3.59.67 \(\int \frac {-4+x+e^5 (-48-12 x+6 x^2)+e^{10} (-144-108 x+9 x^3-8 x^4+2 x^5)+(e^5 (-24+6 x)+e^{10} (-144-36 x+18 x^2)) \log (-4+x)+e^{10} (-36+9 x) \log ^2(-4+x)+(12-3 x+e^5 (144+18 x-12 x^2)+e^{10} (432+216 x-18 x^2-9 x^3)+(e^5 (72-18 x)+e^{10} (432+54 x-36 x^2)) \log (-4+x)+e^{10} (108-27 x) \log ^2(-4+x)) \log (x)}{e^{10} (-4 x^4+x^5)} \, dx\)

Optimal. Leaf size=25 \[ 2 x+\frac {\left (\frac {1}{e^5}+3 (2+x+\log (-4+x))\right )^2 \log (x)}{x^3} \]

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Rubi [F]  time = 17.46, 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 {-4+x+e^5 \left (-48-12 x+6 x^2\right )+e^{10} \left (-144-108 x+9 x^3-8 x^4+2 x^5\right )+\left (e^5 (-24+6 x)+e^{10} \left (-144-36 x+18 x^2\right )\right ) \log (-4+x)+e^{10} (-36+9 x) \log ^2(-4+x)+\left (12-3 x+e^5 \left (144+18 x-12 x^2\right )+e^{10} \left (432+216 x-18 x^2-9 x^3\right )+\left (e^5 (72-18 x)+e^{10} \left (432+54 x-36 x^2\right )\right ) \log (-4+x)+e^{10} (108-27 x) \log ^2(-4+x)\right ) \log (x)}{e^{10} \left (-4 x^4+x^5\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-4 + x + E^5*(-48 - 12*x + 6*x^2) + E^10*(-144 - 108*x + 9*x^3 - 8*x^4 + 2*x^5) + (E^5*(-24 + 6*x) + E^10
*(-144 - 36*x + 18*x^2))*Log[-4 + x] + E^10*(-36 + 9*x)*Log[-4 + x]^2 + (12 - 3*x + E^5*(144 + 18*x - 12*x^2)
+ E^10*(432 + 216*x - 18*x^2 - 9*x^3) + (E^5*(72 - 18*x) + E^10*(432 + 54*x - 36*x^2))*Log[-4 + x] + E^10*(108
- 27*x)*Log[-4 + x]^2)*Log[x])/(E^10*(-4*x^4 + x^5)),x]

[Out]

