3.8.91 \(\int \frac {3468+2155 x+462 x^2+39 x^3+x^4+e^{-6-6 x} (27+x)+e^{-4-4 x} (414+93 x+3 x^2)+e^{-2-2 x} (2091+876 x+105 x^2+3 x^3)+(-510 x+180 e^{-4-4 x} x-90 x^2+e^{-2-2 x} (930 x+180 x^2)) \log (x)}{64 x+e^{-6-6 x} x+48 x^2+12 x^3+x^4+e^{-4-4 x} (12 x+3 x^2)+e^{-2-2 x} (48 x+24 x^2+3 x^3)} \, dx\)

Optimal. Leaf size=24 \[ x+3 \left (3+\frac {5}{4+e^{-2-2 x}+x}\right )^2 \log (x) \]

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Rubi [F]  time = 25.11, 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 {3468+2155 x+462 x^2+39 x^3+x^4+e^{-6-6 x} (27+x)+e^{-4-4 x} \left (414+93 x+3 x^2\right )+e^{-2-2 x} \left (2091+876 x+105 x^2+3 x^3\right )+\left (-510 x+180 e^{-4-4 x} x-90 x^2+e^{-2-2 x} \left (930 x+180 x^2\right )\right ) \log (x)}{64 x+e^{-6-6 x} x+48 x^2+12 x^3+x^4+e^{-4-4 x} \left (12 x+3 x^2\right )+e^{-2-2 x} \left (48 x+24 x^2+3 x^3\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(3468 + 2155*x + 462*x^2 + 39*x^3 + x^4 + E^(-6 - 6*x)*(27 + x) + E^(-4 - 4*x)*(414 + 93*x + 3*x^2) + E^(-
2 - 2*x)*(2091 + 876*x + 105*x^2 + 3*x^3) + (-510*x + 180*E^(-4 - 4*x)*x - 90*x^2 + E^(-2 - 2*x)*(930*x + 180*
x^2))*Log[x])/(64*x + E^(-6 - 6*x)*x + 48*x^2 + 12*x^3 + x^4 + E^(-4 - 4*x)*(12*x + 3*x^2) + E^(-2 - 2*x)*(48*
x + 24*x^2 + 3*x^3)),x]

[Out]

