3.28.78 \(\int \frac {e^{-2 x} (4 e^{2 x} x^4 \log ^2(3)+e^x (4 x^3 \log (3)-32 x^2 \log ^2(3)) \log (x)+e^x ((-6 x^2+6 x^3-2 x^4) \log (3)+(-32 x^2+16 x^3) \log ^2(3)) \log ^2(x)+(4 x^2-64 x \log (3)+e^x (-4 x^2+2 x^3) \log (3)+256 \log ^2(3)) \log ^3(x)+(-10 x+2 x^2-2 x^3+(80-16 x+32 x^2) \log (3)-128 x \log ^2(3)) \log ^4(x)+(6-2 x+4 x^2-32 x \log (3)) \log ^5(x)-2 x \log ^6(x))}{x \log ^2(3)} \, dx\)

Optimal. Leaf size=31 \[ \left (-x^2+e^{-x} \log ^2(x) \left (8+\frac {-x+\log (x)}{\log (3)}\right )\right )^2 \]

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Rubi [F]  time = 15.63, 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 {e^{-2 x} \left (4 e^{2 x} x^4 \log ^2(3)+e^x \left (4 x^3 \log (3)-32 x^2 \log ^2(3)\right ) \log (x)+e^x \left (\left (-6 x^2+6 x^3-2 x^4\right ) \log (3)+\left (-32 x^2+16 x^3\right ) \log ^2(3)\right ) \log ^2(x)+\left (4 x^2-64 x \log (3)+e^x \left (-4 x^2+2 x^3\right ) \log (3)+256 \log ^2(3)\right ) \log ^3(x)+\left (-10 x+2 x^2-2 x^3+\left (80-16 x+32 x^2\right ) \log (3)-128 x \log ^2(3)\right ) \log ^4(x)+\left (6-2 x+4 x^2-32 x \log (3)\right ) \log ^5(x)-2 x \log ^6(x)\right )}{x \log ^2(3)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(4*E^(2*x)*x^4*Log[3]^2 + E^x*(4*x^3*Log[3] - 32*x^2*Log[3]^2)*Log[x] + E^x*((-6*x^2 + 6*x^3 - 2*x^4)*Log[
3] + (-32*x^2 + 16*x^3)*Log[3]^2)*Log[x]^2 + (4*x^2 - 64*x*Log[3] + E^x*(-4*x^2 + 2*x^3)*Log[3] + 256*Log[3]^2
)*Log[x]^3 + (-10*x + 2*x^2 - 2*x^3 + (80 - 16*x + 32*x^2)*Log[3] - 128*x*Log[3]^2)*Log[x]^4 + (6 - 2*x + 4*x^
2 - 32*x*Log[3])*Log[x]^5 - 2*x*Log[x]^6)/(E^(2*x)*x*Log[3]^2),x]

[Out]

x^4 - 4/(E^x*Log[3]) - (4*x)/(E^x*Log[3]) - (8*(1 - 4*Log[3]))/(E^x*Log[3]) + (8*ExpIntegralEi[-x]*(1 - Log[81
]))/Log[3] + (32*Log[x])/E^x + (32*x*Log[x])/E^x - (8*Log[x])/(E^x*Log[3]) - (8*x*Log[x])/(E^x*Log[3]) - (4*x^
2*Log[x])/(E^x*Log[3]) - (2*(3 + 16*Log[3])*Defer[Int][(x*Log[x]^2)/E^x, x])/Log[3] + (2*(3 + 8*Log[3])*Defer[
Int][(x^2*Log[x]^2)/E^x, x])/Log[3] - (2*Defer[Int][(x^3*Log[x]^2)/E^x, x])/Log[3] - (64*Defer[Int][Log[x]^3/E
^(2*x), x])/Log[3] + 256*Defer[Int][Log[x]^3/(E^(2*x)*x), x] + (4*Defer[Int][(x*Log[x]^3)/E^(2*x), x])/Log[3]^
2 - (4*Defer[Int][(x*Log[x]^3)/E^x, x])/Log[3] + (2*Defer[Int][(x^2*Log[x]^3)/E^x, x])/Log[3] - (2*(5 + 8*Log[
3]*(1 + 8*Log[3]))*Defer[Int][Log[x]^4/E^(2*x), x])/Log[3]^2 + (80*Defer[Int][Log[x]^4/(E^(2*x)*x), x])/Log[3]
+ (2*(1 + 16*Log[3])*Defer[Int][(x*Log[x]^4)/E^(2*x), x])/Log[3]^2 - (2*Defer[Int][(x^2*Log[x]^4)/E^(2*x), x]
)/Log[3]^2 - (2*(1 + 16*Log[3])*Defer[Int][Log[x]^5/E^(2*x), x])/Log[3]^2 + (6*Defer[Int][Log[x]^5/(E^(2*x)*x)
, x])/Log[3]^2 + (4*Defer[Int][(x*Log[x]^5)/E^(2*x), x])/Log[3]^2 - (2*Defer[Int][Log[x]^6/E^(2*x), x])/Log[3]
^2