(-27*(6 + E^(-5)))/(8*x^2) + (3*(1 + 6*E^5)^2)/(16*E^10*x^2) - (3*(1 - 6*E^5 - 72*E^10))/(16*E^10*x^2) - 147/(
16*x) - (27*(3 - E^(-5)))/(32*x) - (43*(6 + E^(-5)))/(32*x) + (24 + E^(-5))/(8*x) - (3*(2 + 3*E^5))/(2*E^5*x)
+ (3*(1 + 6*E^5)^2)/(16*E^10*x) - (3*(1 - 6*E^5 - 72*E^10))/(16*E^10*x) + 2*x + (141*Log[4 - x])/64 - (45*(3 -
E^(-5))*Log[4 - x])/128 - (49*(6 + E^(-5))*Log[4 - x])/128 + ((24 + E^(-5))*Log[4 - x])/32 - (33*Log[-4 + x])
/(4*x^2) + (9*(3 - E^(-5))*Log[-4 + x])/(8*x^2) + (9*(6 + E^(-5))*Log[-4 + x])/(8*x^2) - (9*Log[-4 + x])/x + (
9*(3 - E^(-5))*Log[-4 + x])/(8*x) + (9*(6 + E^(-5))*Log[-4 + x])/(8*x) + (3*(4 - x)*Log[-4 + x])/(32*x) - (9*L
og[4]*Log[-4 + x])/4 - (3*(2 + 3*E^5)*Log[4]*Log[-4 + x])/(8*E^5) + (3*(1 + 6*E^5)^2*Log[4]*Log[-4 + x])/(64*E
^10) - (3*(1 - 6*E^5 - 72*E^10)*Log[4]*Log[-4 + x])/(64*E^10) + (3*Log[-4 + x]^2)/64 - (3*Log[-4 + x]^2)/x^3 -
(3*Log[-4 + x]*Log[x/4])/32 + (9*Log[-4 + x]^2*Log[x/4])/8 - (9*(3 - E^(-5))*Log[-4 + x]^2*Log[x/4])/64 - (9*
(6 + E^(-5))*Log[-4 + x]^2*Log[x/4])/64 - (135*Log[x])/64 + (45*(3 - E^(-5))*Log[x])/128 + (49*(6 + E^(-5))*Lo
g[x])/128 - ((24 + E^(-5))*Log[x])/32 + ((1 + 6*E^5)^2*Log[x])/(E^10*x^3) - (3*(6 + E^(-5))*Log[x])/(4*x^2) +
(3*(1 + 6*E^5)^2*Log[x])/(8*E^10*x^2) - (3*(1 - 6*E^5 - 72*E^10)*Log[x])/(8*E^10*x^2) - (9*(3 - E^(-5))*Log[x]
)/(16*x) - (15*(6 + E^(-5))*Log[x])/(16*x) - (3*(2 + 3*E^5)*Log[x])/(2*E^5*x) + (3*(1 + 6*E^5)^2*Log[x])/(16*E
^10*x) - (3*(1 - 6*E^5 - 72*E^10)*Log[x])/(16*E^10*x) - (9*Log[4]*Log[x])/4 - (27*(1 - 3*E^5)*Log[4]*Log[x])/(
64*E^5) + (33*(1 + 6*E^5)*Log[4]*Log[x])/(64*E^5) + (9*Log[4 - x]*Log[x])/4 - (27*(3 - E^(-5))*Log[4 - x]*Log[
x])/64 - (33*(6 + E^(-5))*Log[4 - x]*Log[x])/64 + (6*(6 + E^(-5))*Log[-4 + x]*Log[x])/x^3 + (9*(3 - E^(-5))*Lo
g[-4 + x]*Log[x])/(4*x^2) + (9*(6 + E^(-5))*Log[-4 + x]*Log[x])/(4*x^2) - (9*Log[-4 + x]*Log[x])/x + (9*(3 - E
^(-5))*Log[-4 + x]*Log[x])/(8*x) + (9*(6 + E^(-5))*Log[-4 + x]*Log[x])/(8*x) - (9*Log[-4 + x]^2*Log[x])/8 + (9
*(3 - E^(-5))*Log[-4 + x]^2*Log[x])/64 + (9*(6 + E^(-5))*Log[-4 + x]^2*Log[x])/64 + (27*(3 - E^(-5))*Log[x]^2)
/128 + (33*(6 + E^(-5))*Log[x]^2)/128 + (3*(2 + 3*E^5)*Log[x]^2)/(16*E^5) - (3*(1 + 6*E^5)^2*Log[x]^2)/(128*E^
10) + (3*(1 - 6*E^5 - 72*E^10)*Log[x]^2)/(128*E^10) - (9*Log[1 - x/4]*Log[x]^2)/8 + (9*(3 - E^(-5))*Log[1 - x/
4]*Log[x]^2)/64 + (9*(6 + E^(-5))*Log[1 - x/4]*Log[x]^2)/64 + (9*Log[-4 + x]*Log[x]^2)/8 - (9*(3 - E^(-5))*Log
[-4 + x]*Log[x]^2)/64 - (9*(6 + E^(-5))*Log[-4 + x]*Log[x]^2)/64 + (69*PolyLog[2, 1 - x/4])/32 + (3*(2 + 3*E^5
)*PolyLog[2, 1 - x/4])/(8*E^5) - (3*(1 + 6*E^5)^2*PolyLog[2, 1 - x/4])/(64*E^10) + (3*(1 - 6*E^5 - 72*E^10)*Po
lyLog[2, 1 - x/4])/(64*E^10) + (9*Log[-4 + x]*PolyLog[2, 1 - x/4])/4 - (9*(3 - E^(-5))*Log[-4 + x]*PolyLog[2,
1 - x/4])/32 - (9*(6 + E^(-5))*Log[-4 + x]*PolyLog[2, 1 - x/4])/32 + (9*PolyLog[2, x/4])/4 - (27*(3 - E^(-5))*
PolyLog[2, x/4])/64 - (33*(6 + E^(-5))*PolyLog[2, x/4])/64 - (9*Log[x]*PolyLog[2, x/4])/4 + (9*(3 - E^(-5))*Lo
g[x]*PolyLog[2, x/4])/32 + (9*(6 + E^(-5))*Log[x]*PolyLog[2, x/4])/32 - (9*PolyLog[3, 1 - x/4])/4 + (9*(3 - E^
(-5))*PolyLog[3, 1 - x/4])/32 + (9*(6 + E^(-5))*PolyLog[3, 1 - x/4])/32 + (9*PolyLog[3, x/4])/4 - (9*(3 - E^(-