x - 924/(4 + x)^2 + (231*x^2)/(4*(4 + x)^2) + 462/(4 + x) + (99*Log[x])/2 + (75*Log[x])/(4 + x)^2 - (45*x*Log[
x])/(2*(4 + x)) + 150*Log[x]*Defer[Int][1/((4 + x)^3*(1 + E^(2 + 2*x)*(4 + x))^3), x] + 300*Log[x]*Defer[Int][
1/((4 + x)^2*(1 + E^(2 + 2*x)*(4 + x))^3), x] + (75*Defer[Int][1/(x*(1 + E^(2 + 2*x)*(4 + x))^2), x])/16 - 450
*Log[x]*Defer[Int][1/((4 + x)^3*(1 + E^(2 + 2*x)*(4 + x))^2), x] - (75*Defer[Int][1/((4 + x)^2*(1 + E^(2 + 2*x
)*(4 + x))^2), x])/4 - 690*Log[x]*Defer[Int][1/((4 + x)^2*(1 + E^(2 + 2*x)*(4 + x))^2), x] - (75*Defer[Int][1/
((4 + x)*(1 + E^(2 + 2*x)*(4 + x))^2), x])/16 - 180*Log[x]*Defer[Int][1/((4 + x)*(1 + E^(2 + 2*x)*(4 + x))^2),
x] - 510*Defer[Int][1/((4 + x)^3*(1 + E^(2 + 2*x)*(4 + x))), x] + 450*Log[x]*Defer[Int][1/((4 + x)^3*(1 + E^(
2 + 2*x)*(4 + x))), x] - 90*Defer[Int][1/((4 + x)^2*(1 + E^(2 + 2*x)*(4 + x))), x] + 480*Log[x]*Defer[Int][1/(
(4 + x)^2*(1 + E^(2 + 2*x)*(4 + x))), x] + 180*Log[x]*Defer[Int][1/((4 + x)*(1 + E^(2 + 2*x)*(4 + x))), x] - 2
040*Defer[Int][1/((4 + x)^3*(x + E^(2 + 2*x)*x*(4 + x))), x] - 150*Defer[Int][Defer[Int][1/((4 + x)^3*(1 + E^(
2 + 2*x)*(4 + x))^3), x]/x, x] - 300*Defer[Int][Defer[Int][1/((4 + x)^2*(1 + E^(2 + 2*x)*(4 + x))^3), x]/x, x]
+ 450*Defer[Int][Defer[Int][1/((4 + x)^3*(1 + E^(2 + 2*x)*(4 + x))^2), x]/x, x] + 690*Defer[Int][Defer[Int][1
/((4 + x)^2*(1 + E^(2 + 2*x)*(4 + x))^2), x]/x, x] + 180*Defer[Int][Defer[Int][1/((4 + x)*(1 + E^(2 + 2*x)*(4
+ x))^2), x]/x, x] - 450*Defer[Int][Defer[Int][1/((4 + x)^3*(1 + E^(2 + 2*x)*(4 + x))), x]/x, x] - 480*Defer[I
nt][Defer[Int][1/((4 + x)^2*(1 + E^(2 + 2*x)*(4 + x))), x]/x, x] - 180*Defer[Int][Defer[Int][1/((4 + x)*(1 + E
^(2 + 2*x)*(4 + x))), x]/x, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {27+x+3 e^{2+2 x} \left (138+31 x+x^2\right )+3 e^{4+4 x} \left (697+292 x+35 x^2+x^3\right )+e^{6+6 x} \left (3468+2155 x+462 x^2+39 x^3+x^4\right )-30 e^{2+2 x} \left (-2+e^{2+2 x}\right ) x \left (3+e^{2+2 x} (17+3 x)\right ) \log (x)}{x \left (1+e^{2+2 x} (4+x)\right )^3} \, dx\\ &=\int \left (\frac {150 (9+2 x) \log (x)}{(4+x)^3 \left (1+4 e^{2+2 x}+e^{2+2 x} x\right )^3}+\frac {3468+2155 x+462 x^2+39 x^3+x^4-510 x \log (x)-90 x^2 \log (x)}{x (4+x)^3}+\frac {30 \left (-68-29 x-3 x^2+175 x \log (x)+64 x^2 \log (x)+6 x^3 \log (x)\right )}{x (4+x)^3 \left (1+4 e^{2+2 x}+e^{2+2 x} x\right )}-\frac {15 \left (-20-5 x+406 x \log (x)+142 x^2 \log (x)+12 x^3 \log (x)\right )}{x (4+x)^3 \left (1+4 e^{2+2 x}+e^{2+2 x} x\right )^2}\right ) \, dx\\ &=-\left (15 \int \frac {-20-5 x+406 x \log (x)+142 x^2 \log (x)+12 x^3 \log (x)}{x (4+x)^3 \left (1+4 e^{2+2 x}+e^{2+2 x} x\right )^2} \, dx\right )+30 \int \frac {-68-29 x-3 x^2+175 x \log (x)+64 x^2 \log (x)+6 x^3 \log (x)}{x (4+x)^3 \left (1+4 e^{2+2 x}+e^{2+2 x} x\right )} \, dx+150 \int \frac {(9+2 x) \log (x)}{(4+x)^3 \left (1+4 e^{2+2 x}+e^{2+2 x} x\right )^3} \, dx+\int \frac {3468+2155 x+462 x^2+39 x^3+x^4-510 x \log (x)-90 x^2 \log (x)}{x (4+x)^3} \, dx\\ &=-\left (15 \int \left (\frac {-20-5 x+406 x \log (x)+142 x^2 \log (x)+12 x^3 \log (x)}{64 x \left (1+4 e^{2+2 x}+e^{2+2 x} x\right )^2}-\frac {-20-5 x+406 x \log (x)+142 x^2 \log (x)+12 x^3 \log (x)}{4 (4+x)^3 \left (1+4 e^{2+2 x}+e^{2+2 x} x\right )^2}-\frac {-20-5 x+406 x \log (x)+142 x^2 \log (x)+12 x^3 \log (x)}{16 (4+x)^2 \left (1+4 e^{2+2 x}+e^{2+2 x} x\right )^2}-\frac {-20-5 x+406 x \log (x)+142 x^2 \log (x)+12 x^3 \log (x)}{64 (4+x) \left (1+4 e^{2+2 x}+e^{2+2 x} x\right )^2}\right ) \, dx\right )+30 \int \frac {-68-29 x-3 x^2+x \left (175+64 x+6 x^2\right ) \log (x)}{(4+x)^3 \left (x+e^{2+2 x} x (4+x)\right )} \, dx-150 \int \frac {\int \frac {1}{(4+x)^3 \left (1+e^{2+2 x} (4+x)\right )^3} \, dx+2 \int \frac {1}{(4+x)^2 \left (1+e^{2+2 x} (4+x)\right )^3} \, dx}{x} \, dx+(150 \log (x)) \int \frac {1}{(4+x)^3 \left (1+e^{2+2 x} (4+x)\right )^3} \, dx+(300 \log (x)) \int \frac {1}{(4+x)^2 \left (1+e^{2+2 x} (4+x)\right )^3} \, dx+\int \left (\frac {2155}{(4+x)^3}+\frac {3468}{x (4+x)^3}+\frac {462 x}{(4+x)^3}+\frac {39 x^2}{(4+x)^3}+\frac {x^3}{(4+x)^3}-\frac {30 (17+3 x) \log (x)}{(4+x)^3}\right ) \, dx\\ &=-\frac {2155}{2 (4+x)^2}-\frac {15}{64} \int \frac {-20-5 x+406 x \log (x)+142 x^2 \log (x)+12 x^3 \log (x)}{x \left (1+4 e^{2+2 x}+e^{2+2 x} x\right )^2} \, dx+\frac {15}{64} \int \frac {-20-5 x+406 x \log (x)+142 x^2 \log (x)+12 x^3 \log (x)}{(4+x) \left (1+4 e^{2+2 x}+e^{2+2 x} x\right )^2} \, dx+\frac {15}{16} \int \frac {-20-5 x+406 x \log (x)+142 x^2 \log (x)+12 x^3 \log (x)}{(4+x)^2 \left (1+4 e^{2+2 x}+e^{2+2 x} x\right )^2} \, dx+\frac {15}{4} \int \frac {-20-5 x+406 x \log (x)+142 x^2 \log (x)+12 x^3 \log (x)}{(4+x)^3 \left (1+4 e^{2+2 x}+e^{2+2 x} x\right )^2} \, dx-30 \int \frac {(17+3 x) \log (x)}{(4+x)^3} \, dx+30 \int \left (-\frac {29}{(4+x)^3 \left (1+4 e^{2+2 x}+e^{2+2 x} x\right )}-\frac {68}{x (4+x)^3 \left (1+4 e^{2+2 x}+e^{2+2 x} x\right )}-\frac {3 x}{(4+x)^3 \left (1+4 e^{2+2 x}+e^{2+2 x} x\right )}+\frac {175 \log (x)}{(4+x)^3 \left (1+4 e^{2+2 x}+e^{2+2 x} x\right )}+\frac {64 x \log (x)}{(4+x)^3 \left (1+4 e^{2+2 x}+e^{2+2 x} x\right )}+\frac {6 x^2 \log (x)}{(4+x)^3 \left (1+4 e^{2+2 x}+e^{2+2 x} x\right )}\right ) \, dx+39 \int \frac {x^2}{(4+x)^3} \, dx-150 \int \left (\frac {\int \frac {1}{(4+x)^3 \left (1+e^{2+2 x} (4+x)\right )^3} \, dx}{x}+\frac {2 \int \frac {1}{(4+x)^2 \left (1+e^{2+2 x} (4+x)\right )^3} \, dx}{x}\right ) \, dx+462 \int \frac {x}{(4+x)^3} \, dx+3468 \int \frac {1}{x (4+x)^3} \, dx+(150 \log (x)) \int \frac {1}{(4+x)^3 \left (1+e^{2+2 x} (4+x)\right )^3} \, dx+(300 \log (x)) \int \frac {1}{(4+x)^2 \left (1+e^{2+2 x} (4+x)\right )^3} \, dx+\int \frac {x^3}{(4+x)^3} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [B]  time = 0.18, size = 55, normalized size = 2.29 \begin {gather*} \frac {x \left (1+e^{2+2 x} (4+x)\right )^2+3 \left (3+e^{2+2 x} (17+3 x)\right )^2 \log (x)}{\left (1+e^{2+2 x} (4+x)\right )^2} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(3468 + 2155*x + 462*x^2 + 39*x^3 + x^4 + E^(-6 - 6*x)*(27 + x) + E^(-4 - 4*x)*(414 + 93*x + 3*x^2)
+ E^(-2 - 2*x)*(2091 + 876*x + 105*x^2 + 3*x^3) + (-510*x + 180*E^(-4 - 4*x)*x - 90*x^2 + E^(-2 - 2*x)*(930*x
+ 180*x^2))*Log[x])/(64*x + E^(-6 - 6*x)*x + 48*x^2 + 12*x^3 + x^4 + E^(-4 - 4*x)*(12*x + 3*x^2) + E^(-2 - 2*x
)*(48*x + 24*x^2 + 3*x^3)),x]

