∫ e−5−x(−1+x−2x2+x3−(−1+x) log(7 4)+e5+x(1−6x+11x2−6x3+x4−(2−6x+2x2) log(7 4)+log2(7 4))) ___________________________________________________________________________________________________________________________________1−6x+11x2 −6x3+x4−(2−6x+2x2) log(7 4)+log2(7 4) dx

Optimal. Leaf size=27 \[ x+\frac {e^{-5-x} x}{-1+3 x-x^2+\log \left (\frac {7}{4}\right )} \]

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Rubi [C] time = 8.40, antiderivative size = 1653, normalized size of antiderivative = 61.22, number of steps used = 67, number of rules used = 6, integrand size = 116, $\frac {\text {number of rules}}{\text {integrand size}}$ = 0.052, Rules used = {6688, 6742, 2268, 2178, 2177, 6728}

Int[(E^(-5 - x)*(-1 + x - 2*x^2 + x^3 - (-1 + x)*Log[7/4] + E^(5 + x)*(1 - 6*x + 11*x^2 - 6*x^3 + x^4 - (2 - 6

*x + 2*x^2)*Log[7/4] + Log[7/4]^2)))/(1 - 6*x + 11*x^2 - 6*x^3 + x^4 - (2 - 6*x + 2*x^2)*Log[7/4] + Log[7/4]^2

x - (18*E^((-13 + Sqrt[5 + 4*Log[7/4]])/2)*ExpIntegralEi[(3 - 2*x - Sqrt[5 + 4*Log[7/4]])/2])/(5 + 4*Log[7/4])

^(3/2) + (18*E^((-13 - Sqrt[5 + 4*Log[7/4]])/2)*ExpIntegralEi[(3 - 2*x + Sqrt[5 + 4*Log[7/4]])/2])/(5 + 4*Log[

7/4])^(3/2) - (E^((-13 + Sqrt[5 + 4*Log[7/4]])/2)*ExpIntegralEi[(3 - 2*x - Sqrt[5 + 4*Log[7/4]])/2]*(1 - Log[7

/4]))/(5 + 4*Log[7/4])^(3/2) + (E^((-13 - Sqrt[5 + 4*Log[7/4]])/2)*ExpIntegralEi[(3 - 2*x + Sqrt[5 + 4*Log[7/4

]])/2]*(1 - Log[7/4]))/(5 + 4*Log[7/4])^(3/2) + (3*E^((-13 + Sqrt[5 + 4*Log[7/4]])/2)*ExpIntegralEi[(3 - 2*x -

Sqrt[5 + 4*Log[7/4]])/2]*(8 + Log[7/4]))/(5 + 4*Log[7/4])^(3/2) - (3*E^((-13 - Sqrt[5 + 4*Log[7/4]])/2)*ExpIn

tegralEi[(3 - 2*x + Sqrt[5 + 4*Log[7/4]])/2]*(8 + Log[7/4]))/(5 + 4*Log[7/4])^(3/2) + (2*E^((-13 + Sqrt[5 + 4*

Log[7/4]])/2)*ExpIntegralEi[(3 - 2*x - Sqrt[5 + 4*Log[7/4]])/2]*(1 - Log[7/4]))/(5 + 4*Log[7/4]) + (2*E^((-13

- Sqrt[5 + 4*Log[7/4]])/2)*ExpIntegralEi[(3 - 2*x + Sqrt[5 + 4*Log[7/4]])/2]*(1 - Log[7/4]))/(5 + 4*Log[7/4])

+ (2*E^((-13 + Sqrt[5 + 4*Log[7/4]])/2)*ExpIntegralEi[(3 - 2*x - Sqrt[5 + 4*Log[7/4]])/2])/Sqrt[5 + 4*Log[7/4]

] - (2*E^((-13 - Sqrt[5 + 4*Log[7/4]])/2)*ExpIntegralEi[(3 - 2*x + Sqrt[5 + 4*Log[7/4]])/2])/Sqrt[5 + 4*Log[7/

4]] + (E^((-13 + Sqrt[5 + 4*Log[7/4]])/2)*ExpIntegralEi[(3 - 2*x - Sqrt[5 + 4*Log[7/4]])/2]*(1 - 9/Sqrt[5 + 4*

Log[7/4]]))/2 + (E^((-13 - Sqrt[5 + 4*Log[7/4]])/2)*ExpIntegralEi[(3 - 2*x + Sqrt[5 + 4*Log[7/4]])/2]*(1 + 9/S

qrt[5 + 4*Log[7/4]]))/2 + (3*E^((-13 + Sqrt[5 + 4*Log[7/4]])/2)*ExpIntegralEi[(3 - 2*x - Sqrt[5 + 4*Log[7/4]])

/2]*(3 - Sqrt[5 + 4*Log[7/4]]))/(5 + 4*Log[7/4]) - (E^((-13 + Sqrt[5 + 4*Log[7/4]])/2)*ExpIntegralEi[(3 - 2*x

- Sqrt[5 + 4*Log[7/4]])/2]*(1 - Log[7/4])*(3 - Sqrt[5 + 4*Log[7/4]]))/(2*(5 + 4*Log[7/4])) - (E^((-13 + Sqrt[5