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \frac {e^{-2 x} \left (4 e^{2 x} x^4 \log ^2(3)+e^x \left (4 x^3 \log (3)-32 x^2 \log ^2(3)\right ) \log (x)+e^x \left (\left (-6 x^2+6 x^3-2 x^4\right ) \log (3)+\left (-32 x^2+16 x^3\right ) \log ^2(3)\right ) \log ^2(x)+\left (4 x^2-64 x \log (3)+e^x \left (-4 x^2+2 x^3\right ) \log (3)+256 \log ^2(3)\right ) \log ^3(x)+\left (-10 x+2 x^2-2 x^3+\left (80-16 x+32 x^2\right ) \log (3)-128 x \log ^2(3)\right ) \log ^4(x)+\left (6-2 x+4 x^2-32 x \log (3)\right ) \log ^5(x)-2 x \log ^6(x)\right )}{x} \, dx}{\log ^2(3)}\\ &=\frac {\int \left (4 x^3 \log ^2(3)+2 e^{-x} x \log (3) \log (x) \left (2 x-16 \log (3)-x^2 \log (x)+3 x \left (1+\frac {8 \log (3)}{3}\right ) \log (x)-3 \left (1+\frac {16 \log (3)}{3}\right ) \log (x)-2 \log ^2(x)+x \log ^2(x)\right )+\frac {2 e^{-2 x} \log ^3(x) \left (2 x^2-32 x \log (3)+128 \log ^2(3)-x^3 \log (x)+40 \log (3) \log (x)+x^2 (1+16 \log (3)) \log (x)-5 x \left (1+\frac {8}{5} \log (3) (1+8 \log (3))\right ) \log (x)+3 \log ^2(x)+2 x^2 \log ^2(x)-x (1+16 \log (3)) \log ^2(x)-x \log ^3(x)\right )}{x}\right ) \, dx}{\log ^2(3)}\\ &=x^4+\frac {2 \int \frac {e^{-2 x} \log ^3(x) \left (2 x^2-32 x \log (3)+128 \log ^2(3)-x^3 \log (x)+40 \log (3) \log (x)+x^2 (1+16 \log (3)) \log (x)-5 x \left (1+\frac {8}{5} \log (3) (1+8 \log (3))\right ) \log (x)+3 \log ^2(x)+2 x^2 \log ^2(x)-x (1+16 \log (3)) \log ^2(x)-x \log ^3(x)\right )}{x} \, dx}{\log ^2(3)}+\frac {2 \int e^{-x} x \log (x) \left (2 x-16 \log (3)-x^2 \log (x)+3 x \left (1+\frac {8 \log (3)}{3}\right ) \log (x)-3 \left (1+\frac {16 \log (3)}{3}\right ) \log (x)-2 \log ^2(x)+x \log ^2(x)\right ) \, dx}{\log (3)}\\ &=x^4+\frac {2 \int \left (\frac {2 e^{-2 x} (x-8 \log (3))^2 \log ^3(x)}{x}+\frac {e^{-2 x} \left (-x^3+40 \log (3)+x^2 (1+16 \log (3))-x \left (5+8 \log (3)+64 \log ^2(3)\right )\right ) \log ^4(x)}{x}+\frac {e^{-2 x} \left (3+2 x^2-x (1+16 \log (3))\right ) \log ^5(x)}{x}-e^{-2 x} \log ^6(x)\right ) \, dx}{\log ^2(3)}+\frac {2 \int \left (2 e^{-x} x (x-8 \log (3)) \log (x)+e^{-x} x \left (-3-x^2-16 \log (3)+x (3+8 \log (3))\right ) \log ^2(x)+e^{-x} (-2+x) x \log ^3(x)\right ) \, dx}{\log (3)}\\ &=x^4+\frac {2 \int \frac {e^{-2 x} \left (-x^3+40 \log (3)+x^2 (1+16 \log (3))-x \left (5+8 \log (3)+64 \log ^2(3)\right )\right ) \log ^4(x)}{x} \, dx}{\log ^2(3)}+\frac {2 \int \frac {e^{-2 x} \left (3+2 x^2-x (1+16 \log (3))\right ) \log ^5(x)}{x} \, dx}{\log ^2(3)}-\frac {2 \int e^{-2 x} \log ^6(x) \, dx}{\log ^2(3)}+\frac {4 \int \frac {e^{-2 x} (x-8 \log (3))^2 \log ^3(x)}{x} \, dx}{\log ^2(3)}+\frac {2 \int e^{-x} x \left (-3-x^2-16 \log (3)+x (3+8 \log (3))\right ) \log ^2(x) \, dx}{\log (3)}+\frac {2 \int e^{-x} (-2+x) x \log ^3(x) \, dx}{\log (3)}+\frac {4 \int e^{-x} x (x-8 \log (3)) \log (x) \, dx}{\log (3)}\\ &=x^4+32 e^{-x} \log (x)+32 e^{-x} x \log (x)-\frac {8 e^{-x} \log (x)}{\log (3)}-\frac {8 e^{-x} x \log (x)}{\log (3)}-\frac {4 e^{-x} x^2 \log (x)}{\log (3)}-\frac {2 \int e^{-2 x} \log ^6(x) \, dx}{\log ^2(3)}+\frac {2 \int \left (-e^{-2 x} x^2 \log ^4(x)+\frac {40 e^{-2 x} \log (3) \log ^4(x)}{x}+e^{-2 x} x (1+16 \log (3)) \log ^4(x)-5 e^{-2 x} \left (1+\frac {8}{5} \log (3) (1+8 \log (3))\right ) \log ^4(x)\right ) \, dx}{\log ^2(3)}+\frac {2 \int \left (\frac {3 e^{-2 x} \log ^5(x)}{x}+2 e^{-2 x} x \log ^5(x)-e^{-2 x} (1+16 \log (3)) \log ^5(x)\right ) \, dx}{\log ^2(3)}+\frac {4 \int \left (e^{-2 x} x \log ^3(x)-16 e^{-2 x} \log (3) \log ^3(x)+\frac {64 e^{-2 x} \log ^2(3) \log ^3(x)}{x}\right ) \, dx}{\log ^2(3)}+\frac {2 \int \left (-e^{-x} x^3 \log ^2(x)+e^{-x} x (-3-16 \log (3)) \log ^2(x)+e^{-x} x^2 (3+8 \log (3)) \log ^2(x)\right ) \, dx}{\log (3)}+\frac {2 \int \left (-2 e^{-x} x \log ^3(x)+e^{-x} x^2 \log ^3(x)\right ) \, dx}{\log (3)}-\frac {4 \int \frac {e^{-x} \left (-x^2-2 (1-4 \log (3))-2 x (1-4 \log (3))\right )}{x} \, dx}{\log (3)}\\ &=x^4+32 e^{-x} \log (x)+32 e^{-x} x \log (x)-\frac {8 e^{-x} \log (x)}{\log (3)}-\frac {8 e^{-x} x \log (x)}{\log (3)}-\frac {4 e^{-x} x^2 \log (x)}{\log (3)}+256 \int \frac {e^{-2 x} \log ^3(x)}{x} \, dx-\frac {2 \int e^{-2 x} x^2 \log ^4(x) \, dx}{\log ^2(3)}-\frac {2 \int e^{-2 x} \log ^6(x) \, dx}{\log ^2(3)}+\frac {4 \int e^{-2 x} x \log ^3(x) \, dx}{\log ^2(3)}+\frac {4 \int e^{-2 x} x \log ^5(x) \, dx}{\log ^2(3)}+\frac {6 \int \frac {e^{-2 x} \log ^5(x)}{x} \, dx}{\log ^2(3)}-\frac {2 \int e^{-x} x^3 \log ^2(x) \, dx}{\log (3)}+\frac {2 \int e^{-x} x^2 \log ^3(x) \, dx}{\log (3)}-\frac {4 \int \left (-e^{-x} x-2 