[Out]

(x*(1 + E^(2 + 2*x)*(4 + x))^2 + 3*(3 + E^(2 + 2*x)*(17 + 3*x))^2*Log[x])/(1 + E^(2 + 2*x)*(4 + x))^2

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fricas [B]  time = 0.81, size = 98, normalized size = 4.08 \begin {gather*} \frac {x^{3} + 8 \, x^{2} + 2 \, {\left (x^{2} + 4 \, x\right )} e^{\left (-2 \, x - 2\right )} + x e^{\left (-4 \, x - 4\right )} + 3 \, {\left (9 \, x^{2} + 6 \, {\left (3 \, x + 17\right )} e^{\left (-2 \, x - 2\right )} + 102 \, x + 9 \, e^{\left (-4 \, x - 4\right )} + 289\right )} \log \relax (x) + 16 \, x}{x^{2} + 2 \, {\left (x + 4\right )} e^{\left (-2 \, x - 2\right )} + 8 \, x + e^{\left (-4 \, x - 4\right )} + 16} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((180*x*exp(-x-1)^4+(180*x^2+930*x)*exp(-x-1)^2-90*x^2-510*x)*log(x)+(x+27)*exp(-x-1)^6+(3*x^2+93*x+
414)*exp(-x-1)^4+(3*x^3+105*x^2+876*x+2091)*exp(-x-1)^2+x^4+39*x^3+462*x^2+2155*x+3468)/(x*exp(-x-1)^6+(3*x^2+
12*x)*exp(-x-1)^4+(3*x^3+24*x^2+48*x)*exp(-x-1)^2+x^4+12*x^3+48*x^2+64*x),x, algorithm="fricas")

[Out]

(x^3 + 8*x^2 + 2*(x^2 + 4*x)*e^(-2*x - 2) + x*e^(-4*x - 4) + 3*(9*x^2 + 6*(3*x + 17)*e^(-2*x - 2) + 102*x + 9*
e^(-4*x - 4) + 289)*log(x) + 16*x)/(x^2 + 2*(x + 4)*e^(-2*x - 2) + 8*x + e^(-4*x - 4) + 16)

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giac [B]  time = 6.60, size = 160, normalized size = 6.67 \begin {gather*} \frac {x^{3} e^{\left (4 \, x + 4\right )} + 27 \, x^{2} e^{\left (4 \, x + 4\right )} \log \relax (x) + 8 \, x^{2} e^{\left (4 \, x + 4\right )} + 2 \, x^{2} e^{\left (2 \, x + 2\right )} + 306 \, x e^{\left (4 \, x + 4\right )} \log \relax (x) + 54 \, x e^{\left (2 \, x + 2\right )} \log \relax (x) + 16 \, x e^{\left (4 \, x + 4\right )} + 8 \, x e^{\left (2 \, x + 2\right )} + 867 \, e^{\left (4 \, x + 4\right )} \log \relax (x) + 306 \, e^{\left (2 \, x + 2\right )} \log \relax (x) + x + 27 \, \log \relax (x)}{x^{2} e^{\left (4 \, x + 4\right )} + 8 \, x e^{\left (4 \, x + 4\right )} + 2 \, x e^{\left (2 \, x + 2\right )} + 16 \, e^{\left (4 \, x + 4\right )} + 8 \, e^{\left (2 \, x + 2\right )} + 1} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((180*x*exp(-x-1)^4+(180*x^2+930*x)*exp(-x-1)^2-90*x^2-510*x)*log(x)+(x+27)*exp(-x-1)^6+(3*x^2+93*x+
414)*exp(-x-1)^4+(3*x^3+105*x^2+876*x+2091)*exp(-x-1)^2+x^4+39*x^3+462*x^2+2155*x+3468)/(x*exp(-x-1)^6+(3*x^2+
12*x)*exp(-x-1)^4+(3*x^3+24*x^2+48*x)*exp(-x-1)^2+x^4+12*x^3+48*x^2+64*x),x, algorithm="giac")

