3.4.36 \(\int \frac {1}{18} ((27 x-18 x^2+3 x^3+(36 x-24 x^2+4 x^3) \log (\frac {4}{x})) \log (x)+(9 x-15 x^2+4 x^3+(36 x-36 x^2+8 x^3) \log (\frac {4}{x})) \log ^2(x)+e^{2 e^x} ((3 x+4 x \log (\frac {4}{x})) \log (x)+(x+3 e^x x^2+(4 x+4 e^x x^2) \log (\frac {4}{x})) \log ^2(x))+e^{e^x} ((18 x-6 x^2+(24 x-8 x^2) \log (\frac {4}{x})) \log (x)+(6 x-5 x^2+e^x (9 x^2-3 x^3)+(24 x-12 x^2+e^x (12 x^2-4 x^3)) \log (\frac {4}{x})) \log ^2(x))) \, dx\)

Optimal. Leaf size=33 \[ \frac {1}{9} \left (3+e^{e^x}-x\right )^2 x^2 \left (\frac {3}{4}+\log \left (\frac {4}{x}\right )\right ) \log ^2(x) \]

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Rubi [F]  time = 40.85, 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 {1}{18} \left (\left (27 x-18 x^2+3 x^3+\left (36 x-24 x^2+4 x^3\right ) \log \left (\frac {4}{x}\right )\right ) \log (x)+\left (9 x-15 x^2+4 x^3+\left (36 x-36 x^2+8 x^3\right ) \log \left (\frac {4}{x}\right )\right ) \log ^2(x)+e^{2 e^x} \left (\left (3 x+4 x \log \left (\frac {4}{x}\right )\right ) \log (x)+\left (x+3 e^x x^2+\left (4 x+4 e^x x^2\right ) \log \left (\frac {4}{x}\right )\right ) \log ^2(x)\right )+e^{e^x} \left (\left (18 x-6 x^2+\left (24 x-8 x^2\right ) \log \left (\frac {4}{x}\right )\right ) \log (x)+\left (6 x-5 x^2+e^x \left (9 x^2-3 x^3\right )+\left (24 x-12 x^2+e^x \left (12 x^2-4 x^3\right )\right ) \log \left (\frac {4}{x}\right )\right ) \log ^2(x)\right )\right ) \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[((27*x - 18*x^2 + 3*x^3 + (36*x - 24*x^2 + 4*x^3)*Log[4/x])*Log[x] + (9*x - 15*x^2 + 4*x^3 + (36*x - 36*x^
2 + 8*x^3)*Log[4/x])*Log[x]^2 + E^(2*E^x)*((3*x + 4*x*Log[4/x])*Log[x] + (x + 3*E^x*x^2 + (4*x + 4*E^x*x^2)*Lo
g[4/x])*Log[x]^2) + E^E^x*((18*x - 6*x^2 + (24*x - 8*x^2)*Log[4/x])*Log[x] + (6*x - 5*x^2 + E^x*(9*x^2 - 3*x^3
) + (24*x - 12*x^2 + E^x*(12*x^2 - 4*x^3))*Log[4/x])*Log[x]^2))/18,x]

[Out]

(5*x^2)/8 - (13*x^3)/81 + x^4/72 + (x^2*Log[4/x])/2 - (4*x^3*Log[4/x])/27 + (x^4*Log[4/x])/72 - (x^4*(1 + Log[
4/x]))/72 - (x^2*(5 + 4*Log[4/x]))/8 + (x^3*(13 + 12*Log[4/x]))/81 - (3*x^2*Log[x])/4 + (x^3*Log[x])/3 - (x^4*
Log[x])/24 - x^2*Log[4/x]*Log[x] + (4*x^3*Log[4/x]*Log[x])/9 - (x^4*Log[4/x]*Log[x])/18 + (x^2*(3 + 4*Log[4/x]
)*Log[x])/4 - (x^3*(3 + 4*Log[4/x])*Log[x])/9 + (x^4*(3 + 4*Log[4/x])*Log[x])/72 + (3*x^2*Log[x]^2)/4 - (x^3*L
og[x]^2)/2 + (x^4*Log[x]^2)/12 + x^2*Log[4/x]*Log[x]^2 - (2*x^3*Log[4/x]*Log[x]^2)/3 + (x^4*Log[4/x]*Log[x]^2)
/9 + Log[x]*Defer[Int][E^E^x*x, x] + (4*Log[4/x]*Log[x]*Defer[Int][E^E^x*x, x])/3 + (Log[x]*Defer[Int][E^(2*E^
x)*x, x])/6 + (2*Log[4/x]*Log[x]*Defer[Int][E^(2*E^x)*x, x])/9 - (Log[x]*Defer[Int][E^E^x*x^2, x])/3 - (4*Log[
4/x]*Log[x]*Defer[Int][E^E^x*x^2, x])/9 + Defer[Int][E^E^x*x*Log[x]^2, x]/3 + Defer[Int][E^(2*E^x)*x*Log[x]^2,
x]/18 - (5*Defer[Int][E^E^x*x^2*Log[x]^2, x])/18 + Defer[Int][E^(E^x + x)*x^2*Log[x]^2, x]/2 + Defer[Int][E^(
2*E^x + x)*x^2*Log[x]^2, x]/6 - Defer[Int][E^(E^x + x)*x^3*Log[x]^2, x]/6 + (4*Defer[Int][E^E^x*x*Log[4/x]*Log
[x]^2, x])/3 + (2*Defer[Int][E^(2*E^x)*x*Log[4/x]*Log[x]^2, x])/9 - (2*Defer[Int][E^E^x*x^2*Log[4/x]*Log[x]^2,
x])/3 + (2*Defer[Int][E^(E^x + x)*x^2*Log[4/x]*Log[x]^2, x])/3 + (2*Defer[Int][E^(2*E^x + x)*x^2*Log[4/x]*Log
[x]^2, x])/9 - (2*Defer[Int][E^(E^x + x)*x^3*Log[4/x]*Log[x]^2, x])/9 - Defer[Int][Defer[Int][E^E^x*x, x]/x, x
] - (4*Log[4/x]*Defer[Int][Defer[Int][E^E^x*x, x]/x, x])/3 + (4*Log[x]*Defer[Int][Defer[Int][E^E^x*x, x]/x, x]
)/3 - Defer[Int][Defer[Int][E^(2*E^x)*x, x]/x, x]/6 - (2*Log[4/x]*Defer[Int][Defer[Int][E^(2*E^x)*x, x]/x, x])
/9 + (2*Log[x]*Defer[Int][Defer[Int][E^(2*E^x)*x, x]/x, x])/9 + Defer[Int][Defer[Int][E^E^x*x^2, x]/x, x]/3 +
(4*Log[4/x]*Defer[Int][Defer[Int][E^E^x*x^2, x]/x, x])/9 - (4*Log[x]*Defer[Int][Defer[Int][E^E^x*x^2, x]/x, x]
)/9 - (8*Defer[Int][Defer[Int][Defer[Int][E^E^x*x, x]/x, x]/x, x])/3 - (4*Defer[Int][Defer[Int][Defer[Int][E^(
2*E^x)*x, x]/x, x]/x, x])/9 + (8*Defer[Int][Defer[Int][Defer[Int][E^E^x*x^2, x]/x, x]/x, x])/9