e^{-x} (1-4 \log (3))+\frac {2 e^{-x} (-1+4 \log (3))}{x}\right ) \, dx}{\log (3)}-\frac {4 \int e^{-x} x \log ^3(x) \, dx}{\log (3)}-\frac {64 \int e^{-2 x} \log ^3(x) \, dx}{\log (3)}+\frac {80 \int \frac {e^{-2 x} \log ^4(x)}{x} \, dx}{\log (3)}+\frac {(2 (-3-16 \log (3))) \int e^{-x} x \log ^2(x) \, dx}{\log (3)}+\frac {(2 (3+8 \log (3))) \int e^{-x} x^2 \log ^2(x) \, dx}{\log (3)}+\frac {(2 (1+16 \log (3))) \int e^{-2 x} x \log ^4(x) \, dx}{\log ^2(3)}-\frac {(2 (1+16 \log (3))) \int e^{-2 x} \log ^5(x) \, dx}{\log ^2(3)}-\frac {(2 (5+8 \log (3) (1+8 \log (3)))) \int e^{-2 x} \log ^4(x) \, dx}{\log ^2(3)}\\ &=x^4+32 e^{-x} \log (x)+32 e^{-x} x \log (x)-\frac {8 e^{-x} \log (x)}{\log (3)}-\frac {8 e^{-x} x \log (x)}{\log (3)}-\frac {4 e^{-x} x^2 \log (x)}{\log (3)}+256 \int \frac {e^{-2 x} \log ^3(x)}{x} \, dx-\frac {2 \int e^{-2 x} x^2 \log ^4(x) \, dx}{\log ^2(3)}-\frac {2 \int e^{-2 x} \log ^6(x) \, dx}{\log ^2(3)}+\frac {4 \int e^{-2 x} x \log ^3(x) \, dx}{\log ^2(3)}+\frac {4 \int e^{-2 x} x \log ^5(x) \, dx}{\log ^2(3)}+\frac {6 \int \frac {e^{-2 x} \log ^5(x)}{x} \, dx}{\log ^2(3)}-\frac {2 \int e^{-x} x^3 \log ^2(x) \, dx}{\log (3)}+\frac {2 \int e^{-x} x^2 \log ^3(x) \, dx}{\log (3)}+\frac {4 \int e^{-x} x \, dx}{\log (3)}-\frac {4 \int e^{-x} x \log ^3(x) \, dx}{\log (3)}-\frac {64 \int e^{-2 x} \log ^3(x) \, dx}{\log (3)}+\frac {80 \int \frac {e^{-2 x} \log ^4(x)}{x} \, dx}{\log (3)}+\frac {(2 (-3-16 \log (3))) \int e^{-x} x \log ^2(x) \, dx}{\log (3)}+\frac {(8 (1-4 \log (3))) \int e^{-x} \, dx}{\log (3)}+\frac {(2 (3+8 \log (3))) \int e^{-x} x^2 \log ^2(x) \, dx}{\log (3)}+\frac {(2 (1+16 \log (3))) \int e^{-2 x} x \log ^4(x) \, dx}{\log ^2(3)}-\frac {(2 (1+16 \log (3))) \int e^{-2 x} \log ^5(x) \, dx}{\log ^2(3)}-\frac {(2 (5+8 \log (3) (1+8 \log (3)))) \int e^{-2 x} \log ^4(x) \, dx}{\log ^2(3)}+\frac {(8 (1-\log (81))) \int \frac {e^{-x}}{x} \, dx}{\log (3)}\\ &=x^4-\frac {4 e^{-x} x}{\log (3)}-\frac {8 e^{-x} (1-4 \log (3))}{\log (3)}+\frac {8 \text {Ei}(-x) (1-\log (81))}{\log (3)}+32 e^{-x} \log (x)+32 e^{-x} x \log (x)-\frac {8 e^{-x} \log (x)}{\log (3)}-\frac {8 e^{-x} x \log (x)}{\log (3)}-\frac {4 e^{-x} x^2 \log (x)}{\log (3)}+256 \int \frac {e^{-2 x} \log ^3(x)}{x} \, dx-\frac {2 \int e^{-2 x} x^2 \log ^4(x) \, dx}{\log ^2(3)}-\frac {2 \int e^{-2 x} \log ^6(x) \, dx}{\log ^2(3)}+\frac {4 \int e^{-2 x} x \log ^3(x) \, dx}{\log ^2(3)}+\frac {4 \int e^{-2 x} x \log ^5(x) \, dx}{\log ^2(3)}+\frac {6 \int \frac {e^{-2 x} \log ^5(x)}{x} \, dx}{\log ^2(3)}-\frac {2 \int e^{-x} x^3 \log ^2(x) \, dx}{\log (3)}+\frac {2 \int e^{-x} x^2 \log ^3(x) \, dx}{\log (3)}+\frac {4 \int e^{-x} \, dx}{\log (3)}-\frac {4 \int e^{-x} x \log ^3(x) \, dx}{\log (3)}-\frac {64 \int e^{-2 x} \log ^3(x) \, dx}{\log (3)}+\frac {80 \int \frac {e^{-2 x} \log ^4(x)}{x} \, dx}{\log (3)}+\frac {(2 (-3-16 \log (3))) \int e^{-x} x \log ^2(x) \, dx}{\log (3)}+\frac {(2 (3+8 \log (3))) \int e^{-x} x^2 \log ^2(x) \, dx}{\log (3)}+\frac {(2 (1+16 \log (3))) \int e^{-2 x} x \log ^4(x) \, dx}{\log ^2(3)}-\frac {(2 (1+16 \log (3))) \int e^{-2 x} \log ^5(x) \, dx}{\log ^2(3)}-\frac {(2 (5+8 \log (3) (1+8 \log (3)))) \int e^{-2 x} \log ^4(x) \, dx}{\log ^2(3)}\\ &=x^4-\frac {4 e^{-x}}{\log (3)}-\frac {4 e^{-x} x}{\log (3)}-\frac {8 e^{-x} (1-4 \log (3))}{\log (3)}+\frac {8 \text {Ei}(-x) (1-\log (81))}{\log (3)}+32 e^{-x} \log (x)+32 e^{-x} x \log (x)-\frac {8 e^{-x} \log (x)}{\log (3)}-\frac {8 e^{-x} x \log (x)}{\log (3)}-\frac {4 e^{-x} x^2 \log (x)}{\log (3)}+256 \int \frac {e^{-2 x} \log ^3(x)}{x} \, dx-\frac {2 \int e^{-2 x} x^2 \log ^4(x) \, dx}{\log ^2(3)}-\frac {2 \int e^{-2 x} \log ^6(x) \, dx}{\log ^2(3)}+\frac {4 \int e^{-2 x} x \log ^3(x) \, dx}{\log ^2(3)}+\frac {4 \int e^{-2 x} x \log ^5(x) \, dx}{\log ^2(3)}+\frac {6 \int \frac {e^{-2 x} \log ^5(x)}{x} \, dx}{\log ^2(3)}-\frac {2 \int e^{-x} x^3 \log ^2(x) \, dx}{\log (3)}+\frac {2 \int e^{-x} x^2 \log ^3(x) \, dx}{\log (3)}-\frac {4 \int e^{-x} x \log ^3(x) \, dx}{\log (3)}-\frac {64 \int e^{-2 x} \log ^3(x) \, dx}{\log (3)}+\frac {80 \int \frac {e^{-2 x} \log ^4(x)}{x} \, dx}{\log (3)}+\frac {(2 (-3-16 \log (3))) \int e^{-x} x \log ^2(x) \, dx}{\log (3)}+\frac {(2 (3+8 \log (3))) \int e^{-x} x^2 \log ^2(x) \, dx}{\log (3)}+\frac {(2 (1+16 \log (3))) \int e^{-2 x} x \log ^4(x) \, dx}{\log ^2(3)}-\frac {(2 (1+16 \log (3))) \int e^{-2 x} \log ^5(x) \, dx}{\log ^2(3)}-\frac {(2 (5+8 \log (3) (1+8 \log (3)))) \int e^{-2 x} \log ^4(x) \, dx}{\log ^2(3)}\\ \end {aligned} \end {gather*}

