∫ e(1−x) log(x)+(−x+x2) log2(x)+(−2ex+2x2 log(x)) log(−3+3x)+(e(1−x)+(−x+x2) log(x)) log2(−3+3x)+(e(−1+x)−x+x2+(e(1−x)+x−x2) log(x)+(e(1−x)+x−x2) log2(−3+3x)) log(−x+x log(x)+x log2(−3+3x))________________________________________________________________________________________________________________________________________________________ (x2−x3+(−x2+x3) log(x)+(−x2+x3) log2(−3+3x)) log2(−x+x log(x)+x log2(−3+3x)) dx

3.94.21 \(\int \frac {e (1-x) \log (x)+(-x+x^2) \log ^2(x)+(-2 e x+2 x^2 \log (x)) \log (-3+3 x)+(e (1-x)+(-x+x^2) \log (x)) \log ^2(-3+3 x)+(e (-1+x)-x+x^2+(e (1-x)+x-x^2) \log (x)+(e (1-x)+x-x^2) \log ^2(-3+3 x)) \log (-x+x \log (x)+x \log ^2(-3+3 x))}{(x^2-x^3+(-x^2+x^3) \log (x)+(-x^2+x^3) \log ^2(-3+3 x)) \log ^2(-x+x \log (x)+x \log ^2(-3+3 x))} \, dx\)

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

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Rubi [F] time = 76.45, 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 (1-x) \log (x)+\left (-x+x^2\right ) \log ^2(x)+\left (-2 e x+2 x^2 \log (x)\right ) \log (-3+3 x)+\left (e (1-x)+\left (-x+x^2\right ) \log (x)\right ) \log ^2(-3+3 x)+\left (e (-1+x)-x+x^2+\left (e (1-x)+x-x^2\right ) \log (x)+\left (e (1-x)+x-x^2\right ) \log ^2(-3+3 x)\right ) \log \left (-x+x \log (x)+x \log ^2(-3+3 x)\right )}{\left (x^2-x^3+\left (-x^2+x^3\right ) \log (x)+\left (-x^2+x^3\right ) \log ^2(-3+3 x)\right ) \log ^2\left (-x+x \log (x)+x \log ^2(-3+3 x)\right )} \, dx \end {gather*}

Veriﬁcation is not applicable to the result.

[In]

Int[(E*(1 - x)*Log[x] + (-x + x^2)*Log[x]^2 + (-2*E*x + 2*x^2*Log[x])*Log[-3 + 3*x] + (E*(1 - x) + (-x + x^2)*

Log[x])*Log[-3 + 3*x]^2 + (E*(-1 + x) - x + x^2 + (E*(1 - x) + x - x^2)*Log[x] + (E*(1 - x) + x - x^2)*Log[-3

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

x]^2)*Log[-x + x*Log[x] + x*Log[-3 + 3*x]^2]^2),x]

[Out]

E*Defer[Int][Log[x]/((1 - Log[3*(-1 + x)]^2 - Log[x])*Log[-x + x*Log[3*(-1 + x)]^2 + x*Log[x]]^2), x] + E*Defe

r[Int][Log[x]/((1 - x)*(1 - Log[3*(-1 + x)]^2 - Log[x])*Log[-x + x*Log[3*(-1 + x)]^2 + x*Log[x]]^2), x] + E*De

fer[Int][Log[x]/((-1 + x)*(1 - Log[3*(-1 + x)]^2 - Log[x])*Log[-x + x*Log[3*(-1 + x)]^2 + x*Log[x]]^2), x] + E

*Defer[Int][Log[x]/(x^2*(1 - Log[3*(-1 + x)]^2 - Log[x])*Log[-x + x*Log[3*(-1 + x)]^2 + x*Log[x]]^2), x] + E*D

efer[Int][Log[x]/(x*(1 - Log[3*(-1 + x)]^2 - Log[x])*Log[-x + x*Log[3*(-1 + x)]^2 + x*Log[x]]^2), x] + 2*Defer

[Int][Log[x]^2/((1 - Log[3*(-1 + x)]^2 - Log[x])*Log[-x + x*Log[3*(-1 + x)]^2 + x*Log[x]]^2), x] + Defer[Int][

Log[x]^2/((1 - x)*(1 - Log[3*(-1 + x)]^2 - Log[x])*Log[-x + x*Log[3*(-1 + x)]^2 + x*Log[x]]^2), x] + Defer[Int

