2*x^2) - 10*E^(-2 - 6*x + x^2)*Log[3/x] + 5*Log[3/x]^2 + E^(-4 - 12*x + 2*x^2)*x*Log[x] - 2*E
^(-2 - 6*x + x^2)*x*Log[3/x]*Log[x] + x*Log[3/x]^2*Log[x] + (3*Defer[Int][E^(2*(-3 + x)^2)/x, x])/E^22 + 6*Log
[3/x]*Defer[Int][E^(-2 - 6*x + x^2)/x, x] - 6*Log[x]*Defer[Int][E^(-2 - 6*x + x^2)/x, x] - (6*Log[3/x]*Defer[I
nt][E^(9 - 6*x + x^2)/x, x])/E^11 + (6*Log[x]*Defer[Int][E^(9 - 6*x + x^2)/x, x])/E^11 - 3*Defer[Int][E^(-4 -
12*x + 2*x^2)/x, x] + 12*Defer[Int][Defer[Int][E^(-2 - 6*x + x^2)/x, x]/x, x] - (12*Defer[Int][Defer[Int][E^(9
- 6*x + x^2)/x, x]/x, x])/E^11

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (e^{-4-12 x+2 x^2} \left (-59+20 x+\log (x)-12 x \log (x)+4 x^2 \log (x)\right )+\frac {\log \left (\frac {3}{x}\right ) \left (-10+x \log \left (\frac {3}{x}\right )-2 x \log (x)+x \log \left (\frac {3}{x}\right ) \log (x)\right )}{x}-\frac {2 e^{-2-6 x+x^2} \left (-5-29 x \log \left (\frac {3}{x}\right )+10 x^2 \log \left (\frac {3}{x}\right )-x \log (x)+x \log \left (\frac {3}{x}\right ) \log (x)-6 x^2 \log \left (\frac {3}{x}\right ) \log (x)+2 x^3 \log \left (\frac {3}{x}\right ) \log (x)\right )}{x}\right ) \, dx\\ &=-\left (2 \int \frac {e^{-2-6 x+x^2} \left (-5-29 x \log \left (\frac {3}{x}\right )+10 x^2 \log \left (\frac {3}{x}\right )-x \log (x)+x \log \left (\frac {3}{x}\right ) \log (x)-6 x^2 \log \left (\frac {3}{x}\right ) \log (x)+2 x^3 \log \left (\frac {3}{x}\right ) \log (x)\right )}{x} \, dx\right )+\int e^{-4-12 x+2 x^2} \left (-59+20 x+\log (x)-12 x \log (x)+4 x^2 \log (x)\right ) \, dx+\int \frac {\log \left (\frac {3}{x}\right ) \left (-10+x \log \left (\frac {3}{x}\right )-2 x \log (x)+x \log \left (\frac {3}{x}\right ) \log (x)\right )}{x} \, dx\\ &=-\left (2 \int \frac {e^{-2-6 x+x^2} \left (-5-x \log (x)+x \log \left (\frac {3}{x}\right ) \left (-29+10 x+\left (1-6 x+2 x^2\right ) \log (x)\right )\right )}{x} \, dx\right )+\int \left (-59 e^{-4-12 x+2 x^2}+20 e^{-4-12 x+2 x^2} x+e^{-4-12 x+2 x^2} \log (x)-12 e^{-4-12 x+2 x^2} x \log (x)+4 e^{-4-12 x+2 x^2} x^2 \log (x)\right ) \, dx+\int \left (\frac {\log \left (\frac {3}{x}\right ) \left (-10+x \log \left (\frac {3}{x}\right )\right )}{x}+\left (-2+\log \left (\frac {3}{x}\right )\right ) \log \left (\frac {3}{x}\right ) \log (x)\right ) \, dx\\ &=-\left (2 \int \left (\frac {e^{-2-6 x+x^2} \left (-5-29 x \log \left (\frac {3}{x}\right )+10 x^2 \log \left (\frac {3}{x}\right )\right )}{x}+e^{-2-6 x+x^2} \left (-1+\log \left (\frac {3}{x}\right )-6 x \log \left (\frac {3}{x}\right )+2 x^2 \log \left (\frac {3}{x}\right )\right ) \log (x)\right ) \, dx\right )+4 \int e^{-4-12 x+2 x^2} x^2 \log (x) \, dx-12 \int e^{-4-12 x+2 x^2} x \log (x) \, dx+20 \int e^{-4-12 x+2 x^2} x \, dx-59 \int e^{-4-12 x+2 x^2} \, dx+\int \frac {\log \left (\frac {3}{x}\right ) \left (-10+x \log \left (\frac {3}{x}\right )\right )}{x} \, dx+\int e^{-4-12 x+2 x^2} \log (x) \, dx+\int \left (-2+\log \left (\frac {3}{x}\right )\right ) \log \left (\frac {3}{x}\right ) \log (x) \, dx\\ &=5 e^{-4-12 x+2 x^2}+e^{-4-12 x+2 