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Mathematica [C]  time = 0.75, size = 302, normalized size = 9.74 \begin {gather*} \frac {e^{-2 x} \left (32 e^{2 x} \log ^2(3)-32 e^{2 x} \gamma \log ^2(3)+e^{2 x} x^4 \log ^2(3)-2 e^{2 x} x^2 \log (9)-2 e^x \Gamma (2,-x) \log (9)-2 e^x x \Gamma (2,-x) \log (9)-2 e^{2 x} \text {Ei}(-x) \left (16 \log ^2(3)-\log (81)\right )-2 e^{2 x} \Gamma (0,x) \left (16 \log ^2(3)-\log (81)\right )-2 e^{2 x} \log (81)-2 e^{2 x} \gamma \log (531441)+2 e^{2 x} \gamma \log (43046721)-2 e^x \log (81) \log (x)-2 e^x x \log (81) \log (x)-2 e^x x \log (729) \log (x)+2 e^x x \log (59049) \log (x)-2 e^x \log (531441) \log (x)+2 e^x \log (43046721) \log (x)-16 e^x x^2 \log ^2(3) \log ^2(x)+e^x x^3 \log (9) \log ^2(x)-e^x x^2 \log (9) \log ^3(x)+x^2 \log ^4(x)+64 \log ^2(3) \log ^4(x)-2 x \log (6561) \log ^4(x)-2 x \log ^5(x)+2 \log (6561) \log ^5(x)+\log ^6(x)\right )}{\log ^2(3)} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(4*E^(2*x)*x^4*Log[3]^2 + E^x*(4*x^3*Log[3] - 32*x^2*Log[3]^2)*Log[x] + E^x*((-6*x^2 + 6*x^3 - 2*x^4
)*Log[3] + (-32*x^2 + 16*x^3)*Log[3]^2)*Log[x]^2 + (4*x^2 - 64*x*Log[3] + E^x*(-4*x^2 + 2*x^3)*Log[3] + 256*Lo
g[3]^2)*Log[x]^3 + (-10*x + 2*x^2 - 2*x^3 + (80 - 16*x + 32*x^2)*Log[3] - 128*x*Log[3]^2)*Log[x]^4 + (6 - 2*x
+ 4*x^2 - 32*x*Log[3])*Log[x]^5 - 2*x*Log[x]^6)/(E^(2*x)*x*Log[3]^2),x]