[Out]

(x^3*e^(4*x + 4) + 27*x^2*e^(4*x + 4)*log(x) + 8*x^2*e^(4*x + 4) + 2*x^2*e^(2*x + 2) + 306*x*e^(4*x + 4)*log(x
) + 54*x*e^(2*x + 2)*log(x) + 16*x*e^(4*x + 4) + 8*x*e^(2*x + 2) + 867*e^(4*x + 4)*log(x) + 306*e^(2*x + 2)*lo
g(x) + x + 27*log(x))/(x^2*e^(4*x + 4) + 8*x*e^(4*x + 4) + 2*x*e^(2*x + 2) + 16*e^(4*x + 4) + 8*e^(2*x + 2) +
1)

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maple [A]  time = 0.05, size = 35, normalized size = 1.46

method	result	size
risch	\(\frac {15 \left (6 \,{\mathrm e}^{-2 x -2}+6 x +29\right ) \ln \relax (x )}{\left ({\mathrm e}^{-2 x -2}+4+x \right )^{2}}+x +27 \ln \relax (x )\)	\(35\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((180*x*exp(-x-1)^4+(180*x^2+930*x)*exp(-x-1)^2-90*x^2-510*x)*ln(x)+(x+27)*exp(-x-1)^6+(3*x^2+93*x+414)*ex
p(-x-1)^4+(3*x^3+105*x^2+876*x+2091)*exp(-x-1)^2+x^4+39*x^3+462*x^2+2155*x+3468)/(x*exp(-x-1)^6+(3*x^2+12*x)*e
xp(-x-1)^4+(3*x^3+24*x^2+48*x)*exp(-x-1)^2+x^4+12*x^3+48*x^2+64*x),x,method=_RETURNVERBOSE)

[Out]

15*(6*exp(-2*x-2)+6*x+29)/(exp(-2*x-2)+4+x)^2*ln(x)+x+27*ln(x)

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maxima [B]  time = 0.68, size = 124, normalized size = 5.17 \begin {gather*} \frac {{\left (x^{3} e^{4} + 8 \, x^{2} e^{4} + 16 \, x e^{4} + 3 \, {\left (9 \, x^{2} e^{4} + 102 \, x e^{4} + 289 \, e^{4}\right )} \log \relax (x)\right )} e^{\left (4 \, x\right )} + 2 \, {\left (x^{2} e^{2} + 4 \, x e^{2} + 9 \, {\left (3 \, x e^{2} + 17 \, e^{2}\right )} \log \relax (x)\right )} e^{\left (2 \, x\right )} + x + 27 \, \log \relax (x)}{{\left (x^{2} e^{4} + 8 \, x e^{4} + 16 \, e^{4}\right )} e^{\left (4 \, x\right )} + 2 \, {\left (x e^{2} + 4 \, e^{2}\right )} e^{\left (2 \, x\right )} + 1} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((180*x*exp(-x-1)^4+(180*x^2+930*x)*exp(-x-1)^2-90*x^2-510*x)*log(x)+(x+27)*exp(-x-1)^6+(3*x^2+93*x+
414)*exp(-x-1)^4+(3*x^3+105*x^2+876*x+2091)*exp(-x-1)^2+x^4+39*x^3+462*x^2+2155*x+3468)/(x*exp(-x-1)^6+(3*x^2+
12*x)*exp(-x-1)^4+(3*x^3+24*x^2+48*x)*exp(-x-1)^2+x^4+12*x^3+48*x^2+64*x),x, algorithm="maxima")

[Out]