][Log[x]^2/((-1 + x)*(1 - Log[3*(-1 + x)]^2 - Log[x])*Log[-x + x*Log[3*(-1 + x)]^2 + x*Log[x]]^2), x] + Defer[

Int][(x*Log[x]^2)/((1 - Log[3*(-1 + x)]^2 - Log[x])*Log[-x + x*Log[3*(-1 + x)]^2 + x*Log[x]]^2), x] + E*Defer[

Int][Log[x]/((-1 + Log[3*(-1 + x)]^2 + Log[x])*Log[-x + x*Log[3*(-1 + x)]^2 + x*Log[x]]^2), x] + E*Defer[Int][

Log[x]/(x*(-1 + Log[3*(-1 + x)]^2 + Log[x])*Log[-x + x*Log[3*(-1 + x)]^2 + x*Log[x]]^2), x] + 2*Defer[Int][Log

[x]^2/((-1 + Log[3*(-1 + x)]^2 + Log[x])*Log[-x + x*Log[3*(-1 + x)]^2 + x*Log[x]]^2), x] + Defer[Int][Log[x]^2

/(x*(-1 + Log[3*(-1 + x)]^2 + Log[x])*Log[-x + x*Log[3*(-1 + x)]^2 + x*Log[x]]^2), x] + Defer[Int][(x*Log[x]^2

)/((-1 + Log[3*(-1 + x)]^2 + Log[x])*Log[-x + x*Log[3*(-1 + x)]^2 + x*Log[x]]^2), x] + 2*E*Defer[Int][Log[-3 +

3*x]/((1 - Log[3*(-1 + x)]^2 - Log[x])*Log[-x + x*Log[3*(-1 + x)]^2 + x*Log[x]]^2), x] + 2*E*Defer[Int][Log[-

3 + 3*x]/((-1 + x)*(1 - Log[3*(-1 + x)]^2 - Log[x])*Log[-x + x*Log[3*(-1 + x)]^2 + x*Log[x]]^2), x] + 2*Defer[

Int][(Log[x]*Log[-3 + 3*x])/((1 - Log[3*(-1 + x)]^2 - Log[x])*Log[-x + x*Log[3*(-1 + x)]^2 + x*Log[x]]^2), x]

+ 2*Defer[Int][(Log[x]*Log[-3 + 3*x])/((1 - x)*(1 - Log[3*(-1 + x)]^2 - Log[x])*Log[-x + x*Log[3*(-1 + x)]^2 +

x*Log[x]]^2), x] + 2*Defer[Int][(x*Log[x]*Log[-3 + 3*x])/((1 - Log[3*(-1 + x)]^2 - Log[x])*Log[-x + x*Log[3*(

-1 + x)]^2 + x*Log[x]]^2), x] + 2*E*Defer[Int][Log[-3 + 3*x]/((-1 + Log[3*(-1 + x)]^2 + Log[x])*Log[-x + x*Log

[3*(-1 + x)]^2 + x*Log[x]]^2), x] + 2*E*Defer[Int][Log[-3 + 3*x]/(x*(-1 + Log[3*(-1 + x)]^2 + Log[x])*Log[-x +

x*Log[3*(-1 + x)]^2 + x*Log[x]]^2), x] + 2*Defer[Int][(Log[x]*Log[-3 + 3*x])/((-1 + Log[3*(-1 + x)]^2 + Log[x

])*Log[-x + x*Log[3*(-1 + x)]^2 + x*Log[x]]^2), x] + 2*Defer[Int][(x*Log[x]*Log[-3 + 3*x])/((-1 + Log[3*(-1 +

x)]^2 + Log[x])*Log[-x + x*Log[3*(-1 + x)]^2 + x*Log[x]]^2), x] + E*Defer[Int][Log[-3 + 3*x]^2/((1 - Log[3*(-1

+ x)]^2 - Log[x])*Log[-x + x*Log[3*(-1 + x)]^2 + x*Log[x]]^2), x] + E*Defer[Int][Log[-3 + 3*x]^2/((1 - x)*(1

- Log[3*(-1 + x)]^2 - Log[x])*Log[-x + x*Log[3*(-1 + x)]^2 + x*Log[x]]^2), x] + E*Defer[Int][Log[-3 + 3*x]^2/(