5))*PolyLog[3, x/4])/32 - (9*(6 + E^(-5))*PolyLog[3, x/4])/32 - 27*Defer[Int][(Log[-4 + x]^2*Log[x])/x^4, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \frac {-4+x+e^5 \left (-48-12 x+6 x^2\right )+e^{10} \left (-144-108 x+9 x^3-8 x^4+2 x^5\right )+\left (e^5 (-24+6 x)+e^{10} \left (-144-36 x+18 x^2\right )\right ) \log (-4+x)+e^{10} (-36+9 x) \log ^2(-4+x)+\left (12-3 x+e^5 \left (144+18 x-12 x^2\right )+e^{10} \left (432+216 x-18 x^2-9 x^3\right )+\left (e^5 (72-18 x)+e^{10} \left (432+54 x-36 x^2\right )\right ) \log (-4+x)+e^{10} (108-27 x) \log ^2(-4+x)\right ) \log (x)}{-4 x^4+x^5} \, dx}{e^{10}}\\ &=\frac {\int \frac {-4+x+e^5 \left (-48-12 x+6 x^2\right )+e^{10} \left (-144-108 x+9 x^3-8 x^4+2 x^5\right )+\left (e^5 (-24+6 x)+e^{10} \left (-144-36 x+18 x^2\right )\right ) \log (-4+x)+e^{10} (-36+9 x) \log ^2(-4+x)+\left (12-3 x+e^5 \left (144+18 x-12 x^2\right )+e^{10} \left (432+216 x-18 x^2-9 x^3\right )+\left (e^5 (72-18 x)+e^{10} \left (432+54 x-36 x^2\right )\right ) \log (-4+x)+e^{10} (108-27 x) \log ^2(-4+x)\right ) \log (x)}{(-4+x) x^4} \, dx}{e^{10}}\\ &=\frac {\int \left (\frac {1+12 e^5 \left (1+3 e^5\right )+6 e^5 \left (1+6 e^5\right ) x+9 e^{10} x^2+2 e^{10} x^4+6 e^5 \left (1+6 e^5\right ) \log (-4+x)+18 e^{10} x \log (-4+x)+9 e^{10} \log ^2(-4+x)}{x^4}+\frac {3 \left (1+6 e^5+3 e^5 x+3 e^5 \log (-4+x)\right ) \left (-4 \left (1+6 e^5\right )+x+e^5 x^2-12 e^5 \log (-4+x)+3 e^5 x \log (-4+x)\right ) \log (x)}{(4-x) x^4}\right ) \, dx}{e^{10}}\\ &=\frac {\int \frac {1+12 e^5 \left (1+3 e^5\right )+6 e^5 \left (1+6 e^5\right ) x+9 e^{10} x^2+2 e^{10} x^4+6 e^5 \left (1+6 e^5\right ) \log (-4+x)+18 e^{10} x \log (-4+x)+9 e^{10} \log ^2(-4+x)}{x^4} \, dx}{e^{10}}+\frac {3 \int \frac {\left (1+6 e^5+3 e^5 x+3 e^5 \log (-4+x)\right ) \left (-4 \left (1+6 e^5\right )+x+e^5 x^2-12 e^5 \log (-4+x)+3 e^5 x \log (-4+x)\right ) \log (x)}{(4-x) x^4} \, dx}{e^{10}}\\ &=\frac {\int \left (\frac {\left (1+6 e^5\right )^2+6 e^5 \left (1+6 e^5\right ) x+9 e^{10} x^2+2 e^{10} x^4}{x^4}+\frac {6 e^5 \left (1+6 e^5+3 e^5 x\right ) \log (-4+x)}{x^4}+\frac {9 e^{10} \log ^2(-4+x)}{x^4}\right ) \, dx}{e^{10}}+\frac {3 \int \frac {\left (1+3 e^5 (2+x)+3 e^5 \log (-4+x)\right ) \left (-4+x+e^5 \left (-24+x^2\right )+3 e^5 (-4+x) \log (-4+x)\right ) \log (x)}{(4-x) x^4} \, dx}{e^{10}}\\ &=9 \int \frac {\log ^2(-4+x)}{x^4} \, dx+\frac {\int \frac {\left (1+6 e^5\right )^2+6 e^5 \left (1+6 e^5\right ) x+9 e^{10} x^2+2 e^{10} x^4}{x^4} \, dx}{e^{10}}+\frac {3 \int \left (\frac {\left (1+6 e^5+3 e^5 x+3 e^5 \log (-4+x)\right ) \left (-4 \left (1+6 e^5\right )+x+e^5 x^2-12 e^5 \log (-4+x)+3 e^5 x \log (-4+x)\right ) \log (x)}{256 (4-x)}+\frac {\left (1+6 e^5+3 e^5 x+3 e^5 \log (-4+x)\right ) \left (-4 \left (1+6 e^5\right )+x+e^5 x^2-12 e^5 \log (-4+x)+3 e^5 x \log (-4+x)\right ) \log (x)}{4 x^4}+\frac {\left (1+6 e^5+3 e^5 x+3 e^5 \log (-4+x)\right ) \left (-4 \left (1+6 e^5\right )+x+e^5 x^2-12 e^5 \log (-4+x)+3 e^5 x \log (-4+x)\right ) \log (x)}{16 x^3}+\frac {\left (1+6 e^5+3 e^5 x+3 e^5 \log (-4+x)\right ) \left (-4 \left (1+6 e^5\right )+x+e^5 x^2-12 e^5 \log (-4+x)+3 e^5 x \log (-4+x)\right ) \log (x)}{64 x^2}+\frac {\left (1+6 e^5+3 e^5 x+3 e^5 \log (-4+x)\right ) \left (-4 \left (1+6 e^5\right )+x+e^5 x^2-12 e^5 \log (-4+x)+3 e^5 x \log (-4+x)\right ) \log (x)}{256 x}\right ) \, dx}{e^{10}}+\frac {6 \int \frac {\left (1+6 e^5+3 