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{18} \int \left (\left (27 x-18 x^2+3 x^3+\left (36 x-24 x^2+4 x^3\right ) \log \left (\frac {4}{x}\right )\right ) \log (x)+\left (9 x-15 x^2+4 x^3+\left (36 x-36 x^2+8 x^3\right ) \log \left (\frac {4}{x}\right )\right ) \log ^2(x)+e^{2 e^x} \left (\left (3 x+4 x \log \left (\frac {4}{x}\right )\right ) \log (x)+\left (x+3 e^x x^2+\left (4 x+4 e^x x^2\right ) \log \left (\frac {4}{x}\right )\right ) \log ^2(x)\right )+e^{e^x} \left (\left (18 x-6 x^2+\left (24 x-8 x^2\right ) \log \left (\frac {4}{x}\right )\right ) \log (x)+\left (6 x-5 x^2+e^x \left (9 x^2-3 x^3\right )+\left (24 x-12 x^2+e^x \left (12 x^2-4 x^3\right )\right ) \log \left (\frac {4}{x}\right )\right ) \log ^2(x)\right )\right ) \, dx\\ &=\frac {1}{18} \int \left (27 x-18 x^2+3 x^3+\left (36 x-24 x^2+4 x^3\right ) \log \left (\frac {4}{x}\right )\right ) \log (x) \, dx+\frac {1}{18} \int \left (9 x-15 x^2+4 x^3+\left (36 x-36 x^2+8 x^3\right ) \log \left (\frac {4}{x}\right )\right ) \log ^2(x) \, dx+\frac {1}{18} \int e^{2 e^x} \left (\left (3 x+4 x \log \left (\frac {4}{x}\right )\right ) \log (x)+\left (x+3 e^x x^2+\left (4 x+4 e^x x^2\right ) \log \left (\frac {4}{x}\right )\right ) \log ^2(x)\right ) \, dx+\frac {1}{18} \int e^{e^x} \left (\left (18 x-6 x^2+\left (24 x-8 x^2\right ) \log \left (\frac {4}{x}\right )\right ) \log (x)+\left (6 x-5 x^2+e^x \left (9 x^2-3 x^3\right )+\left (24 x-12 x^2+e^x \left (12 x^2-4 x^3\right )\right ) \log \left (\frac {4}{x}\right )\right ) \log ^2(x)\right ) \, dx\\ &=\frac {1}{18} \int (3-x)^2 x \left (3+4 \log \left (\frac {4}{x}\right )\right ) \log (x) \, dx+\frac {1}{18} \int (3-x) x \left (3-4 x-4 (-3+2 x) \log \left (\frac {4}{x}\right )\right ) \log ^2(x) \, dx+\frac {1}{18} \int e^{e^x} x \log (x) \left (18-6 x-8 (-3+x) \log \left (\frac {4}{x}\right )+\left (6-5 x-3 e^x (-3+x) x-4 \left (-6-3 \left (-1+e^x\right ) x+e^x x^2\right ) \log \left (\frac {4}{x}\right )\right ) \log (x)\right ) \, dx+\frac {1}{18} \int e^{2 e^x} x \log (x) \left (3+\log (x)+3 e^x x \log (x)+4 \log \left (\frac {4}{x}\right ) \left (1+\log (x)+e^x x \log (x)\right )\right ) \, dx\\ &=\frac {1}{18} \int \left (9 x \left (3+4 \log \left (\frac {4}{x}\right )\right ) \log (x)-6 x^2 \left (3+4 \log \left (\frac {4}{x}\right )\right ) \log (x)+x^3 \left (3+4 \log \left (\frac {4}{x}\right )\right ) \log (x)\right ) \, dx+\frac {1}{18} \int \left (-3 x \left (-3+4 x-12 \log \left (\frac {4}{x}\right )+8 x \log \left (\frac {4}{x}\right )\right ) \log ^2(x)+x^2 \left (-3+4 x-12 \log \left (\frac {4}{x}\right )+8 x \log \left (\frac {4}{x}\right )\right ) \log ^2(x)\right ) \, dx+\frac {1}{18} \int \left (e^{2 e^x+x} x^2 \left (3+4 \log \left (\frac {4}{x}\right )\right ) \log ^2(x)+e^{2 e^x} x \log (x) \left (3+4 \log \left (\frac {4}{x}\right )+\log (x)+4 \log \left (\frac {4}{x}\right ) \log (x)\right )\right ) \, dx+\frac {1}{18} \int \left (-e^{e^x+x} (-3+x) x^2 \left (3+4 \log \left (\frac {4}{x}\right )\right ) \log ^2(x)-e^{e^x} x \log (x) \left (-18+6 x-24 \log \left (\frac {4}{x}\right )+8 x \log \left (\frac {4}{x}\right )-6 \log (x)+5 x \log (x)-24 \log \left (\frac {4}{x}\right ) \log (x)+12 x \log \left (\frac {4}{x}\right ) \log (x)\right )\right ) \, dx\\ &=\frac {1}{18} \int x^3 \left (3+4 \log \left (\frac {4}{x}\right )\right ) \log (x) \, dx+\frac {1}{18} \int e^{2 e^x+x} x^2 \left (3+4 \log \left (\frac {4}{x}\right )\right ) \log ^2(x) \, dx-\frac {1}{18} \int e^{e^x+x} (-3+x) x^2 \left (3+4 \log \left (\frac {4}{x}\right )\right ) \log ^2(x) \, dx+\frac {1}{18} \int x^2 \left (-3+4 x-12 \log \left (\frac {4}{x}\right )+8 x \log \left (\frac {4}{x}\right )\right ) \log ^2(x) \, dx+\frac {1}{18} \int e^{2 e^x} x \log (x) \left (3+4 \log \left (\frac {4}{x}\right )+\log (x)+4 \log \left (\frac {4}{x}\right ) \log (x)\right ) \, dx-\frac {1}{18} \int e^{e^x} x \log (x) \left (-18+6 x-24 \log \left (\frac {4}{x}\right )+8 x \log \left (\frac {4}{x}\right )-6 \log (x)+5 x \log (x)-24 \log \left (\frac {4}{x}\right ) \log (x)+12 x \log \left (\frac {4}{x}\right ) \log (x)\right ) \, dx-\frac {1}{6} \int x \left (-3+4 x-12 \log \left (\frac {4}{x}\right )+8 x \log \left (\frac {4}{x}\right )\right ) \log ^2(x) \, dx-\frac {1}{3} \int x^2 \left (3+4 \log \left (\frac {4}{x}\right )\right ) \log (x) \, dx+\frac {1}{2} \int x \left (3+4 \log \left (\frac {4}{x}\right )\right ) \log (x) \, dx\\ &=\frac {1}{2} x^2 \log (x)-\frac {4}{27} x^3 \log (x)+\frac {1}{72} x^4 \log (x)+\frac {1}{4} x^2 \left (3+4 \log \left (\frac {4}{x}\right )\right ) \log (x)-\frac {1}{9} x^3 \left (3+4 \log \left (\frac {4}{x}\right )\right ) \log (x)+\frac {1}{72} x^4 \left (3+4 \log \left (\frac {4}{x}\right )\right ) \log (x)-\frac {1}{18} \int x^3 \left (1+\log \left (\frac {4}{x}\right )\right ) \, dx+\frac {1}{18} \int \left (3 e^{2 e^x+x} x^2 \log ^2(x)+4 e^{2 e^x+x} x^2 \log \left (\frac {4}{x}\right ) \log ^2(x)\right ) \, dx+\frac {1}{18} \int \left (-3 x^2 \log ^2(x)+4 x^3 \log ^2(x)-12 x^2 \log \left (\frac {4}{x}\right ) \log ^2(x)+8 x^3 \log \left (\frac {4}{x}\right ) \log ^2(x)\right ) \, dx-\frac {1}{18} \int \left (-3 e^{e^x+x} x^2 \left (3+4 \log \left (\frac {4}{x}\right )\right ) \log ^2(x)+e^{e^x+x} x^3 \left (3+4 \log \left (\frac {4}{x}\right )\right ) \log ^2(x)\right ) \, dx+\frac {1}{18} \int e^{2 e^x} x \log (x) \left (3+\log (x)+4 \log \left (\frac {4}{x}\right ) (1+\log (x))\right ) \, dx-\frac {1}{18} \int e^{e^x} x \log (x) \left (6 (-3+x)+(-6+5 x) \log (x)+4 \log \left (\frac {4}{x}\right ) (2 (-3+x)+3 (-2+x) \log (x))\right ) \, dx-\frac {1}{6} \int \left (-3 x \log ^2(x)+4 x^2 \log ^2(x)-12 x \log \left (\frac {4}{x}\right ) \log ^2(x)+8 x^2 \log \left (\frac {4}{x}\right ) \log ^2(x)\right ) \, dx+\frac {1}{3} \int \frac {1}{9} x^2 \left (13+12 \log \left (\frac {4}{x}\right )\right ) \, dx-\frac {1}{2} \int \frac {1}{2} x \left (5+4 \log \left (\frac {4}{x}\right )\right ) \, dx\\ &=-\frac {x^4}{288}-\frac {1}{72} x^4 \left (1+\log \left (\frac {4}{x}\right )\right )+\frac {1}{2} x^2 \log (x)-\frac {4}{27} x^3 \log (x)+\frac {1}{72} x^4 \log (x)+\frac {1}{4} x^2 \left (3+4 \log \left (\frac {4}{x}\right )\right ) \log (x)-\frac {1}{9} x^3 \left (3+4 \log \left (\frac {4}{x}\right )\right ) \log (x)+\frac {1}{72} x^4 \left (3+4 \log \left (\frac {4}{x}\right )\right ) \log (x)+\frac {1}{27} \int x^2 \left (13+12 \log \left (\frac {4}{x}\right )\right ) \, dx-\frac {1}{18} \int e^{e^x+x} x^3 \left (3+4 \log \left (\frac {4}{x}\right )\right ) \log ^2(x) \, dx+\frac {1}{18} \int \left (e^{2 e^x} x \left (3+4 \log \left (\frac {4}{x}\right )\right ) \log (x)+e^{2 e^x} x \left (1+4 \log \left (\frac {4}{x}\right )\right ) \log ^2(x)\right ) \, dx-\frac {1}{18} \int \left (2 e^{e^x} (-3+x) x \left (3+4 \log \left (\frac {4}{x}\right )\right ) \log (x)+e^{e^x} x \left (-6+5 x-24 \log \left (\frac {4}{x}\right )+12 x \log \left (\frac {4}{x}\right )\right ) \log ^2(x)\right ) \, dx-\frac {1}{6} \int x^2 \log ^2(x) \, dx+\frac {1}{6} \int e^{2 e^x+x} x^2 \log ^2(x) \, dx+\frac {1}{6} \int e^{e^x+x} x^2 \left (3+4 \log \left (\frac {4}{x}\right )\right ) \log ^2(x) \, dx+\frac {2}{9} \int x^3 \log ^2(x) \, dx+\frac {2}{9} \int e^{2 e^x+x} x^2 \log \left (\frac {4}{x}\right ) \log ^2(x) \, dx-\frac {1}{4} \int x \left (5+4 \log \left (\frac {4}{x}\right )\right ) \, dx+\frac {4}{9} \int x^3 \log \left (\frac {4}{x}\right ) \log ^2(x) \, dx+\frac {1}{2} \int x \log ^2(x) \, dx-\frac {2}{3} \int x^2 \log ^2(x) \, dx-\frac {2}{3} \int x^2 \log \left (\frac {4}{x}\right ) \log ^2(x) \, dx-\frac {4}{3} \int x^2 \log \left (\frac {4}{x}\right ) \log ^2(x) \, dx+2 \int x \log \left (\frac {4}{x}\right ) \log ^2(x) \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.20, size = 33, normalized size = 1.00 \begin {gather*} \frac {1}{36} \left (3+e^{e^x}-x\right )^2 x^2 \left (3+4 \log \left (\frac {4}{x}\right )\right ) \log ^2(x) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[((27*x - 18*x^2 + 3*x^3 + (36*x - 24*x^2 + 4*x^3)*Log[4/x])*Log[x] + (9*x - 15*x^2 + 4*x^3 + (36*x -
36*x^2 + 8*x^3)*Log[4/x])*Log[x]^2 + E^(2*E^x)*((3*x + 4*x*Log[4/x])*Log[x] + (x + 3*E^x*x^2 + (4*x + 4*E^x*x
^2)*Log[4/x])*Log[x]^2) + E^E^x*((18*x - 6*x^2 + (24*x - 8*x^2)*Log[4/x])*Log[x] + (6*x - 5*x^2 + E^x*(9*x^2 -
3*x^3) + (24*x - 12*x^2 + E^x*(12*x^2 - 4*x^3))*Log[4/x])*Log[x]^2))/18,x]