(-1 + x)*(1 - Log[3*(-1 + x)]^2 - Log[x])*Log[-x + x*Log[3*(-1 + x)]^2 + x*Log[x]]^2), x] + E*Defer[Int][Log[-

3 + 3*x]^2/(x^2*(1 - Log[3*(-1 + x)]^2 - Log[x])*Log[-x + x*Log[3*(-1 + x)]^2 + x*Log[x]]^2), x] + E*Defer[Int

][Log[-3 + 3*x]^2/(x*(1 - Log[3*(-1 + x)]^2 - Log[x])*Log[-x + x*Log[3*(-1 + x)]^2 + x*Log[x]]^2), x] + 2*Defe

r[Int][(Log[x]*Log[-3 + 3*x]^2)/((1 - Log[3*(-1 + x)]^2 - Log[x])*Log[-x + x*Log[3*(-1 + x)]^2 + x*Log[x]]^2),

x] + Defer[Int][(Log[x]*Log[-3 + 3*x]^2)/((1 - x)*(1 - Log[3*(-1 + x)]^2 - Log[x])*Log[-x + x*Log[3*(-1 + x)]

^2 + x*Log[x]]^2), x] + Defer[Int][(Log[x]*Log[-3 + 3*x]^2)/((-1 + x)*(1 - Log[3*(-1 + x)]^2 - Log[x])*Log[-x

+ x*Log[3*(-1 + x)]^2 + x*Log[x]]^2), x] + Defer[Int][(x*Log[x]*Log[-3 + 3*x]^2)/((1 - Log[3*(-1 + x)]^2 - Log

[x])*Log[-x + x*Log[3*(-1 + x)]^2 + x*Log[x]]^2), x] + E*Defer[Int][Log[-3 + 3*x]^2/((-1 + Log[3*(-1 + x)]^2 +

Log[x])*Log[-x + x*Log[3*(-1 + x)]^2 + x*Log[x]]^2), x] + E*Defer[Int][Log[-3 + 3*x]^2/(x*(-1 + Log[3*(-1 + x

)]^2 + Log[x])*Log[-x + x*Log[3*(-1 + x)]^2 + x*Log[x]]^2), x] + 2*Defer[Int][(Log[x]*Log[-3 + 3*x]^2)/((-1 +

Log[3*(-1 + x)]^2 + Log[x])*Log[-x + x*Log[3*(-1 + x)]^2 + x*Log[x]]^2), x] + Defer[Int][(Log[x]*Log[-3 + 3*x]

^2)/(x*(-1 + Log[3*(-1 + x)]^2 + Log[x])*Log[-x + x*Log[3*(-1 + x)]^2 + x*Log[x]]^2), x] + Defer[Int][(x*Log[x

]*Log[-3 + 3*x]^2)/((-1 + Log[3*(-1 + x)]^2 + Log[x])*Log[-x + x*Log[3*(-1 + x)]^2 + x*Log[x]]^2), x] + Defer[

Int][1/((1 - Log[3*(-1 + x)]^2 - Log[x])*Log[-x + x*Log[3*(-1 + x)]^2 + x*Log[x]]), x] - (1 - E)*Defer[Int][1/

((1 - Log[3*(-1 + x)]^2 - Log[x])*Log[-x + x*Log[3*(-1 + x)]^2 + x*Log[x]]), x] + Defer[Int][1/((1 - x)*(1 - L

og[3*(-1 + x)]^2 - Log[x])*Log[-x + x*Log[3*(-1 + x)]^2 + x*Log[x]]), x] - (1 - E)*Defer[Int][1/((1 - x)*(1 -

Log[3*(-1 + x)]^2 - Log[x])*Log[-x + x*Log[3*(-1 + x)]^2 + x*Log[x]]), x] + E*Defer[Int][1/((-1 + x)*(1 - Log[

3*(-1 + x)]^2 - Log[x])*Log[-x + x*Log[3*(-1 + x)]^2 + x*Log[x]]), x] - (1 - E)*Defer[Int][1/(x*(1 - Log[3*(-1