e^5 x\right ) \log (-4+x)}{x^4} \, dx}{e^5}\\ &=-\frac {2 \left (6+\frac {1}{e^5}\right ) \log (-4+x)}{x^3}-\frac {9 \log (-4+x)}{x^2}-\frac {3 \log ^2(-4+x)}{x^3}+6 \int \frac {\log (-4+x)}{(-4+x) x^3} \, dx+\frac {3 \int \frac {\left (1+6 e^5+3 e^5 x+3 e^5 \log (-4+x)\right ) \left (-4 \left (1+6 e^5\right )+x+e^5 x^2-12 e^5 \log (-4+x)+3 e^5 x \log (-4+x)\right ) \log (x)}{4-x} \, dx}{256 e^{10}}+\frac {3 \int \frac {\left (1+6 e^5+3 e^5 x+3 e^5 \log (-4+x)\right ) \left (-4 \left (1+6 e^5\right )+x+e^5 x^2-12 e^5 \log (-4+x)+3 e^5 x \log (-4+x)\right ) \log (x)}{x} \, dx}{256 e^{10}}+\frac {3 \int \frac {\left (1+6 e^5+3 e^5 x+3 e^5 \log (-4+x)\right ) \left (-4 \left (1+6 e^5\right )+x+e^5 x^2-12 e^5 \log (-4+x)+3 e^5 x \log (-4+x)\right ) \log (x)}{x^2} \, dx}{64 e^{10}}+\frac {3 \int \frac {\left (1+6 e^5+3 e^5 x+3 e^5 \log (-4+x)\right ) \left (-4 \left (1+6 e^5\right )+x+e^5 x^2-12 e^5 \log (-4+x)+3 e^5 x \log (-4+x)\right ) \log (x)}{x^3} \, dx}{16 e^{10}}+\frac {3 \int \frac {\left (1+6 e^5+3 e^5 x+3 e^5 \log (-4+x)\right ) \left (-4 \left (1+6 e^5\right )+x+e^5 x^2-12 e^5 \log (-4+x)+3 e^5 x \log (-4+x)\right ) \log (x)}{x^4} \, dx}{4 e^{10}}+\frac {\int \left (2 e^{10}+\frac {\left (1+6 e^5\right )^2}{x^4}+\frac {6 e^5 \left (1+6 e^5\right )}{x^3}+\frac {9 e^{10}}{x^2}\right ) \, dx}{e^{10}}-\frac {6 \int \frac {2 \left (1+6 e^5\right )+9 e^5 x}{6 (4-x) x^3} \, dx}{e^5}\\ &=-\frac {\left (1+6 e^5\right )^2}{3 e^{10} x^3}-\frac {3 \left (6+\frac {1}{e^5}\right )}{x^2}-\frac {9}{x}+2 x-\frac {2 \left (6+\frac {1}{e^5}\right ) \log (-4+x)}{x^3}-\frac {9 \log (-4+x)}{x^2}-\frac {3 \log ^2(-4+x)}{x^3}+6 \operatorname {Subst}\left (\int \frac {\log (x)}{x (4+x)^3} \, dx,x,-4+x\right )+\frac {3 \int \frac {\left (1+3 e^5 (2+x)+3 e^5 \log (-4+x)\right ) \left (-4+x+e^5 \left (-24+x^2\right )+3 e^5 (-4+x) \log (-4+x)\right ) \log (x)}{4-x} \, dx}{256 e^{10}}+\frac {3 \int \frac {\left (1+3 e^5 (2+x)+3 e^5 \log (-4+x)\right ) \left (-4+x+e^5 \left (-24+x^2\right )+3 e^5 (-4+x) \log (-4+x)\right ) \log (x)}{x} \, dx}{256 e^{10}}+\frac {3 \int \frac {\left (1+3 e^5 (2+x)+3 e^5 \log (-4+x)\right ) \left (-4+x+e^5 \left (-24+x^2\right )+3 e^5 (-4+x) \log (-4+x)\right ) \log (x)}{x^2} \, dx}{64 e^{10}}+\frac {3 \int \frac {\left (1+3 e^5 (2+x)+3 e^5 \log (-4+x)\right ) \left (-4+x+e^5 \left (-24+x^2\right )+3 e^5 (-4+x) \log (-4+x)\right ) \log (x)}{x^3} \, dx}{16 e^{10}}+\frac {3 \int \frac {\left (1+3 e^5 (2+x)+3 e^5 \log (-4+x)\right ) \left (-4+x+e^5 \left (-24+x^2\right )+3 e^5 (-4+x) \log (-4+x)\right ) \log (x)}{x^4} \, dx}{4 e^{10}}-\frac {\int \frac {2 \left (1+6 e^5\right )+9 e^5 x}{(4-x) x^3} \, dx}{e^5}\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.18, size = 40, normalized size = 1.60 \begin {gather*} -\frac {-2 e^{10} x-\frac {\left (1+3 e^5 (2+x)+3 e^5 \log (-4+x)\right )^2 \log (x)}{x^3}}{e^{10}} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-4 + x + E^5*(-48 - 12*x + 6*x^2) + E^10*(-144 - 108*x + 9*x^3 - 8*x^4 + 2*x^5) + (E^5*(-24 + 6*x)
+ E^10*(-144 - 36*x + 18*x^2))*Log[-4 + x] + E^10*(-36 + 9*x)*Log[-4 + x]^2 + (12 - 3*x + E^5*(144 + 18*x - 12
*x^2) + E^10*(432 + 216*x - 18*x^2 - 9*x^3) + (E^5*(72 - 18*x) + E^10*(432 + 54*x - 36*x^2))*Log[-4 + x] + E^1
0*(108 - 27*x)*Log[-4 + x]^2)*Log[x])/(E^10*(-4*x^4 + x^5)),x]