[Out]

((3 + E^E^x - x)^2*x^2*(3 + 4*Log[4/x])*Log[x]^2)/36

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fricas [B]  time = 1.17, size = 324, normalized size = 9.82 \begin {gather*} \frac {1}{9} \, {\left (x^{4} - 6 \, x^{3} + 9 \, x^{2}\right )} \log \left (\frac {4}{x}\right )^{3} + \frac {1}{3} \, {\left (x^{4} - 6 \, x^{3} + 9 \, x^{2}\right )} \log \relax (2)^{2} + \frac {1}{36} \, {\left (3 \, x^{4} - 18 \, x^{3} + 27 \, x^{2} - 16 \, {\left (x^{4} - 6 \, x^{3} + 9 \, x^{2}\right )} \log \relax (2)\right )} \log \left (\frac {4}{x}\right )^{2} + \frac {1}{36} \, {\left (4 \, x^{2} \log \left (\frac {4}{x}\right )^{3} + 12 \, x^{2} \log \relax (2)^{2} - {\left (16 \, x^{2} \log \relax (2) - 3 \, x^{2}\right )} \log \left (\frac {4}{x}\right )^{2} + 4 \, {\left (4 \, x^{2} \log \relax (2)^{2} - 3 \, x^{2} \log \relax (2)\right )} \log \left (\frac {4}{x}\right )\right )} e^{\left (2 \, e^{x}\right )} - \frac {1}{18} \, {\left (4 \, {\left (x^{3} - 3 \, x^{2}\right )} \log \left (\frac {4}{x}\right )^{3} + 12 \, {\left (x^{3} - 3 \, x^{2}\right )} \log \relax (2)^{2} + {\left (3 \, x^{3} - 9 \, x^{2} - 16 \, {\left (x^{3} - 3 \, x^{2}\right )} \log \relax (2)\right )} \log \left (\frac {4}{x}\right )^{2} + 4 \, {\left (4 \, {\left (x^{3} - 3 \, x^{2}\right )} \log \relax (2)^{2} - 3 \, {\left (x^{3} - 3 \, x^{2}\right )} \log \relax (2)\right )} \log \left (\frac {4}{x}\right )\right )} e^{\left (e^{x}\right )} + \frac {1}{9} \, {\left (4 \, {\left (x^{4} - 6 \, x^{3} + 9 \, x^{2}\right )} \log \relax (2)^{2} - 3 \, {\left (x^{4} - 6 \, x^{3} + 9 \, x^{2}\right )} \log \relax (2)\right )} \log \left (\frac {4}{x}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/18*(((4*exp(x)*x^2+4*x)*log(4/x)+3*exp(x)*x^2+x)*log(x)^2+(4*x*log(4/x)+3*x)*log(x))*exp(exp(x))^2
+1/18*((((-4*x^3+12*x^2)*exp(x)-12*x^2+24*x)*log(4/x)+(-3*x^3+9*x^2)*exp(x)-5*x^2+6*x)*log(x)^2+((-8*x^2+24*x)
*log(4/x)-6*x^2+18*x)*log(x))*exp(exp(x))+1/18*((8*x^3-36*x^2+36*x)*log(4/x)+4*x^3-15*x^2+9*x)*log(x)^2+1/18*(
(4*x^3-24*x^2+36*x)*log(4/x)+3*x^3-18*x^2+27*x)*log(x),x, algorithm="fricas")

[Out]

1/9*(x^4 - 6*x^3 + 9*x^2)*log(4/x)^3 + 1/3*(x^4 - 6*x^3 + 9*x^2)*log(2)^2 + 1/36*(3*x^4 - 18*x^3 + 27*x^2 - 16
*(x^4 - 6*x^3 + 9*x^2)*log(2))*log(4/x)^2 + 1/36*(4*x^2*log(4/x)^3 + 12*x^2*log(2)^2 - (16*x^2*log(2) - 3*x^2)
*log(4/x)^2 + 4*(4*x^2*log(2)^2 - 3*x^2*log(2))*log(4/x))*e^(2*e^x) - 1/18*(4*(x^3 - 3*x^2)*log(4/x)^3 + 12*(x
^3 - 3*x^2)*log(2)^2 + (3*x^3 - 9*x^2 - 16*(x^3 - 3*x^2)*log(2))*log(4/x)^2 + 4*(4*(x^3 - 3*x^2)*log(2)^2 - 3*
(x^3 - 3*x^2)*log(2))*log(4/x))*e^(e^x) + 1/9*(4*(x^4 - 6*x^3 + 9*x^2)*log(2)^2 - 3*(x^4 - 6*x^3 + 9*x^2)*log(
2))*log(4/x)

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giac [B]  time = 0.54, size = 227, normalized size = 6.88 \begin {gather*} \frac {2}{9} \, x^{4} \log \relax (2) \log \relax (x)^{2} - \frac {1}{9} \, x^{4} \log \relax (x)^{3} + \frac {1}{12} \, x^{4} \log \relax (x)^{2} - \frac {4}{3} \, x^{3} \log \relax (2) \log \relax (x)^{2} + \frac {2}{9} \, x^{2} e^{\left (2 \, e^{x}\right )} \log \relax (2) \log \relax (x)^{2} + \frac {2}{3} \, x^{3} \log \relax (x)^{3} - \frac {1}{9} \, x^{2} e^{\left (2 \, e^{x}\right )} \log \relax (x)^{3} - \frac {1}{2} \, x^{3} \log \relax (x)^{2} + \frac {1}{12} \, x^{2} e^{\left (2 \, e^{x}\right )} \log \relax (x)^{2} + 2 \, x^{2} \log \relax (2) \log \relax (x)^{2} - x^{2} \log \relax (x)^{3} + \frac {3}{4} \, x^{2} \log \relax (x)^{2} - \frac {1}{18} \, {\left (8 \, x^{3} e^{\left (x + e^{x}\right )} \log \relax (2) \log \relax (x)^{2} - 4 \, x^{3} e^{\left (x + e^{x}\right )} \log \relax (x)^{3} + 3 \, x^{3} e^{\left (x + e^{x}\right )} \log \relax (x)^{2} - 24 \, x^{2} e^{\left (x + e^{x}\right )} \log \relax (2) \log \relax (x)^{2} + 12 \, x^{2} e^{\left (x + e^{x}\right )} \log \relax (x)^{3} - 9 \, x^{2} e^{\left (x + e^{x}\right )} \log \relax (x)^{2}\right )} e^{\left (-x\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/18*(((4*exp(x)*x^2+4*x)*log(4/x)+3*exp(x)*x^2+x)*log(x)^2+(4*x*log(4/x)+3*x)*log(x))*exp(exp(x))^2
+1/18*((((-4*x^3+12*x^2)*exp(x)-12*x^2+24*x)*log(4/x)+(-3*x^3+9*x^2)*exp(x)-5*x^2+6*x)*log(x)^2+((-8*x^2+24*x)
*log(4/x)-6*x^2+18*x)*log(x))*exp(exp(x))+1/18*((8*x^3-36*x^2+36*x)*log(4/x)+4*x^3-15*x^2+9*x)*log(x)^2+1/18*(
(4*x^3-24*x^2+36*x)*log(4/x)+3*x^3-18*x^2+27*x)*log(x),x, algorithm="giac")