+ x)]^2 - Log[x])*Log[-x + x*Log[3*(-1 + x)]^2 + x*Log[x]]), x] + Defer[Int][x/((1 - Log[3*(-1 + x)]^2 - Log[

x])*Log[-x + x*Log[3*(-1 + x)]^2 + x*Log[x]]), x] + Defer[Int][Log[x]/((1 - Log[3*(-1 + x)]^2 - Log[x])*Log[-x

+ x*Log[3*(-1 + x)]^2 + x*Log[x]]), x] + (1 - E)*Defer[Int][Log[x]/((1 - Log[3*(-1 + x)]^2 - Log[x])*Log[-x +

x*Log[3*(-1 + x)]^2 + x*Log[x]]), x] + (1 - E)*Defer[Int][Log[x]/((1 - x)*(1 - Log[3*(-1 + x)]^2 - Log[x])*Lo

g[-x + x*Log[3*(-1 + x)]^2 + x*Log[x]]), x] + E*Defer[Int][Log[x]/((1 - x)*(1 - Log[3*(-1 + x)]^2 - Log[x])*Lo

g[-x + x*Log[3*(-1 + x)]^2 + x*Log[x]]), x] + Defer[Int][Log[x]/((-1 + x)*(1 - Log[3*(-1 + x)]^2 - Log[x])*Log

[-x + x*Log[3*(-1 + x)]^2 + x*Log[x]]), x] + E*Defer[Int][Log[x]/(x^2*(1 - Log[3*(-1 + x)]^2 - Log[x])*Log[-x

+ x*Log[3*(-1 + x)]^2 + x*Log[x]]), x] + (1 - E)*Defer[Int][Log[x]/(x*(1 - Log[3*(-1 + x)]^2 - Log[x])*Log[-x

+ x*Log[3*(-1 + x)]^2 + x*Log[x]]), x] + E*Defer[Int][Log[x]/(x*(1 - Log[3*(-1 + x)]^2 - Log[x])*Log[-x + x*Lo

g[3*(-1 + x)]^2 + x*Log[x]]), x] + Defer[Int][(x*Log[x])/((1 - Log[3*(-1 + x)]^2 - Log[x])*Log[-x + x*Log[3*(-

1 + x)]^2 + x*Log[x]]), x] + Defer[Int][1/((-1 + Log[3*(-1 + x)]^2 + Log[x])*Log[-x + x*Log[3*(-1 + x)]^2 + x*

Log[x]]), x] - (1 - E)*Defer[Int][1/((-1 + Log[3*(-1 + x)]^2 + Log[x])*Log[-x + x*Log[3*(-1 + x)]^2 + x*Log[x]

]), x] + E*Defer[Int][1/(x^2*(-1 + Log[3*(-1 + x)]^2 + Log[x])*Log[-x + x*Log[3*(-1 + x)]^2 + x*Log[x]]), x] +

E*Defer[Int][1/(x*(-1 + Log[3*(-1 + x)]^2 + Log[x])*Log[-x + x*Log[3*(-1 + x)]^2 + x*Log[x]]), x] + Defer[Int

][x/((-1 + Log[3*(-1 + x)]^2 + Log[x])*Log[-x + x*Log[3*(-1 + x)]^2 + x*Log[x]]), x] + Defer[Int][Log[x]/((-1

+ Log[3*(-1 + x)]^2 + Log[x])*Log[-x + x*Log[3*(-1 + x)]^2 + x*Log[x]]), x] + (1 - E)*Defer[Int][Log[x]/((-1 +

Log[3*(-1 + x)]^2 + Log[x])*Log[-x + x*Log[3*(-1 + x)]^2 + x*Log[x]]), x] + Defer[Int][(x*Log[x])/((-1 + Log[

3*(-1 + x)]^2 + Log[x])*Log[-x + x*Log[3*(-1 + x)]^2 + x*Log[x]]), x] + Defer[Int][Log[-3 + 3*x]^2/((1 - Log[3

*(-1 + x)]^2 - Log[x])*Log[-x + x*Log[3*(-1 + x)]^2 + x*Log[x]]), x] + (1 - E)*Defer[Int][Log[-3 + 3*x]^2/((1

- Log[3*(-1 + x)]^2 - Log[x])*Log[-x + x*Log[3*(-1 + x)]^2 + x*Log[x]]), x] + (1 - E)*Defer[Int][Log[-3 + 3*x]