((x^3*e^4 + 8*x^2*e^4 + 16*x*e^4 + 3*(9*x^2*e^4 + 102*x*e^4 + 289*e^4)*log(x))*e^(4*x) + 2*(x^2*e^2 + 4*x*e^2
+ 9*(3*x*e^2 + 17*e^2)*log(x))*e^(2*x) + x + 27*log(x))/((x^2*e^4 + 8*x*e^4 + 16*e^4)*e^(4*x) + 2*(x*e^2 + 4*e
^2)*e^(2*x) + 1)

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mupad [F]  time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int \frac {2155\,x+{\mathrm {e}}^{-4\,x-4}\,\left (3\,x^2+93\,x+414\right )-\ln \relax (x)\,\left (510\,x-{\mathrm {e}}^{-2\,x-2}\,\left (180\,x^2+930\,x\right )-180\,x\,{\mathrm {e}}^{-4\,x-4}+90\,x^2\right )+{\mathrm {e}}^{-2\,x-2}\,\left (3\,x^3+105\,x^2+876\,x+2091\right )+{\mathrm {e}}^{-6\,x-6}\,\left (x+27\right )+462\,x^2+39\,x^3+x^4+3468}{64\,x+{\mathrm {e}}^{-4\,x-4}\,\left (3\,x^2+12\,x\right )+x\,{\mathrm {e}}^{-6\,x-6}+{\mathrm {e}}^{-2\,x-2}\,\left (3\,x^3+24\,x^2+48\,x\right )+48\,x^2+12\,x^3+x^4} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((2155*x + exp(- 4*x - 4)*(93*x + 3*x^2 + 414) - log(x)*(510*x - exp(- 2*x - 2)*(930*x + 180*x^2) - 180*x*e
xp(- 4*x - 4) + 90*x^2) + exp(- 2*x - 2)*(876*x + 105*x^2 + 3*x^3 + 2091) + exp(- 6*x - 6)*(x + 27) + 462*x^2
+ 39*x^3 + x^4 + 3468)/(64*x + exp(- 4*x - 4)*(12*x + 3*x^2) + x*exp(- 6*x - 6) + exp(- 2*x - 2)*(48*x + 24*x^
2 + 3*x^3) + 48*x^2 + 12*x^3 + x^4),x)

[Out]

int((2155*x + exp(- 4*x - 4)*(93*x + 3*x^2 + 414) - log(x)*(510*x - exp(- 2*x - 2)*(930*x + 180*x^2) - 180*x*e
xp(- 4*x - 4) + 90*x^2) + exp(- 2*x - 2)*(876*x + 105*x^2 + 3*x^3 + 2091) + exp(- 6*x - 6)*(x + 27) + 462*x^2
+ 39*x^3 + x^4 + 3468)/(64*x + exp(- 4*x - 4)*(12*x + 3*x^2) + x*exp(- 6*x - 6) + exp(- 2*x - 2)*(48*x + 24*x^
2 + 3*x^3) + 48*x^2 + 12*x^3 + x^4), x)

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sympy [B]  time = 0.46, size = 61, normalized size = 2.54 \begin {gather*} x + \frac {90 x \log {\relax (x )} + 90 e^{- 2 x - 2} \log {\relax (x )} + 435 \log {\relax (x )}}{x^{2} + 8 x + \left (2 x + 8\right ) e^{- 2 x - 2} + e^{- 4 x - 4} + 16} + 27 \log {\relax (x )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((180*x*exp(-x-1)**4+(180*x**2+930*x)*exp(-x-1)**2-90*x**2-510*x)*ln(x)+(x+27)*exp(-x-1)**6+(3*x**2+
93*x+414)*exp(-x-1)**4+(3*x**3+105*x**2+876*x+2091)*exp(-x-1)**2+x**4+39*x**3+462*x**2+2155*x+3468)/(x*exp(-x-
1)**6+(3*x**2+12*x)*exp(-x-1)**4+(3*x**3+24*x**2+48*x)*exp(-x-1)**2+x**4+12*x**3+48*x**2+64*x),x)

[Out]

x + (90*x*log(x) + 90*exp(-2*x - 2)*log(x) + 435*log(x))/(x**2 + 8*x + (2*x + 8)*exp(-2*x - 2) + exp(-4*x - 4)
+ 16) + 27*log(x)

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