x^2} x \log (x)-2 \int \frac {e^{-2-6 x+x^2} \left (-5-29 x \log \left (\frac {3}{x}\right )+10 x^2 \log \left (\frac {3}{x}\right )\right )}{x} \, dx-2 \int e^{-2-6 x+x^2} \left (-1+\log \left (\frac {3}{x}\right )-6 x \log \left (\frac {3}{x}\right )+2 x^2 \log \left (\frac {3}{x}\right )\right ) \log (x) \, dx-4 \int \frac {e^{-22-12 x} \left (4 e^{2 \left (9+x^2\right )} (3+x)-35 e^{12 x} \sqrt {2 \pi } \text {erfi}\left (\sqrt {2} (3-x)\right )\right )}{16 x} \, dx+12 \int \frac {e^{2 (-3+x)^2}-3 \sqrt {2 \pi } \text {erfi}\left (\sqrt {2} (3-x)\right )}{4 e^{22} x} \, dx+60 \int e^{-4-12 x+2 x^2} \, dx-\frac {59 \int e^{\frac {1}{8} (-12+4 x)^2} \, dx}{e^{22}}-\int -\frac {\sqrt {\frac {\pi }{2}} \text {erfi}\left (3 \sqrt {2}-\sqrt {2} x\right )}{2 e^{22} x} \, dx+\int \left (-\frac {10 \log \left (\frac {3}{x}\right )}{x}+\log ^2\left (\frac {3}{x}\right )\right ) \, dx+\int \left (-2 \log \left (\frac {3}{x}\right ) \log (x)+\log ^2\left (\frac {3}{x}\right ) \log (x)\right ) \, dx\\ &=5 e^{-4-12 x+2 x^2}+\frac {59 \sqrt {\frac {\pi }{2}} \text {erfi}\left (\sqrt {2} (3-x)\right )}{2 e^{22}}+e^{-4-12 x+2 x^2} x \log (x)-\frac {1}{4} \int \frac {e^{-22-12 x} \left (4 e^{2 \left (9+x^2\right )} (3+x)-35 e^{12 x} \sqrt {2 \pi } \text {erfi}\left (\sqrt {2} (3-x)\right )\right )}{x} \, dx-2 \int \frac {e^{-2-6 x+x^2} \left (-5+x (-29+10 x) \log \left (\frac {3}{x}\right )\right )}{x} \, dx-2 \int \log \left (\frac {3}{x}\right ) \log (x) \, dx-2 \int e^{-2-6 x+x^2} \left (-1+\left (1-6 x+2 x^2\right ) \log \left (\frac {3}{x}\right )\right ) \log (x) \, dx-10 \int \frac {\log \left (\frac {3}{x}\right )}{x} \, dx+\frac {3 \int \frac {e^{2 (-3+x)^2}-3 \sqrt {2 \pi } \text {erfi}\left (\sqrt {2} (3-x)\right )}{x} \, dx}{e^{22}}+\frac {60 \int e^{\frac {1}{8} (-12+4 x)^2} \, dx}{e^{22}}+\frac {\sqrt {\frac {\pi }{2}} \int \frac {\text {erfi}\left (3 \sqrt {2}-\sqrt {2} x\right )}{x} \, dx}{2 e^{22}}+\int \log ^2\left (\frac {3}{x}\right ) \, dx+\int \log ^2\left (\frac {3}{x}\right ) \log (x) \, dx\\ &=5 e^{-4-12 x+2 x^2}+\frac {59 \sqrt {\frac {\pi }{2}} \text {erfi}\left (\sqrt {2} (3-x)\right )}{2 e^{22}}-\frac {15 \sqrt {2 \pi } \text {erfi}\left (\sqrt {2} (3-x)\right )}{e^{22}}+5 \log ^2\left (\frac {3}{x}\right )+x \log ^2\left (\frac {3}{x}\right )+e^{-4-12 x+2 x^2} x \log (x)+x \log ^2\left (\frac {3}{x}\right ) \log (x)-\frac {1}{4} \int \left (\frac {4 e^{-4-12 x+2 x^2} (3+x)}{x}-\frac {35 \sqrt {2 \pi } \text {erfi}\left (3 \sqrt {2}-\sqrt {2} x\right )}{e^{22} x}\right ) \, dx+2 \int \log \left (\frac {3}{x}\right ) \, dx+2 \int \left (1+\log \left (\frac {3}{x}\right )\right ) \, dx-2 \int \left (-\frac {5 e^{-2-6 x+x^2}}{x}+e^{-2-6 x+x^2} (-29+10 x) \log \left (\frac {3}{x}\right )\right ) \, dx-2 \int \left (-e^{-2-6 x+x^2} \log (x)+e^{-2-6 x+x^2} \log \left (\frac {3}{x}\right ) \log (x)-6 e^{-2-6 x+x^2} x \log \left (\frac {3}{x}\right ) \log (x)+2 e^{-2-6 x+x^2} x^2 \log \left (\frac {3}{x}\right ) \log (x)\right ) \, dx+\frac {3 \int \left (\frac {e^{2 (-3+x)^2}}{x}-\frac {3 \sqrt {2 \pi } \text {erfi}\left (3 \sqrt {2}-\sqrt {2} x\right )}{x}\right ) \, dx}{e^{22}}+\frac {\sqrt {\frac {\pi }{2}} \int \frac {\text {erfi}\left (3 \sqrt {2}-\sqrt {2} x\right )}{x} \, dx}{2 e^{22}}-\int \left (2+2 \log \left (\frac {3}{x}\right )+\log ^2\left (\frac {3}{x}\right )\right ) \, dx\\ &=5 e^{-4-12 x+2 x^2}+2 x+\frac {59 \sqrt {\frac {\pi }{2}} \text {erfi}\left (\sqrt {2} (3-x)\right )}{2 e^{22}}-\frac {15 \sqrt {2 \pi } \text {erfi}\left (\sqrt {2} (3-x)\right )}{e^{22}}+2 x \log \left (\frac {3}{x}\right )+5 \log ^2\left (\frac {3}{x}\right )+x \log ^2\left (\frac {3}{x}\right )+e^{-4-12 x+2 x^2} x \log (x)+x \log ^2\left (\frac {3}{x}\right ) \log (x)-2 \int e^{-2-6 x+x^2} (-29+10 x) \log \left (\frac {3}{x}\right ) \, dx+2 \int e^{-2-6 x+x^2} \log (x) \, dx-2 \int e^{-2-6 x+x^2} \log \left (\frac {3}{x}\right ) \log (x) \, dx-4 \int e^{-2-6 x+x^2} x^2 \log \left (\frac {3}{x}\right ) \log (x) \, dx+10 \int \frac {e^{-2-6 x+x^2}}{x} \, dx+12 \int e^{-2-6 x+x^2} x \log \left (\frac {3}{x}\right ) \log (x) \, dx+\frac {3 \int \frac {e^{2 (-3+x)^2}}{x} \, dx}{e^{22}}+\frac {\sqrt {\frac {\pi }{2}} \int \frac {\text {erfi}\left (3 \sqrt {2}-\sqrt {2} x\right )}{x} \, dx}{2 e^{22}}+\frac {\left (35 \sqrt {\frac {\pi }{2}}\right ) \int \frac {\text {erfi}\left (3 \sqrt {2}-\sqrt {2} x\right )}{x} \, dx}{2 e^{22}}-\frac {\left (9 \sqrt {2 \pi }\right ) \int \frac {\text {erfi}\left (3 \sqrt {2}-\sqrt {2} x\right )}{x} \, dx}{e^{22}}-\int \frac {e^{-4-12 x+2 x^2} (3+x)}{x} \, dx-\int \log ^2\left (\frac {3}{x}\right ) \, dx\\ &=5 e^{-4-12 x+2 x^2}+2 x+\frac {59 \sqrt {\frac {\pi }{2}} \text {erfi}\left (\sqrt {2} (3-x)\right )}{2 e^{22}}-\frac {15 \sqrt {2 \pi } \text {erfi}\left (\sqrt {2} (3-x)\right )}{e^{22}}-10 e^{-2-6 x+x^2} \log \left (\frac {3}{x}\right )+2 x \log \left (\frac {3}{x}\right )+\frac {\sqrt {\pi } \text {erfi}(3-x) \log \left (\frac {3}{x}\right )}{e^{11}}+5 \log ^2\left (\frac {3}{x}\right )+e^{-4-12 x+2 x^2} x \log (x)-\frac {\sqrt {\pi } \text {erfi}(3-x) \log (x)}{e^{11}}-2 e^{-2-6 x+x^2} x \log \left (\frac {3}{x}\right ) \log (x)+x \log ^2\left (\frac {3}{x}\right ) \log (x)-2 \int -\frac {\sqrt {\pi } \text {erfi}(3-x)}{2 e^{11} x} \, dx-2 \int \frac {5 e^{-2-6 x+x^2}-\frac {\sqrt {\pi } \text {erfi}(3-x)}{2 e^{11}}}{x} \, dx-2 \int \log \left (\frac {3}{x}\right ) \, dx+2 \int -\frac {\sqrt {\pi } \text {erfi}(3-x) \log \left (\frac {3}{x}\right )}{2 e^{11} x} \, dx+2 \int \frac {\sqrt {\pi } \text {erfi}(3-x) \log (x)}{2 e^{11} x} \, dx+4 \int \frac {e^{-11-6 x} \left (2 e^{9+x^2} (3+x)-17 e^{6 x} \sqrt {\pi } \text {erfi}(3-x)\right ) \log \left (\frac {3}{x}\right )}{4 x} \, dx+4 \int \frac {e^{-11-6 x} \left (-2 e^{9+x^2} (3+x)+17 e^{6 x} \sqrt {\pi } \text {erfi}(3-x)\right ) \log (x)}{4 x} \, dx+10 \int \frac {e^{-2-6 x+x^2}}{x} \, dx-12 \int \frac {\left (e^{(-3+x)^2}-3 \sqrt {\pi } \text {erfi}(3-x)\right ) \log \left (\frac {3}{x}\right )}{2 e^{11} x} \, dx-12 \int \frac {\left (-e^{(-3+x)^2}+3 \sqrt {\pi } \text {erfi}(3-x)\right ) \log (x)}{2 e^{11} x} \, dx+\frac {3 \int \frac {e^{2 (-3+x)^2}}{x} \, dx}{e^{22}}+\frac {\sqrt {\frac {\pi }{2}} \int \frac {\text {erfi}\left (3 \sqrt {2}-\sqrt {2} x\right )}{x} \, dx}{2 e^{22}}+\frac {\left (35 \sqrt {\frac {\pi }{2}}\right ) \int \frac {\text {erfi}\left (3 \sqrt {2}-\sqrt {2} x\right )}{x} \, dx}{2 e^{22}}-\frac {\left (9 \sqrt {2 \pi }\right ) \int \frac {\text {erfi}\left (3 \sqrt {2}-\sqrt {2} x\right )}{x} \, dx}{e^{22}}-\int \left (e^{-4-12 x+2 x^2}+\frac {3 e^{-4-12 x+2 x^2}}{x}\right ) \, dx\\ &=5 e^{-4-12 x+2 x^2}+\frac {59 \sqrt {\frac {\pi }{2}} \text {erfi}\left (\sqrt {2} (3-x)\right )}{2 e^{22}}-\frac {15 \sqrt {2 \pi } \text {erfi}\left (\sqrt {2} (3-x)\right )}{e^{22}}-10 e^{-2-6 x+x^2} \log \left (\frac {3}{x}\right )+\frac {\sqrt {\pi } \text {erfi}(3-x) \log \left (\frac {3}{x}\right )}{e^{11}}+5 \log ^2\left (\frac {3}{x}\right )+e^{-4-12 x+2 x^2} x \log (x)-\frac {\sqrt {\pi } \text {erfi}(3-x) \log (x)}{e^{11}}-2 e^{-2-6 x+x^2} x \log \left (\frac {3}{x}\right ) \log (x)+x \log ^2\left (\frac {3}{x}\right ) \log (x)-2 \int \left (\frac {5 e^{-2-6 x+x^2}}{x}-\frac {\sqrt {\pi } \text {erfi}(3-x)}{2 e^{11} x}\right ) \, dx-3 \int \frac {e^{-4-12 x+2 x^2}}{x} \, dx+10 \int \frac {e^{-2-6 x+x^2}}{x} \, dx+\frac {3 \int \frac {e^{2 (-3+x)^2}}{x} \, dx}{e^{22}}-\frac {6 \int \frac {\left (e^{(-3+x)^2}-3 \sqrt {\pi } \text {erfi}(3-x)\right ) \log \left (\frac {3}{x}\right )}{x} \, dx}{e^{11}}-\frac {6 \int \frac {\left (-e^{(-3+x)^2}+3 \sqrt {\pi } \text {erfi}(3-x)\right ) \log (x)}{x} \, dx}{e^{11}}+\frac {\sqrt {\frac {\pi }{2}} \int \frac {\text {erfi}\left (3 \sqrt {2}-\sqrt {2} x\right )}{x} \, dx}{2 e^{22}}+\frac {\left (35 \sqrt {\frac {\pi }{2}}\right ) \int \frac {\text {erfi}\left (3 \sqrt {2}-\sqrt {2} x\right )}{x} \, dx}{2 e^{22}}+\frac {\sqrt {\pi } \int \frac {\text {erfi}(3-x)}{x} \, dx}{e^{11}}-\frac {\sqrt {\pi } \int \frac {\text {erfi}(3-x) \log \left (\frac {3}{x}\right )}{x} \, dx}{e^{11}}+\frac {\sqrt {\pi } \int \frac {\text {erfi}(3-x) \log (x)}{x} \, dx}{e^{11}}-\frac {\left (9 \sqrt {2 \pi }\right ) \int \frac {\text {erfi}\left (3 \sqrt {2}-\sqrt {2} x\right )}{x} \, dx}{e^{22}}-\int e^{-4-12 x+2 x^2} \, dx+\int \frac {e^{-11-6 x} \left (2 e^{9+x^2} (3+x)-17 e^{6 x} \sqrt {\pi } \text {erfi}(3-x)\right ) \log \left (\frac {3}{x}\right )}{x} \, dx+\int \frac {e^{-11-6 x} \left (-2 e^{9+x^2} (3+x)+17 e^{6 x} \sqrt {\pi } \text {erfi}(3-x)\right ) \log (x)}{x} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.18, size = 37, normalized size = 1.19 \begin {gather*} e^{-4-12 x} \left (e^{x^2}-e^{2+6 x} \log \left (\frac {3}{x}\right )\right )^2 (5+x \log (x)) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(10*E^(-2 - 6*x + x^2) + E^(-4 - 12*x + 2*x^2)*(-59*x + 20*x^2) + (-10 + E^(-2 - 6*x + x^2)*(58*x -
20*x^2))*Log[3/x] + x*Log[3/x]^2 + (2*E^(-2 - 6*x + x^2)*x + E^(-4 - 12*x + 2*x^2)*(x - 12*x^2 + 4*x^3) + (-2*
x + E^(-2 - 6*x + x^2)*(-2*x + 12*x^2 - 4*x^3))*Log[3/x] + x*Log[3/x]^2)*Log[x])/x,x]