^2/((1 - x)*(1 - Log[3*(-1 + x)]^2 - Log[x])*Log[-x + x*Log[3*(-1 + x)]^2 + x*Log[x]]), x] + E*Defer[Int][Log[

-3 + 3*x]^2/((1 - x)*(1 - Log[3*(-1 + x)]^2 - Log[x])*Log[-x + x*Log[3*(-1 + x)]^2 + x*Log[x]]), x] + Defer[In

t][Log[-3 + 3*x]^2/((-1 + x)*(1 - Log[3*(-1 + x)]^2 - Log[x])*Log[-x + x*Log[3*(-1 + x)]^2 + x*Log[x]]), x] +

E*Defer[Int][Log[-3 + 3*x]^2/(x^2*(1 - Log[3*(-1 + x)]^2 - Log[x])*Log[-x + x*Log[3*(-1 + x)]^2 + x*Log[x]]),

x] + (1 - E)*Defer[Int][Log[-3 + 3*x]^2/(x*(1 - Log[3*(-1 + x)]^2 - Log[x])*Log[-x + x*Log[3*(-1 + x)]^2 + x*L

og[x]]), x] + E*Defer[Int][Log[-3 + 3*x]^2/(x*(1 - Log[3*(-1 + x)]^2 - Log[x])*Log[-x + x*Log[3*(-1 + x)]^2 +

x*Log[x]]), x] + Defer[Int][(x*Log[-3 + 3*x]^2)/((1 - Log[3*(-1 + x)]^2 - Log[x])*Log[-x + x*Log[3*(-1 + x)]^2

+ x*Log[x]]), x] + Defer[Int][Log[-3 + 3*x]^2/((-1 + Log[3*(-1 + x)]^2 + Log[x])*Log[-x + x*Log[3*(-1 + x)]^2

+ x*Log[x]]), x] + (1 - E)*Defer[Int][Log[-3 + 3*x]^2/((-1 + Log[3*(-1 + x)]^2 + Log[x])*Log[-x + x*Log[3*(-1

+ x)]^2 + x*Log[x]]), x] + Defer[Int][(x*Log[-3 + 3*x]^2)/((-1 + Log[3*(-1 + x)]^2 + Log[x])*Log[-x + x*Log[3

*(-1 + x)]^2 + x*Log[x]]), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-e (-1+x) \log (x)+(-1+x) x \log ^2(x)+2 x \log (3 (-1+x)) (-e+x \log (x))+(-1+x) \log ^2(3 (-1+x)) (-e+x \log (x))-(-1+x) (e+x) \left (-1+\log ^2(3 (-1+x))+\log (x)\right ) \log \left (x \left (-1+\log ^2(3 (-1+x))+\log (x)\right )\right )}{(1-x) x^2 \left (1-\log ^2(3 (-1+x))-\log (x)\right ) \log ^2\left (-x+x \log ^2(3 (-1+x))+x \log (x)\right )} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [A] time = 0.19, size = 28, normalized size = 0.90 \begin {gather*} \frac {e-x \log (x)}{x \log \left (x \left (-1+\log ^2(3 (-1+x))+\log (x)\right )\right )} \end {gather*}

Antiderivative was successfully veriﬁed.

[In]

Integrate[(E*(1 - x)*Log[x] + (-x + x^2)*Log[x]^2 + (-2*E*x + 2*x^2*Log[x])*Log[-3 + 3*x] + (E*(1 - x) + (-x +

x^2)*Log[x])*Log[-3 + 3*x]^2 + (E*(-1 + x) - x + x^2 + (E*(1 - x) + x - x^2)*Log[x] + (E*(1 - x) + x - x^2)*L

og[-3 + 3*x]^2)*Log[-x + x*Log[x] + x*Log[-3 + 3*x]^2])/((x^2 - x^3 + (-x^2 + x^3)*Log[x] + (-x^2 + x^3)*Log[-

3 + 3*x]^2)*Log[-x + x*Log[x] + x*Log[-3 + 3*x]^2]^2),x]

[Out]

(E - x*Log[x])/(x*Log[x*(-1 + Log[3*(-1 + x)]^2 + Log[x])])

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fricas [A] time = 0.61, size = 35, normalized size = 1.13 \begin {gather*} -\frac {x \log \relax (x) - e}{x \log \left (x \log \left (3 \, x - 3\right )^{2} + x \log \relax (x) - x\right )} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((((-x+1)*exp(1)-x^2+x)*log(3*x-3)^2+((-x+1)*exp(1)-x^2+x)*log(x)+(x-1)*exp(1)+x^2-x)*log(x*log(3*x-