[Out]

(32*E^(2*x)*Log[3]^2 - 32*E^(2*x)*EulerGamma*Log[3]^2 + E^(2*x)*x^4*Log[3]^2 - 2*E^(2*x)*x^2*Log[9] - 2*E^x*Ga
mma[2, -x]*Log[9] - 2*E^x*x*Gamma[2, -x]*Log[9] - 2*E^(2*x)*ExpIntegralEi[-x]*(16*Log[3]^2 - Log[81]) - 2*E^(2
*x)*Gamma[0, x]*(16*Log[3]^2 - Log[81]) - 2*E^(2*x)*Log[81] - 2*E^(2*x)*EulerGamma*Log[531441] + 2*E^(2*x)*Eul
erGamma*Log[43046721] - 2*E^x*Log[81]*Log[x] - 2*E^x*x*Log[81]*Log[x] - 2*E^x*x*Log[729]*Log[x] + 2*E^x*x*Log[
59049]*Log[x] - 2*E^x*Log[531441]*Log[x] + 2*E^x*Log[43046721]*Log[x] - 16*E^x*x^2*Log[3]^2*Log[x]^2 + E^x*x^3
*Log[9]*Log[x]^2 - E^x*x^2*Log[9]*Log[x]^3 + x^2*Log[x]^4 + 64*Log[3]^2*Log[x]^4 - 2*x*Log[6561]*Log[x]^4 - 2*
x*Log[x]^5 + 2*Log[6561]*Log[x]^5 + Log[x]^6)/(E^(2*x)*Log[3]^2)