[Out]

-((-2*E^10*x - ((1 + 3*E^5*(2 + x) + 3*E^5*Log[-4 + x])^2*Log[x])/x^3)/E^10)

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fricas [B]  time = 0.70, size = 64, normalized size = 2.56 \begin {gather*} \frac {{\left (2 \, x^{4} e^{10} + {\left (9 \, e^{10} \log \left (x - 4\right )^{2} + 9 \, {\left (x^{2} + 4 \, x + 4\right )} e^{10} + 6 \, {\left (x + 2\right )} e^{5} + 6 \, {\left (3 \, {\left (x + 2\right )} e^{10} + e^{5}\right )} \log \left (x - 4\right ) + 1\right )} \log \relax (x)\right )} e^{\left (-10\right )}}{x^{3}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-27*x+108)*exp(5)^2*log(x-4)^2+((-36*x^2+54*x+432)*exp(5)^2+(-18*x+72)*exp(5))*log(x-4)+(-9*x^3-1
8*x^2+216*x+432)*exp(5)^2+(-12*x^2+18*x+144)*exp(5)-3*x+12)*log(x)+(9*x-36)*exp(5)^2*log(x-4)^2+((18*x^2-36*x-
144)*exp(5)^2+(6*x-24)*exp(5))*log(x-4)+(2*x^5-8*x^4+9*x^3-108*x-144)*exp(5)^2+(6*x^2-12*x-48)*exp(5)+x-4)/(x^
5-4*x^4)/exp(5)^2,x, algorithm="fricas")