3)^2+x*log(x)-x)+(log(x)*(x^2-x)+(-x+1)*exp(1))*log(3*x-3)^2+(2*x^2*log(x)-2*x*exp(1))*log(3*x-3)+(x^2-x)*log(

x)^2+(-x+1)*exp(1)*log(x))/((x^3-x^2)*log(3*x-3)^2+(x^3-x^2)*log(x)-x^3+x^2)/log(x*log(3*x-3)^2+x*log(x)-x)^2,

x, algorithm="fricas")

[Out]

-(x*log(x) - e)/(x*log(x*log(3*x - 3)^2 + x*log(x) - x))

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giac [A] time = 3.57, size = 33, normalized size = 1.06 \begin {gather*} -\frac {x \log \relax (x) - e}{x \log \left (\log \left (3 \, x - 3\right )^{2} + \log \relax (x) - 1\right ) + x \log \relax (x)} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((((-x+1)*exp(1)-x^2+x)*log(3*x-3)^2+((-x+1)*exp(1)-x^2+x)*log(x)+(x-1)*exp(1)+x^2-x)*log(x*log(3*x-

3)^2+x*log(x)-x)+(log(x)*(x^2-x)+(-x+1)*exp(1))*log(3*x-3)^2+(2*x^2*log(x)-2*x*exp(1))*log(3*x-3)+(x^2-x)*log(

x)^2+(-x+1)*exp(1)*log(x))/((x^3-x^2)*log(3*x-3)^2+(x^3-x^2)*log(x)-x^3+x^2)/log(x*log(3*x-3)^2+x*log(x)-x)^2,

x, algorithm="giac")

[Out]

-(x*log(x) - e)/(x*log(log(3*x - 3)^2 + log(x) - 1) + x*log(x))

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maple [C] time = 0.74, size = 168, normalized size = 5.42


method	result	size

risch	\(\frac {-2 x \ln \relax (x )+2 \,{\mathrm e}}{x \left (2 \ln \relax (x )+2 \ln \left (\ln \left (3 x -3\right )^{2}+\ln \relax (x )-1\right )-i \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i \left (\ln \left (3 x -3\right )^{2}+\ln \relax (x )-1\right )\right ) \mathrm {csgn}\left (i x \left (\ln \left (3 x -3\right )^{2}+\ln \relax (x )-1\right )\right )+i \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x \left (\ln \left (3 x -3\right )^{2}+\ln \relax (x )-1\right )\right )^{2}+i \pi \,\mathrm {csgn}\left (i \left (\ln \left (3 x -3\right )^{2}+\ln \relax (x )-1\right )\right ) \mathrm {csgn}\left (i x \left (\ln \left (3 x -3\right )^{2}+\ln \relax (x )-1\right )\right )^{2}-i \pi \mathrm {csgn}\left (i x \left (\ln \left (3 x -3\right )^{2}+\ln \relax (x )-1\right )\right )^{3}\right )}\)	\(168\)

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int(((((1-x)*exp(1)-x^2+x)*ln(3*x-3)^2+((1-x)*exp(1)-x^2+x)*ln(x)+(x-1)*exp(1)+x^2-x)*ln(x*ln(3*x-3)^2+x*ln(x)

-x)+(ln(x)*(x^2-x)+(1-x)*exp(1))*ln(3*x-3)^2+(2*x^2*ln(x)-2*x*exp(1))*ln(3*x-3)+(x^2-x)*ln(x)^2+(1-x)*exp(1)*l

n(x))/((x^3-x^2)*ln(3*x-3)^2+(x^3-x^2)*ln(x)-x^3+x^2)/ln(x*ln(3*x-3)^2+x*ln(x)-x)^2,x,method=_RETURNVERBOSE)

[Out]

2*(-x*ln(x)+exp(1))/x/(2*ln(x)+2*ln(ln(3*x-3)^2+ln(x)-1)-I*Pi*csgn(I*x)*csgn(I*(ln(3*x-3)^2+ln(x)-1))*csgn(I*x