[Out]

E^(-4 - 12*x)*(E^x^2 - E^(2 + 6*x)*Log[3/x])^2*(5 + x*Log[x])

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fricas [B]  time = 2.52, size = 96, normalized size = 3.10 \begin {gather*} -x \log \left (\frac {3}{x}\right )^{3} + {\left (2 \, x e^{\left (x^{2} - 6 \, x - 2\right )} + x \log \relax (3) + 5\right )} \log \left (\frac {3}{x}\right )^{2} + {\left (x \log \relax (3) + 5\right )} e^{\left (2 \, x^{2} - 12 \, x - 4\right )} - {\left (x e^{\left (2 \, x^{2} - 12 \, x - 4\right )} + 2 \, {\left (x \log \relax (3) + 5\right )} e^{\left (x^{2} - 6 \, x - 2\right )}\right )} \log \left (\frac {3}{x}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((x*log(3/x)^2+((-4*x^3+12*x^2-2*x)*exp(x^2-6*x-2)-2*x)*log(3/x)+(4*x^3-12*x^2+x)*exp(x^2-6*x-2)^2+2
*x*exp(x^2-6*x-2))*log(x)+x*log(3/x)^2+((-20*x^2+58*x)*exp(x^2-6*x-2)-10)*log(3/x)+(20*x^2-59*x)*exp(x^2-6*x-2
)^2+10*exp(x^2-6*x-2))/x,x, algorithm="fricas")