[Out]

(2*x^4*e^10 + (9*e^10*log(x - 4)^2 + 9*(x^2 + 4*x + 4)*e^10 + 6*(x + 2)*e^5 + 6*(3*(x + 2)*e^10 + e^5)*log(x -
4) + 1)*log(x))*e^(-10)/x^3

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giac [B]  time = 0.20, size = 94, normalized size = 3.76 \begin {gather*} \frac {{\left (2 \, x^{4} e^{10} + 9 \, x^{2} e^{10} \log \relax (x) + 18 \, x e^{10} \log \left (x - 4\right ) \log \relax (x) + 9 \, e^{10} \log \left (x - 4\right )^{2} \log \relax (x) + 36 \, x e^{10} \log \relax (x) + 6 \, x e^{5} \log \relax (x) + 36 \, e^{10} \log \left (x - 4\right ) \log \relax (x) + 6 \, e^{5} \log \left (x - 4\right ) \log \relax (x) + 36 \, e^{10} \log \relax (x) + 12 \, e^{5} \log \relax (x) + \log \relax (x)\right )} e^{\left (-10\right )}}{x^{3}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-27*x+108)*exp(5)^2*log(x-4)^2+((-36*x^2+54*x+432)*exp(5)^2+(-18*x+72)*exp(5))*log(x-4)+(-9*x^3-1
8*x^2+216*x+432)*exp(5)^2+(-12*x^2+18*x+144)*exp(5)-3*x+12)*log(x)+(9*x-36)*exp(5)^2*log(x-4)^2+((18*x^2-36*x-
144)*exp(5)^2+(6*x-24)*exp(5))*log(x-4)+(2*x^5-8*x^4+9*x^3-108*x-144)*exp(5)^2+(6*x^2-12*x-48)*exp(5)+x-4)/(x^
5-4*x^4)/exp(5)^2,x, algorithm="giac")

[Out]

(2*x^4*e^10 + 9*x^2*e^10*log(x) + 18*x*e^10*log(x - 4)*log(x) + 9*e^10*log(x - 4)^2*log(x) + 36*x*e^10*log(x)
+ 6*x*e^5*log(x) + 36*e^10*log(x - 4)*log(x) + 6*e^5*log(x - 4)*log(x) + 36*e^10*log(x) + 12*e^5*log(x) + log(
x))*e^(-10)/x^3

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maple [B]  time = 0.33, size = 90, normalized size = 3.60

method	result	size
risch	\(\frac {9 \ln \relax (x ) \ln \left (x -4\right )^{2}}{x^{3}}+\frac {6 \,{\mathrm e}^{-5} \left (3 x \,{\mathrm e}^{5}+6 \,{\mathrm e}^{5}+1\right ) \ln \relax (x ) \ln \left (x -4\right )}{x^{3}}+\frac {{\mathrm e}^{-10} \left (2 x^{4} {\mathrm e}^{10}+9 x^{2} {\mathrm e}^{10} \ln \relax (x )+36 \,{\mathrm e}^{10} \ln \relax (x ) x +36 \,{\mathrm e}^{10} \ln \relax (x )+6 x \,{\mathrm e}^{5} \ln \relax (x )+12 \,{\mathrm e}^{5} \ln \relax (x )+\ln \relax (x )\right )}{x^{3}}\)	\(90\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((-27*x+108)*exp(5)^2*ln(x-4)^2+((-36*x^2+54*x+432)*exp(5)^2+(-18*x+72)*exp(5))*ln(x-4)+(-9*x^3-18*x^2+21
6*x+432)*exp(5)^2+(-12*x^2+18*x+144)*exp(5)-3*x+12)*ln(x)+(9*x-36)*exp(5)^2*ln(x-4)^2+((18*x^2-36*x-144)*exp(5
)^2+(6*x-24)*exp(5))*ln(x-4)+(2*x^5-8*x^4+9*x^3-108*x-144)*exp(5)^2+(6*x^2-12*x-48)*exp(5)+x-4)/(x^5-4*x^4)/ex
p(5)^2,x,method=_RETURNVERBOSE)