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fricas [B]  time = 0.63, size = 95, normalized size = 3.06 \begin {gather*} \frac {{\left (x^{4} e^{\left (2 \, x\right )} \log \relax (3)^{2} - 2 \, x^{2} e^{x} \log \relax (3) \log \relax (x)^{3} - 2 \, {\left (x - 8 \, \log \relax (3)\right )} \log \relax (x)^{5} + \log \relax (x)^{6} + {\left (x^{2} - 16 \, x \log \relax (3) + 64 \, \log \relax (3)^{2}\right )} \log \relax (x)^{4} + 2 \, {\left (x^{3} \log \relax (3) - 8 \, x^{2} \log \relax (3)^{2}\right )} e^{x} \log \relax (x)^{2}\right )} e^{\left (-2 \, x\right )}}{\log \relax (3)^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-2*x*log(x)^6+(-32*x*log(3)+4*x^2-2*x+6)*log(x)^5+(-128*x*log(3)^2+(32*x^2-16*x+80)*log(3)-2*x^3+2*
x^2-10*x)*log(x)^4+((2*x^3-4*x^2)*log(3)*exp(x)+256*log(3)^2-64*x*log(3)+4*x^2)*log(x)^3+((16*x^3-32*x^2)*log(
3)^2+(-2*x^4+6*x^3-6*x^2)*log(3))*exp(x)*log(x)^2+(-32*x^2*log(3)^2+4*x^3*log(3))*exp(x)*log(x)+4*x^4*log(3)^2
*exp(x)^2)/x/log(3)^2/exp(x)^2,x, algorithm="fricas")

[Out]

(x^4*e^(2*x)*log(3)^2 - 2*x^2*e^x*log(3)*log(x)^3 - 2*(x - 8*log(3))*log(x)^5 + log(x)^6 + (x^2 - 16*x*log(3)
+ 64*log(3)^2)*log(x)^4 + 2*(x^3*log(3) - 8*x^2*log(3)^2)*e^x*log(x)^2)*e^(-2*x)/log(3)^2

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giac [B]  time = 0.22, size = 132, normalized size = 4.26 \begin {gather*} \frac {2 \, x^{3} e^{\left (-x\right )} \log \relax (3) \log \relax (x)^{2} - 16 \, x^{2} e^{\left (-x\right )} \log \relax (3)^{2} \log \relax (x)^{2} - 2 \, x^{2} e^{\left (-x\right )} \log \relax (3) \log \relax (x)^{3} + x^{2} e^{\left (-2 \, x\right )} \log \relax (x)^{4} - 16 \, x e^{\left (-2 \, x\right )} \log \relax (3) \log \relax (x)^{4} + 64 \, e^{\left (-2 \, x\right )} \log \relax (3)^{2} \log \relax (x)^{4} - 2 \, x e^{\left (-2 \, x\right )} \log \relax (x)^{5} + 16 \, e^{\left (-2 \, x\right )} \log \relax (3) \log \relax (x)^{5} + e^{\left (-2 \, x\right )} \log \relax (x)^{6} + x^{4} \log \relax (3)^{2}}{\log \relax (3)^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-2*x*log(x)^6+(-32*x*log(3)+4*x^2-2*x+6)*log(x)^5+(-128*x*log(3)^2+(32*x^2-16*x+80)*log(3)-2*x^3+2*
x^2-10*x)*log(x)^4+((2*x^3-4*x^2)*log(3)*exp(x)+256*log(3)^2-64*x*log(3)+4*x^2)*log(x)^3+((16*x^3-32*x^2)*log(
3)^2+(-2*x^4+6*x^3-6*x^2)*log(3))*exp(x)*log(x)^2+(-32*x^2*log(3)^2+4*x^3*log(3))*exp(x)*log(x)+4*x^4*log(3)^2
*exp(x)^2)/x/log(3)^2/exp(x)^2,x, algorithm="giac")

[Out]

(2*x^3*e^(-x)*log(3)*log(x)^2 - 16*x^2*e^(-x)*log(3)^2*log(x)^2 - 2*x^2*e^(-x)*log(3)*log(x)^3 + x^2*e^(-2*x)*
log(x)^4 - 16*x*e^(-2*x)*log(3)*log(x)^4 + 64*e^(-2*x)*log(3)^2*log(x)^4 - 2*x*e^(-2*x)*log(x)^5 + 16*e^(-2*x)
*log(3)*log(x)^5 + e^(-2*x)*log(x)^6 + x^4*log(3)^2)/log(3)^2