[Out]

2/9*x^4*log(2)*log(x)^2 - 1/9*x^4*log(x)^3 + 1/12*x^4*log(x)^2 - 4/3*x^3*log(2)*log(x)^2 + 2/9*x^2*e^(2*e^x)*l
og(2)*log(x)^2 + 2/3*x^3*log(x)^3 - 1/9*x^2*e^(2*e^x)*log(x)^3 - 1/2*x^3*log(x)^2 + 1/12*x^2*e^(2*e^x)*log(x)^
2 + 2*x^2*log(2)*log(x)^2 - x^2*log(x)^3 + 3/4*x^2*log(x)^2 - 1/18*(8*x^3*e^(x + e^x)*log(2)*log(x)^2 - 4*x^3*
e^(x + e^x)*log(x)^3 + 3*x^3*e^(x + e^x)*log(x)^2 - 24*x^2*e^(x + e^x)*log(2)*log(x)^2 + 12*x^2*e^(x + e^x)*lo
g(x)^3 - 9*x^2*e^(x + e^x)*log(x)^2)*e^(-x)

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maple [B]  time = 2.68, size = 209, normalized size = 6.33

method	result	size
risch	\(-\frac {x^{3} \ln \relax (x )^{2}}{2}+\frac {4 \ln \relax (x )^{2} {\mathrm e}^{{\mathrm e}^{x}} \ln \relax (2) x^{2}}{3}+\frac {3 x^{2} \ln \relax (x )^{2}}{4}+\frac {\ln \relax (x )^{2} {\mathrm e}^{{\mathrm e}^{x}} x^{2}}{2}-\frac {4 \ln \relax (x )^{2} \ln \relax (2) x^{3}}{3}+2 x^{2} \ln \relax (2) \ln \relax (x )^{2}+\frac {x^{4} \ln \relax (x )^{2}}{12}+\frac {2 \,{\mathrm e}^{2 \,{\mathrm e}^{x}} \ln \relax (x )^{2} \ln \relax (2) x^{2}}{9}-\frac {4 \ln \relax (x )^{2} {\mathrm e}^{{\mathrm e}^{x}} \ln \relax (2) x^{3}}{9}+\frac {{\mathrm e}^{2 \,{\mathrm e}^{x}} \ln \relax (x )^{2} x^{2}}{12}-\frac {{\mathrm e}^{2 \,{\mathrm e}^{x}} x^{2} \ln \relax (x )^{3}}{9}+\frac {2 \ln \relax (x )^{2} \ln \relax (2) x^{4}}{9}+\frac {2 \ln \relax (x )^{3} {\mathrm e}^{{\mathrm e}^{x}} x^{3}}{9}-\frac {2 \ln \relax (x )^{3} {\mathrm e}^{{\mathrm e}^{x}} x^{2}}{3}-\frac {\ln \relax (x )^{2} {\mathrm e}^{{\mathrm e}^{x}} x^{3}}{6}-x^{2} \ln \relax (x )^{3}+\frac {2 x^{3} \ln \relax (x )^{3}}{3}-\frac {x^{4} \ln \relax (x )^{3}}{9}\)	\(209\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/18*(((4*exp(x)*x^2+4*x)*ln(4/x)+3*exp(x)*x^2+x)*ln(x)^2+(4*x*ln(4/x)+3*x)*ln(x))*exp(exp(x))^2+1/18*((((
-4*x^3+12*x^2)*exp(x)-12*x^2+24*x)*ln(4/x)+(-3*x^3+9*x^2)*exp(x)-5*x^2+6*x)*ln(x)^2+((-8*x^2+24*x)*ln(4/x)-6*x
^2+18*x)*ln(x))*exp(exp(x))+1/18*((8*x^3-36*x^2+36*x)*ln(4/x)+4*x^3-15*x^2+9*x)*ln(x)^2+1/18*((4*x^3-24*x^2+36
*x)*ln(4/x)+3*x^3-18*x^2+27*x)*ln(x),x,method=_RETURNVERBOSE)

[Out]