[Out]

9/x^3*ln(x)*ln(x-4)^2+6*exp(-5)*(3*x*exp(5)+6*exp(5)+1)/x^3*ln(x)*ln(x-4)+exp(-10)*(2*x^4*exp(10)+9*x^2*exp(10
)*ln(x)+36*exp(10)*ln(x)*x+36*exp(10)*ln(x)+6*x*exp(5)*ln(x)+12*exp(5)*ln(x)+ln(x))/x^3

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maxima [B]  time = 0.52, size = 234, normalized size = 9.36 \begin {gather*} -\frac {1}{192} \, {\left (36 \, {\left (\frac {4 \, {\left (3 \, x^{2} + 6 \, x + 16\right )}}{x^{3}} + 3 \, \log \left (x - 4\right ) - 3 \, \log \relax (x)\right )} e^{10} + 12 \, {\left (\frac {4 \, {\left (3 \, x^{2} + 6 \, x + 16\right )}}{x^{3}} + 3 \, \log \left (x - 4\right ) - 3 \, \log \relax (x)\right )} e^{5} - \frac {384 \, x^{4} e^{10} + 1728 \, e^{10} \log \left (x - 4\right )^{2} \log \relax (x) + 12 \, x^{2} {\left (36 \, e^{10} + 12 \, e^{5} + 1\right )} + 24 \, x {\left (36 \, e^{10} + 12 \, e^{5} + 1\right )} + 3 \, {\left (x^{3} {\left (36 \, e^{10} + 12 \, e^{5} + 1\right )} + 384 \, {\left (3 \, x e^{10} + 6 \, e^{10} + e^{5}\right )} \log \relax (x)\right )} \log \left (x - 4\right ) - 3 \, {\left (x^{3} {\left (36 \, e^{10} + 12 \, e^{5} + 1\right )} - 576 \, x^{2} e^{10} - 384 \, x {\left (6 \, e^{10} + e^{5}\right )} - 2304 \, e^{10} - 768 \, e^{5} - 64\right )} \log \relax (x) + 2304 \, e^{10} + 768 \, e^{5} + 64}{x^{3}} + \frac {4 \, {\left (3 \, x^{2} + 6 \, x + 16\right )}}{x^{3}} + 3 \, \log \left (x - 4\right ) - 3 \, \log \relax (x)\right )} e^{\left (-10\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-27*x+108)*exp(5)^2*log(x-4)^2+((-36*x^2+54*x+432)*exp(5)^2+(-18*x+72)*exp(5))*log(x-4)+(-9*x^3-1
8*x^2+216*x+432)*exp(5)^2+(-12*x^2+18*x+144)*exp(5)-3*x+12)*log(x)+(9*x-36)*exp(5)^2*log(x-4)^2+((18*x^2-36*x-
144)*exp(5)^2+(6*x-24)*exp(5))*log(x-4)+(2*x^5-8*x^4+9*x^3-108*x-144)*exp(5)^2+(6*x^2-12*x-48)*exp(5)+x-4)/(x^
5-4*x^4)/exp(5)^2,x, algorithm="maxima")

[Out]