[Out]

-x*log(3/x)^3 + (2*x*e^(x^2 - 6*x - 2) + x*log(3) + 5)*log(3/x)^2 + (x*log(3) + 5)*e^(2*x^2 - 12*x - 4) - (x*e
^(2*x^2 - 12*x - 4) + 2*(x*log(3) + 5)*e^(x^2 - 6*x - 2))*log(3/x)

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giac [B]  time = 0.22, size = 135, normalized size = 4.35 \begin {gather*} {\left (x e^{6} \log \relax (3)^{2} \log \relax (x) - 2 \, x e^{6} \log \relax (3) \log \relax (x)^{2} + x e^{6} \log \relax (x)^{3} - 2 \, x e^{\left (x^{2} - 6 \, x + 4\right )} \log \relax (3) \log \relax (x) + 2 \, x e^{\left (x^{2} - 6 \, x + 4\right )} \log \relax (x)^{2} + x e^{\left (2 \, x^{2} - 12 \, x + 2\right )} \log \relax (x) - 10 \, e^{6} \log \relax (3) \log \relax (x) + 5 \, e^{6} \log \relax (x)^{2} - 10 \, e^{\left (x^{2} - 6 \, x + 4\right )} \log \relax (3) + 10 \, e^{\left (x^{2} - 6 \, x + 4\right )} \log \relax (x) + 5 \, e^{\left (2 \, x^{2} - 12 \, x + 2\right )}\right )} e^{\left (-6\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((x*log(3/x)^2+((-4*x^3+12*x^2-2*x)*exp(x^2-6*x-2)-2*x)*log(3/x)+(4*x^3-12*x^2+x)*exp(x^2-6*x-2)^2+2
*x*exp(x^2-6*x-2))*log(x)+x*log(3/x)^2+((-20*x^2+58*x)*exp(x^2-6*x-2)-10)*log(3/x)+(20*x^2-59*x)*exp(x^2-6*x-2
)^2+10*exp(x^2-6*x-2))/x,x, algorithm="giac")

[Out]

(x*e^6*log(3)^2*log(x) - 2*x*e^6*log(3)*log(x)^2 + x*e^6*log(x)^3 - 2*x*e^(x^2 - 6*x + 4)*log(3)*log(x) + 2*x*
e^(x^2 - 6*x + 4)*log(x)^2 + x*e^(2*x^2 - 12*x + 2)*log(x) - 10*e^6*log(3)*log(x) + 5*e^6*log(x)^2 - 10*e^(x^2
- 6*x + 4)*log(3) + 10*e^(x^2 - 6*x + 4)*log(x) + 5*e^(2*x^2 - 12*x + 2))*e^(-6)