-1/2*x^3*ln(x)^2+4/3*ln(x)^2*exp(exp(x))*ln(2)*x^2+3/4*x^2*ln(x)^2+1/2*ln(x)^2*exp(exp(x))*x^2-4/3*ln(x)^2*ln(
2)*x^3+2*x^2*ln(2)*ln(x)^2+1/12*x^4*ln(x)^2+2/9*exp(2*exp(x))*ln(x)^2*ln(2)*x^2-4/9*ln(x)^2*exp(exp(x))*ln(2)*
x^3+1/12*exp(2*exp(x))*ln(x)^2*x^2-1/9*exp(2*exp(x))*x^2*ln(x)^3+2/9*ln(x)^2*ln(2)*x^4+2/9*ln(x)^3*exp(exp(x))
*x^3-2/3*ln(x)^3*exp(exp(x))*x^2-1/6*ln(x)^2*exp(exp(x))*x^3-x^2*ln(x)^3+2/3*x^3*ln(x)^3-1/9*x^4*ln(x)^3

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maxima [B]  time = 0.57, size = 223, normalized size = 6.76 \begin {gather*} \frac {1}{36} \, {\left (3 \, x^{4} - 18 \, x^{3} + 27 \, x^{2} + 4 \, {\left (x^{4} - 6 \, x^{3} + 9 \, x^{2}\right )} \log \left (\frac {4}{x}\right )\right )} \log \relax (x)^{2} + \frac {1}{36} \, {\left (x^{2} {\left (8 \, \log \relax (2) + 3\right )} \log \relax (x)^{2} - 4 \, x^{2} \log \relax (x)^{3}\right )} e^{\left (2 \, e^{x}\right )} + \frac {1}{18} \, {\left (4 \, {\left (x^{3} - 3 \, x^{2}\right )} \log \relax (x)^{3} - {\left (x^{3} {\left (8 \, \log \relax (2) + 3\right )} - 3 \, x^{2} {\left (8 \, \log \relax (2) + 3\right )}\right )} \log \relax (x)^{2}\right )} e^{\left (e^{x}\right )} - \frac {1}{108} \, {\left (6 \, x^{4} {\left (2 \, \log \relax (2) + 1\right )} - 4 \, x^{3} {\left (24 \, \log \relax (2) + 13\right )} + 27 \, x^{2} {\left (8 \, \log \relax (2) + 5\right )} - 6 \, {\left (x^{4} - 8 \, x^{3} + 18 \, x^{2}\right )} \log \relax (x)\right )} \log \relax (x) + \frac {1}{108} \, {\left (6 \, x^{4} - 52 \, x^{3} + 135 \, x^{2} + 6 \, {\left (x^{4} - 8 \, x^{3} + 18 \, x^{2}\right )} \log \left (\frac {4}{x}\right )\right )} \log \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/18*(((4*exp(x)*x^2+4*x)*log(4/x)+3*exp(x)*x^2+x)*log(x)^2+(4*x*log(4/x)+3*x)*log(x))*exp(exp(x))^2
+1/18*((((-4*x^3+12*x^2)*exp(x)-12*x^2+24*x)*log(4/x)+(-3*x^3+9*x^2)*exp(x)-5*x^2+6*x)*log(x)^2+((-8*x^2+24*x)
*log(4/x)-6*x^2+18*x)*log(x))*exp(exp(x))+1/18*((8*x^3-36*x^2+36*x)*log(4/x)+4*x^3-15*x^2+9*x)*log(x)^2+1/18*(
(4*x^3-24*x^2+36*x)*log(4/x)+3*x^3-18*x^2+27*x)*log(x),x, algorithm="maxima")

[Out]

1/36*(3*x^4 - 18*x^3 + 27*x^2 + 4*(x^4 - 6*x^3 + 9*x^2)*log(4/x))*log(x)^2 + 1/36*(x^2*(8*log(2) + 3)*log(x)^2
- 4*x^2*log(x)^3)*e^(2*e^x) + 1/18*(4*(x^3 - 3*x^2)*log(x)^3 - (x^3*(8*log(2) + 3) - 3*x^2*(8*log(2) + 3))*lo
g(x)^2)*e^(e^x) - 1/108*(6*x^4*(2*log(2) + 1) - 4*x^3*(24*log(2) + 13) + 27*x^2*(8*log(2) + 5) - 6*(x^4 - 8*x^
3 + 18*x^2)*log(x))*log(x) + 1/108*(6*x^4 - 52*x^3 + 135*x^2 + 6*(x^4 - 8*x^3 + 18*x^2)*log(4/x))*log(x)