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maple [B]  time = 0.11, size = 110, normalized size = 3.55

method	result	size
risch	\(\frac {{\mathrm e}^{-2 x} \ln \relax (x )^{6}}{\ln \relax (3)^{2}}+\frac {2 \left (8 \ln \relax (3)-x \right ) {\mathrm e}^{-2 x} \ln \relax (x )^{5}}{\ln \relax (3)^{2}}+\frac {\left (64 \ln \relax (3)^{2}-16 x \ln \relax (3)+x^{2}\right ) {\mathrm e}^{-2 x} \ln \relax (x )^{4}}{\ln \relax (3)^{2}}-\frac {2 x^{2} {\mathrm e}^{-x} \ln \relax (x )^{3}}{\ln \relax (3)}-\frac {2 x^{2} \left (8 \ln \relax (3)-x \right ) {\mathrm e}^{-x} \ln \relax (x )^{2}}{\ln \relax (3)}+x^{4}\)	\(110\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((-2*x*ln(x)^6+(-32*x*ln(3)+4*x^2-2*x+6)*ln(x)^5+(-128*x*ln(3)^2+(32*x^2-16*x+80)*ln(3)-2*x^3+2*x^2-10*x)*l
n(x)^4+((2*x^3-4*x^2)*ln(3)*exp(x)+256*ln(3)^2-64*x*ln(3)+4*x^2)*ln(x)^3+((16*x^3-32*x^2)*ln(3)^2+(-2*x^4+6*x^
3-6*x^2)*ln(3))*exp(x)*ln(x)^2+(-32*x^2*ln(3)^2+4*x^3*ln(3))*exp(x)*ln(x)+4*x^4*ln(3)^2*exp(x)^2)/x/ln(3)^2/ex
p(x)^2,x,method=_RETURNVERBOSE)

[Out]

1/ln(3)^2*exp(-2*x)*ln(x)^6+2/ln(3)^2*(8*ln(3)-x)*exp(-2*x)*ln(x)^5+1/ln(3)^2*(64*ln(3)^2-16*x*ln(3)+x^2)*exp(
-2*x)*ln(x)^4-2/ln(3)*x^2*exp(-x)*ln(x)^3-2/ln(3)*x^2*(8*ln(3)-x)*exp(-x)*ln(x)^2+x^4

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maxima [B]  time = 0.72, size = 99, normalized size = 3.19 \begin {gather*} \frac {x^{4} \log \relax (3)^{2} - 2 \, {\left (x^{2} \log \relax (3) \log \relax (x)^{3} - {\left (x^{3} \log \relax (3) - 8 \, x^{2} \log \relax (3)^{2}\right )} \log \relax (x)^{2}\right )} e^{\left (-x\right )} - {\left (2 \, {\left (x - 8 \, \log \relax (3)\right )} \log \relax (x)^{5} - \log \relax (x)^{6} - {\left (x^{2} - 16 \, x \log \relax (3) + 64 \, \log \relax (3)^{2}\right )} \log \relax (x)^{4}\right )} e^{\left (-2 \, x\right )}}{\log \relax (3)^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-2*x*log(x)^6+(-32*x*log(3)+4*x^2-2*x+6)*log(x)^5+(-128*x*log(3)^2+(32*x^2-16*x+80)*log(3)-2*x^3+2*
x^2-10*x)*log(x)^4+((2*x^3-4*x^2)*log(3)*exp(x)+256*log(3)^2-64*x*log(3)+4*x^2)*log(x)^3+((16*x^3-32*x^2)*log(
3)^2+(-2*x^4+6*x^3-6*x^2)*log(3))*exp(x)*log(x)^2+(-32*x^2*log(3)^2+4*x^3*log(3))*exp(x)*log(x)+4*x^4*log(3)^2
*exp(x)^2)/x/log(3)^2/exp(x)^2,x, algorithm="maxima")

[Out]

(x^4*log(3)^2 - 2*(x^2*log(3)*log(x)^3 - (x^3*log(3) - 8*x^2*log(3)^2)*log(x)^2)*e^(-x) - (2*(x - 8*log(3))*lo
g(x)^5 - log(x)^6 - (x^2 - 16*x*log(3) + 64*log(3)^2)*log(x)^4)*e^(-2*x))/log(3)^2