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maple [B]  time = 1.12, size = 112, normalized size = 3.61

method	result	size
risch	\(x \ln \relax (x )^{3}+\left (5-2 x \ln \relax (3)+2 x \,{\mathrm e}^{x^{2}-6 x -2}\right ) \ln \relax (x )^{2}+\left (x \ln \relax (3)^{2}+{\mathrm e}^{2 x^{2}-12 x -4} x -2 \ln \relax (3) {\mathrm e}^{x^{2}-6 x -2} x +10 \,{\mathrm e}^{x^{2}-6 x -2}\right ) \ln \relax (x )-10 \ln \relax (3) \ln \relax (x )+5 \,{\mathrm e}^{2 x^{2}-12 x -4}-10 \ln \relax (3) {\mathrm e}^{x^{2}-6 x -2}\)	\(112\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((x*ln(3/x)^2+((-4*x^3+12*x^2-2*x)*exp(x^2-6*x-2)-2*x)*ln(3/x)+(4*x^3-12*x^2+x)*exp(x^2-6*x-2)^2+2*x*exp(x
^2-6*x-2))*ln(x)+x*ln(3/x)^2+((-20*x^2+58*x)*exp(x^2-6*x-2)-10)*ln(3/x)+(20*x^2-59*x)*exp(x^2-6*x-2)^2+10*exp(
x^2-6*x-2))/x,x,method=_RETURNVERBOSE)

[Out]

x*ln(x)^3+(5-2*x*ln(3)+2*x*exp(x^2-6*x-2))*ln(x)^2+(x*ln(3)^2+exp(2*x^2-12*x-4)*x-2*ln(3)*exp(x^2-6*x-2)*x+10*
exp(x^2-6*x-2))*ln(x)-10*ln(3)*ln(x)+5*exp(2*x^2-12*x-4)-10*ln(3)*exp(x^2-6*x-2)

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maxima [B]  time = 0.68, size = 155, normalized size = 5.00 \begin {gather*} x \log \left (\frac {3}{x}\right )^{2} + {\left ({\left (x \log \relax (x) + 5\right )} e^{\left (2 \, x^{2}\right )} + 2 \, {\left (x e^{2} \log \relax (x)^{2} - 5 \, e^{2} \log \relax (3) - {\left (x e^{2} \log \relax (3) - 5 \, e^{2}\right )} \log \relax (x)\right )} e^{\left (x^{2} + 6 \, x\right )} - {\left (x {\left (2 \, \log \relax (3) + 1\right )} e^{4} \log \relax (x)^{2} - x e^{4} \log \relax (x)^{3} - {\left (\log \relax (3)^{2} + 2 \, \log \relax (3) + 2\right )} x e^{4} \log \relax (x) + {\left (\log \relax (3)^{2} + 2 \, \log \relax (3) + 2\right )} x e^{4}\right )} e^{\left (12 \, x\right )}\right )} e^{\left (-12 \, x - 4\right )} + 2 \, x \log \left (\frac {3}{x}\right ) + 5 \, \log \left (\frac {3}{x}\right )^{2} + 2 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((x*log(3/x)^2+((-4*x^3+12*x^2-2*x)*exp(x^2-6*x-2)-2*x)*log(3/x)+(4*x^3-12*x^2+x)*exp(x^2-6*x-2)^2+2
*x*exp(x^2-6*x-2))*log(x)+x*log(3/x)^2+((-20*x^2+58*x)*exp(x^2-6*x-2)-10)*log(3/x)+(20*x^2-59*x)*exp(x^2-6*x-2
)^2+10*exp(x^2-6*x-2))/x,x, algorithm="maxima")

[Out]

x*log(3/x)^2 + ((x*log(x) + 5)*e^(2*x^2) + 2*(x*e^2*log(x)^2 - 5*e^2*log(3) - (x*e^2*log(3) - 5*e^2)*log(x))*e
^(x^2 + 6*x) - (x*(2*log(3) + 1)*e^4*log(x)^2 - x*e^4*log(x)^3 - (log(3)^2 + 2*log(3) + 2)*x*e^4*log(x) + (log
(3)^2 + 2*log(3) + 2)*x*e^4)*e^(12*x))*e^(-12*x - 4) + 2*x*log(3/x) + 5*log(3/x)^2 + 2*x