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mupad [F]  time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int \frac {{\mathrm {e}}^{2\,{\mathrm {e}}^x}\,\left (\left (x+3\,x^2\,{\mathrm {e}}^x+\ln \left (\frac {4}{x}\right )\,\left (4\,x+4\,x^2\,{\mathrm {e}}^x\right )\right )\,{\ln \relax (x)}^2+\left (3\,x+4\,x\,\ln \left (\frac {4}{x}\right )\right )\,\ln \relax (x)\right )}{18}+\frac {\ln \relax (x)\,\left (27\,x+\ln \left (\frac {4}{x}\right )\,\left (4\,x^3-24\,x^2+36\,x\right )-18\,x^2+3\,x^3\right )}{18}+\frac {{\mathrm {e}}^{{\mathrm {e}}^x}\,\left (\left (6\,x+{\mathrm {e}}^x\,\left (9\,x^2-3\,x^3\right )+\ln \left (\frac {4}{x}\right )\,\left (24\,x+{\mathrm {e}}^x\,\left (12\,x^2-4\,x^3\right )-12\,x^2\right )-5\,x^2\right )\,{\ln \relax (x)}^2+\left (18\,x+\ln \left (\frac {4}{x}\right )\,\left (24\,x-8\,x^2\right )-6\,x^2\right )\,\ln \relax (x)\right )}{18}+\frac {{\ln \relax (x)}^2\,\left (9\,x+\ln \left (\frac {4}{x}\right )\,\left (8\,x^3-36\,x^2+36\,x\right )-15\,x^2+4\,x^3\right )}{18} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(2*exp(x))*(log(x)^2*(x + 3*x^2*exp(x) + log(4/x)*(4*x + 4*x^2*exp(x))) + log(x)*(3*x + 4*x*log(4/x)))
)/18 + (log(x)*(27*x + log(4/x)*(36*x - 24*x^2 + 4*x^3) - 18*x^2 + 3*x^3))/18 + (exp(exp(x))*(log(x)*(18*x + l
og(4/x)*(24*x - 8*x^2) - 6*x^2) + log(x)^2*(6*x + exp(x)*(9*x^2 - 3*x^3) + log(4/x)*(24*x + exp(x)*(12*x^2 - 4
*x^3) - 12*x^2) - 5*x^2)))/18 + (log(x)^2*(9*x + log(4/x)*(36*x - 36*x^2 + 8*x^3) - 15*x^2 + 4*x^3))/18,x)

[Out]

int((exp(2*exp(x))*(log(x)^2*(x + 3*x^2*exp(x) + log(4/x)*(4*x + 4*x^2*exp(x))) + log(x)*(3*x + 4*x*log(4/x)))
)/18 + (log(x)*(27*x + log(4/x)*(36*x - 24*x^2 + 4*x^3) - 18*x^2 + 3*x^3))/18 + (exp(exp(x))*(log(x)*(18*x + l
og(4/x)*(24*x - 8*x^2) - 6*x^2) + log(x)^2*(6*x + exp(x)*(9*x^2 - 3*x^3) + log(4/x)*(24*x + exp(x)*(12*x^2 - 4
*x^3) - 12*x^2) - 5*x^2)))/18 + (log(x)^2*(9*x + log(4/x)*(36*x - 36*x^2 + 8*x^3) - 15*x^2 + 4*x^3))/18, x)

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sympy [B]  time = 12.33, size = 187, normalized size = 5.67 \begin {gather*} \left (- \frac {x^{4}}{9} + \frac {2 x^{3}}{3} - x^{2}\right ) \log {\relax (x )}^{3} + \frac {\left (- 72 x^{2} \log {\relax (x )}^{3} + 54 x^{2} \log {\relax (x )}^{2} + 144 x^{2} \log {\relax (2 )} \log {\relax (x )}^{2}\right ) e^{2 e^{x}}}{648} + \left (\frac {x^{4}}{12} + \frac {2 x^{4} \log {\relax (2 )}}{9} - \frac {4 x^{3} \log {\relax (2 )}}{3} - \frac {x^{3}}{2} + \frac {3 x^{2}}{4} + 2 x^{2} \log {\relax (2 )}\right ) \log {\relax (x )}^{2} + \frac {\left (144 x^{3} \log {\relax (x )}^{3} - 288 x^{3} \log {\relax (2 )} \log {\relax (x )}^{2} - 108 x^{3} \log {\relax (x )}^{2} - 432 x^{2} \log {\relax (x )}^{3} + 324 x^{2} \log {\relax (x )}^{2} + 864 x^{2} \log {\relax (2 )} \log {\relax (x )}^{2}\right ) e^{e^{x}}}{648} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/18*(((4*exp(x)*x**2+4*x)*ln(4/x)+3*exp(x)*x**2+x)*ln(x)**2+(4*x*ln(4/x)+3*x)*ln(x))*exp(exp(x))**2
+1/18*((((-4*x**3+12*x**2)*exp(x)-12*x**2+24*x)*ln(4/x)+(-3*x**3+9*x**2)*exp(x)-5*x**2+6*x)*ln(x)**2+((-8*x**2
+24*x)*ln(4/x)-6*x**2+18*x)*ln(x))*exp(exp(x))+1/18*((8*x**3-36*x**2+36*x)*ln(4/x)+4*x**3-15*x**2+9*x)*ln(x)**
2+1/18*((4*x**3-24*x**2+36*x)*ln(4/x)+3*x**3-18*x**2+27*x)*ln(x),x)

[Out]

(-x**4/9 + 2*x**3/3 - x**2)*log(x)**3 + (-72*x**2*log(x)**3 + 54*x**2*log(x)**2 + 144*x**2*log(2)*log(x)**2)*e
xp(2*exp(x))/648 + (x**4/12 + 2*x**4*log(2)/9 - 4*x**3*log(2)/3 - x**3/2 + 3*x**2/4 + 2*x**2*log(2))*log(x)**2
+ (144*x**3*log(x)**3 - 288*x**3*log(2)*log(x)**2 - 108*x**3*log(x)**2 - 432*x**2*log(x)**3 + 324*x**2*log(x)
**2 + 864*x**2*log(2)*log(x)**2)*exp(exp(x))/648

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