-1/192*(36*(4*(3*x^2 + 6*x + 16)/x^3 + 3*log(x - 4) - 3*log(x))*e^10 + 12*(4*(3*x^2 + 6*x + 16)/x^3 + 3*log(x
- 4) - 3*log(x))*e^5 - (384*x^4*e^10 + 1728*e^10*log(x - 4)^2*log(x) + 12*x^2*(36*e^10 + 12*e^5 + 1) + 24*x*(3
6*e^10 + 12*e^5 + 1) + 3*(x^3*(36*e^10 + 12*e^5 + 1) + 384*(3*x*e^10 + 6*e^10 + e^5)*log(x))*log(x - 4) - 3*(x
^3*(36*e^10 + 12*e^5 + 1) - 576*x^2*e^10 - 384*x*(6*e^10 + e^5) - 2304*e^10 - 768*e^5 - 64)*log(x) + 2304*e^10
+ 768*e^5 + 64)/x^3 + 4*(3*x^2 + 6*x + 16)/x^3 + 3*log(x - 4) - 3*log(x))*e^(-10)

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mupad [B]  time = 5.28, size = 74, normalized size = 2.96 \begin {gather*} 2\,x+\frac {\ln \relax (x)\,\left (9\,x^2+6\,{\mathrm {e}}^{-5}\,\left (6\,{\mathrm {e}}^5+1\right )\,x+{\mathrm {e}}^{-10}\,{\left (6\,{\mathrm {e}}^5+1\right )}^2\right )}{x^3}+\frac {9\,{\ln \left (x-4\right )}^2\,\ln \relax (x)}{x^3}+\frac {\ln \left (x-4\right )\,{\mathrm {e}}^{-5}\,\ln \relax (x)\,\left (36\,{\mathrm {e}}^5+18\,x\,{\mathrm {e}}^5+6\right )}{x^3} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(-10)*(log(x - 4)*(exp(10)*(36*x - 18*x^2 + 144) - exp(5)*(6*x - 24)) - x + exp(5)*(12*x - 6*x^2 + 48)
+ exp(10)*(108*x - 9*x^3 + 8*x^4 - 2*x^5 + 144) - log(x)*(log(x - 4)*(exp(10)*(54*x - 36*x^2 + 432) - exp(5)*
(18*x - 72)) - 3*x + exp(5)*(18*x - 12*x^2 + 144) + exp(10)*(216*x - 18*x^2 - 9*x^3 + 432) - log(x - 4)^2*exp(
10)*(27*x - 108) + 12) - log(x - 4)^2*exp(10)*(9*x - 36) + 4))/(4*x^4 - x^5),x)

[Out]

2*x + (log(x)*(exp(-10)*(6*exp(5) + 1)^2 + 9*x^2 + 6*x*exp(-5)*(6*exp(5) + 1)))/x^3 + (9*log(x - 4)^2*log(x))/
x^3 + (log(x - 4)*exp(-5)*log(x)*(36*exp(5) + 18*x*exp(5) + 6))/x^3

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sympy [B]  time = 1.33, size = 97, normalized size = 3.88 \begin {gather*} 2 x + \frac {\left (18 x e^{5} \log {\relax (x )} + 6 \log {\relax (x )} + 36 e^{5} \log {\relax (x )}\right ) \log {\left (x - 4 \right )}}{x^{3} e^{5}} + \frac {\left (9 x^{2} e^{10} + 6 x e^{5} + 36 x e^{10} + 1 + 12 e^{5} + 36 e^{10}\right ) \log {\relax (x )}}{x^{3} e^{10}} + \frac {9 \log {\relax (x )} \log {\left (x - 4 \right )}^{2}}{x^{3}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-27*x+108)*exp(5)**2*ln(x-4)**2+((-36*x**2+54*x+432)*exp(5)**2+(-18*x+72)*exp(5))*ln(x-4)+(-9*x**
3-18*x**2+216*x+432)*exp(5)**2+(-12*x**2+18*x+144)*exp(5)-3*x+12)*ln(x)+(9*x-36)*exp(5)**2*ln(x-4)**2+((18*x**
2-36*x-144)*exp(5)**2+(6*x-24)*exp(5))*ln(x-4)+(2*x**5-8*x**4+9*x**3-108*x-144)*exp(5)**2+(6*x**2-12*x-48)*exp
(5)+x-4)/(x**5-4*x**4)/exp(5)**2,x)

[Out]

2*x + (18*x*exp(5)*log(x) + 6*log(x) + 36*exp(5)*log(x))*exp(-5)*log(x - 4)/x**3 + (9*x**2*exp(10) + 6*x*exp(5
) + 36*x*exp(10) + 1 + 12*exp(5) + 36*exp(10))*exp(-10)*log(x)/x**3 + 9*log(x)*log(x - 4)**2/x**3

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