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mupad [F]  time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int -\frac {{\mathrm {e}}^{-2\,x}\,\left (2\,x\,{\ln \relax (x)}^6+{\ln \relax (x)}^3\,\left (64\,x\,\ln \relax (3)-256\,{\ln \relax (3)}^2-4\,x^2+{\mathrm {e}}^x\,\ln \relax (3)\,\left (4\,x^2-2\,x^3\right )\right )+{\ln \relax (x)}^4\,\left (10\,x-\ln \relax (3)\,\left (32\,x^2-16\,x+80\right )+128\,x\,{\ln \relax (3)}^2-2\,x^2+2\,x^3\right )+{\ln \relax (x)}^5\,\left (2\,x+32\,x\,\ln \relax (3)-4\,x^2-6\right )+{\mathrm {e}}^x\,\ln \relax (x)\,\left (32\,x^2\,{\ln \relax (3)}^2-4\,x^3\,\ln \relax (3)\right )-4\,x^4\,{\mathrm {e}}^{2\,x}\,{\ln \relax (3)}^2+{\mathrm {e}}^x\,{\ln \relax (x)}^2\,\left (\ln \relax (3)\,\left (2\,x^4-6\,x^3+6\,x^2\right )+{\ln \relax (3)}^2\,\left (32\,x^2-16\,x^3\right )\right )\right )}{x\,{\ln \relax (3)}^2} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp(-2*x)*(2*x*log(x)^6 + log(x)^3*(64*x*log(3) - 256*log(3)^2 - 4*x^2 + exp(x)*log(3)*(4*x^2 - 2*x^3))
+ log(x)^4*(10*x - log(3)*(32*x^2 - 16*x + 80) + 128*x*log(3)^2 - 2*x^2 + 2*x^3) + log(x)^5*(2*x + 32*x*log(3)
- 4*x^2 - 6) + exp(x)*log(x)*(32*x^2*log(3)^2 - 4*x^3*log(3)) - 4*x^4*exp(2*x)*log(3)^2 + exp(x)*log(x)^2*(lo
g(3)*(6*x^2 - 6*x^3 + 2*x^4) + log(3)^2*(32*x^2 - 16*x^3))))/(x*log(3)^2),x)

[Out]

int(-(exp(-2*x)*(2*x*log(x)^6 + log(x)^3*(64*x*log(3) - 256*log(3)^2 - 4*x^2 + exp(x)*log(3)*(4*x^2 - 2*x^3))
+ log(x)^4*(10*x - log(3)*(32*x^2 - 16*x + 80) + 128*x*log(3)^2 - 2*x^2 + 2*x^3) + log(x)^5*(2*x + 32*x*log(3)
- 4*x^2 - 6) + exp(x)*log(x)*(32*x^2*log(3)^2 - 4*x^3*log(3)) - 4*x^4*exp(2*x)*log(3)^2 + exp(x)*log(x)^2*(lo
g(3)*(6*x^2 - 6*x^3 + 2*x^4) + log(3)^2*(32*x^2 - 16*x^3))))/(x*log(3)^2), x)

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sympy [B]  time = 1.32, size = 131, normalized size = 4.23 \begin {gather*} x^{4} + \frac {\left (2 x^{3} \log {\relax (3 )}^{2} \log {\relax (x )}^{2} - 2 x^{2} \log {\relax (3 )}^{2} \log {\relax (x )}^{3} - 16 x^{2} \log {\relax (3 )}^{3} \log {\relax (x )}^{2}\right ) e^{- x} + \left (x^{2} \log {\relax (3 )} \log {\relax (x )}^{4} - 2 x \log {\relax (3 )} \log {\relax (x )}^{5} - 16 x \log {\relax (3 )}^{2} \log {\relax (x )}^{4} + \log {\relax (3 )} \log {\relax (x )}^{6} + 16 \log {\relax (3 )}^{2} \log {\relax (x )}^{5} + 64 \log {\relax (3 )}^{3} \log {\relax (x )}^{4}\right ) e^{- 2 x}}{\log {\relax (3 )}^{3}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-2*x*ln(x)**6+(-32*x*ln(3)+4*x**2-2*x+6)*ln(x)**5+(-128*x*ln(3)**2+(32*x**2-16*x+80)*ln(3)-2*x**3+2
*x**2-10*x)*ln(x)**4+((2*x**3-4*x**2)*ln(3)*exp(x)+256*ln(3)**2-64*x*ln(3)+4*x**2)*ln(x)**3+((16*x**3-32*x**2)
*ln(3)**2+(-2*x**4+6*x**3-6*x**2)*ln(3))*exp(x)*ln(x)**2+(-32*x**2*ln(3)**2+4*x**3*ln(3))*exp(x)*ln(x)+4*x**4*
ln(3)**2*exp(x)**2)/x/ln(3)**2/exp(x)**2,x)

[Out]

x**4 + ((2*x**3*log(3)**2*log(x)**2 - 2*x**2*log(3)**2*log(x)**3 - 16*x**2*log(3)**3*log(x)**2)*exp(-x) + (x**
2*log(3)*log(x)**4 - 2*x*log(3)*log(x)**5 - 16*x*log(3)**2*log(x)**4 + log(3)*log(x)**6 + 16*log(3)**2*log(x)*
*5 + 64*log(3)**3*log(x)**4)*exp(-2*x))/log(3)**3

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