*(ln(3*x-3)^2+ln(x)-1))+I*Pi*csgn(I*x)*csgn(I*x*(ln(3*x-3)^2+ln(x)-1))^2+I*Pi*csgn(I*(ln(3*x-3)^2+ln(x)-1))*cs

gn(I*x*(ln(3*x-3)^2+ln(x)-1))^2-I*Pi*csgn(I*x*(ln(3*x-3)^2+ln(x)-1))^3)

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maxima [A] time = 0.65, size = 43, normalized size = 1.39 \begin {gather*} -\frac {x \log \relax (x) - e}{x \log \left (\log \relax (3)^{2} + 2 \, \log \relax (3) \log \left (x - 1\right ) + \log \left (x - 1\right )^{2} + \log \relax (x) - 1\right ) + x \log \relax (x)} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((((-x+1)*exp(1)-x^2+x)*log(3*x-3)^2+((-x+1)*exp(1)-x^2+x)*log(x)+(x-1)*exp(1)+x^2-x)*log(x*log(3*x-

3)^2+x*log(x)-x)+(log(x)*(x^2-x)+(-x+1)*exp(1))*log(3*x-3)^2+(2*x^2*log(x)-2*x*exp(1))*log(3*x-3)+(x^2-x)*log(

x)^2+(-x+1)*exp(1)*log(x))/((x^3-x^2)*log(3*x-3)^2+(x^3-x^2)*log(x)-x^3+x^2)/log(x*log(3*x-3)^2+x*log(x)-x)^2,

x, algorithm="maxima")

[Out]

-(x*log(x) - e)/(x*log(log(3)^2 + 2*log(3)*log(x - 1) + log(x - 1)^2 + log(x) - 1) + x*log(x))

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

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int((log(x*log(x) - x + x*log(3*x - 3)^2)*(x + log(3*x - 3)^2*(exp(1)*(x - 1) - x + x^2) - exp(1)*(x - 1) - x^

2 + log(x)*(exp(1)*(x - 1) - x + x^2)) + log(3*x - 3)^2*(log(x)*(x - x^2) + exp(1)*(x - 1)) + log(x)^2*(x - x^

2) - log(3*x - 3)*(2*x^2*log(x) - 2*x*exp(1)) + exp(1)*log(x)*(x - 1))/(log(x*log(x) - x + x*log(3*x - 3)^2)^2

*(log(x)*(x^2 - x^3) + log(3*x - 3)^2*(x^2 - x^3) - x^2 + x^3)),x)

[Out]

int((log(x*log(x) - x + x*log(3*x - 3)^2)*(x + log(3*x - 3)^2*(exp(1)*(x - 1) - x + x^2) - exp(1)*(x - 1) - x^

2 + log(x)*(exp(1)*(x - 1) - x + x^2)) + log(3*x - 3)^2*(log(x)*(x - x^2) + exp(1)*(x - 1)) + log(x)^2*(x - x^

2) - log(3*x - 3)*(2*x^2*log(x) - 2*x*exp(1)) + exp(1)*log(x)*(x - 1))/(log(x*log(x) - x + x*log(3*x - 3)^2)^2

*(log(x)*(x^2 - x^3) + log(3*x - 3)^2*(x^2 - x^3) - x^2 + x^3)), x)

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sympy [A] time = 2.31, size = 27, normalized size = 0.87 \begin {gather*} \frac {- x \log {\relax (x )} + e}{x \log {\left (x \log {\relax (x )} + x \log {\left (3 x - 3 \right )}^{2} - x \right )}} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((((-x+1)*exp(1)-x**2+x)*ln(3*x-3)**2+((-x+1)*exp(1)-x**2+x)*ln(x)+(x-1)*exp(1)+x**2-x)*ln(x*ln(3*x-

3)**2+x*ln(x)-x)+(ln(x)*(x**2-x)+(-x+1)*exp(1))*ln(3*x-3)**2+(2*x**2*ln(x)-2*x*exp(1))*ln(3*x-3)+(x**2-x)*ln(x

)**2+(-x+1)*exp(1)*ln(x))/((x**3-x**2)*ln(3*x-3)**2+(x**3-x**2)*ln(x)-x**3+x**2)/ln(x*ln(3*x-3)**2+x*ln(x)-x)*

*2,x)

[Out]

(-x*log(x) + E)/(x*log(x*log(x) + x*log(3*x - 3)**2 - x))

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