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mupad [F]  time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int \frac {10\,{\mathrm {e}}^{x^2-6\,x-2}-{\mathrm {e}}^{2\,x^2-12\,x-4}\,\left (59\,x-20\,x^2\right )+\ln \left (\frac {3}{x}\right )\,\left ({\mathrm {e}}^{x^2-6\,x-2}\,\left (58\,x-20\,x^2\right )-10\right )+x\,{\ln \left (\frac {3}{x}\right )}^2+\ln \relax (x)\,\left (x\,{\ln \left (\frac {3}{x}\right )}^2+\left (-2\,x-{\mathrm {e}}^{x^2-6\,x-2}\,\left (4\,x^3-12\,x^2+2\,x\right )\right )\,\ln \left (\frac {3}{x}\right )+2\,x\,{\mathrm {e}}^{x^2-6\,x-2}+{\mathrm {e}}^{2\,x^2-12\,x-4}\,\left (4\,x^3-12\,x^2+x\right )\right )}{x} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((10*exp(x^2 - 6*x - 2) - exp(2*x^2 - 12*x - 4)*(59*x - 20*x^2) + log(3/x)*(exp(x^2 - 6*x - 2)*(58*x - 20*x
^2) - 10) + x*log(3/x)^2 + log(x)*(2*x*exp(x^2 - 6*x - 2) + exp(2*x^2 - 12*x - 4)*(x - 12*x^2 + 4*x^3) - log(3
/x)*(2*x + exp(x^2 - 6*x - 2)*(2*x - 12*x^2 + 4*x^3)) + x*log(3/x)^2))/x,x)

[Out]

int((10*exp(x^2 - 6*x - 2) - exp(2*x^2 - 12*x - 4)*(59*x - 20*x^2) + log(3/x)*(exp(x^2 - 6*x - 2)*(58*x - 20*x
^2) - 10) + x*log(3/x)^2 + log(x)*(2*x*exp(x^2 - 6*x - 2) + exp(2*x^2 - 12*x - 4)*(x - 12*x^2 + 4*x^3) - log(3
/x)*(2*x + exp(x^2 - 6*x - 2)*(2*x - 12*x^2 + 4*x^3)) + x*log(3/x)^2))/x, x)

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sympy [B]  time = 0.76, size = 95, normalized size = 3.06 \begin {gather*} x \log {\relax (x )}^{3} + x \log {\relax (3 )}^{2} \log {\relax (x )} + \left (- 2 x \log {\relax (3 )} + 5\right ) \log {\relax (x )}^{2} + \left (x \log {\relax (x )} + 5\right ) e^{2 x^{2} - 12 x - 4} + \left (2 x \log {\relax (x )}^{2} - 2 x \log {\relax (3 )} \log {\relax (x )} + 10 \log {\relax (x )} - 10 \log {\relax (3 )}\right ) e^{x^{2} - 6 x - 2} - 10 \log {\relax (3 )} \log {\relax (x )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((x*ln(3/x)**2+((-4*x**3+12*x**2-2*x)*exp(x**2-6*x-2)-2*x)*ln(3/x)+(4*x**3-12*x**2+x)*exp(x**2-6*x-2
)**2+2*x*exp(x**2-6*x-2))*ln(x)+x*ln(3/x)**2+((-20*x**2+58*x)*exp(x**2-6*x-2)-10)*ln(3/x)+(20*x**2-59*x)*exp(x
**2-6*x-2)**2+10*exp(x**2-6*x-2))/x,x)

[Out]

x*log(x)**3 + x*log(3)**2*log(x) + (-2*x*log(3) + 5)*log(x)**2 + (x*log(x) + 5)*exp(2*x**2 - 12*x - 4) + (2*x*
log(x)**2 - 2*x*log(3)*log(x) + 10*log(x) - 10*log(3))*exp(x**2 - 6*x - 2) - 10*log(3)*log(x)

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