+ 4*Log[7/4]])/2)*ExpIntegralEi[(3 - 2*x - Sqrt[5 + 4*Log[7/4]])/2]*(8 + Log[7/4])*(3 - Sqrt[5 + 4*Log[7/4]])

)/(2*(5 + 4*Log[7/4])) - (4*E^(-5 - x)*(1 - Log[7/4]))/((5 + 4*Log[7/4])*(3 - 2*x - Sqrt[5 + 4*Log[7/4]])) - (

6*E^(-5 - x)*(3 - Sqrt[5 + 4*Log[7/4]]))/((5 + 4*Log[7/4])*(3 - 2*x - Sqrt[5 + 4*Log[7/4]])) + (E^(-5 - x)*(1

- Log[7/4])*(3 - Sqrt[5 + 4*Log[7/4]]))/((5 + 4*Log[7/4])*(3 - 2*x - Sqrt[5 + 4*Log[7/4]])) + (E^(-5 - x)*(8 +

Log[7/4])*(3 - Sqrt[5 + 4*Log[7/4]]))/((5 + 4*Log[7/4])*(3 - 2*x - Sqrt[5 + 4*Log[7/4]])) + (3*E^((-13 - Sqrt

[5 + 4*Log[7/4]])/2)*ExpIntegralEi[(3 - 2*x + Sqrt[5 + 4*Log[7/4]])/2]*(3 + Sqrt[5 + 4*Log[7/4]]))/(5 + 4*Log[

7/4]) - (E^((-13 - Sqrt[5 + 4*Log[7/4]])/2)*ExpIntegralEi[(3 - 2*x + Sqrt[5 + 4*Log[7/4]])/2]*(1 - Log[7/4])*(

3 + Sqrt[5 + 4*Log[7/4]]))/(2*(5 + 4*Log[7/4])) - (E^((-13 - Sqrt[5 + 4*Log[7/4]])/2)*ExpIntegralEi[(3 - 2*x +

Sqrt[5 + 4*Log[7/4]])/2]*(8 + Log[7/4])*(3 + Sqrt[5 + 4*Log[7/4]]))/(2*(5 + 4*Log[7/4])) - (4*E^(-5 - x)*(1 -

Log[7/4]))/((5 + 4*Log[7/4])*(3 - 2*x + Sqrt[5 + 4*Log[7/4]])) - (6*E^(-5 - x)*(3 + Sqrt[5 + 4*Log[7/4]]))/((

5 + 4*Log[7/4])*(3 - 2*x + Sqrt[5 + 4*Log[7/4]])) + (E^(-5 - x)*(1 - Log[7/4])*(3 + Sqrt[5 + 4*Log[7/4]]))/((5

+ 4*Log[7/4])*(3 - 2*x + Sqrt[5 + 4*Log[7/4]])) + (E^(-5 - x)*(8 + Log[7/4])*(3 + Sqrt[5 + 4*Log[7/4]]))/((5

Int[((b_.)*(F_)^((g_.)*((e_.) + (f_.)*(x_))))^(n_.)*((c_.) + (d_.)*(x_))^(m_), x_Symbol] :> Simp[((c + d*x)^(m

+ 1)*(b*F^(g*(e + f*x)))^n)/(d*(m + 1)), x] - Dist[(f*g*n*Log[F])/(d*(m + 1)), Int[(c + d*x)^(m + 1)*(b*F^(g*

(e + f*x)))^n, x], x] /; FreeQ[{F, b, c, d, e, f, g, n}, x] && LtQ[m, -1] && IntegerQ[2*m] && !$UseGamma ===

Int[(F_)^((g_.)*((e_.) + (f_.)*(x_)))/((c_.) + (d_.)*(x_)), x_Symbol] :> Simp[(F^(g*(e - (c*f)/d))*ExpIntegral

Ei[(f*g*(c + d*x)*Log[F])/d])/d, x] /; FreeQ[{F, c, d, e, f, g}, x] && !$UseGamma === True

Int[(F_)^((g_.)*((d_.) + (e_.)*(x_))^(n_.))/((a_.) + (b_.)*(x_) + (c_.)*(x_)^2), x_Symbol] :> Int[ExpandIntegr

and[F^(g*(d + e*x)^n), 1/(a + b*x + c*x^2), x], x] /; FreeQ[{F, a, b, c, d, e, g, n}, x]

Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; SimplerIntegrandQ[v, u, x]]

Int[(u_)/((a_.) + (b_.)*(x_)^(n_.) + (c_.)*(x_)^(n2_.)), x_Symbol] :> With[{v = RationalFunctionExpand[u/(a +

b*x^n + c*x^(2*n)), x]}, Int[v, x] /; SumQ[v]] /; FreeQ[{a, b, c}, x] && EqQ[n2, 2*n] && IGtQ[n, 0]

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^{-5-x} \left (-1-2 x^2+x^3+x \left (1-\log \left (\frac {7}{4}\right )\right )+e^{5+x} \left (1-3 x+x^2-\log \left (\frac {7}{4}\right )\right )^2+\log \left (\frac {7}{4}\right )\right )}{\left (1-3 x+x^2-\log \left (\frac {7}{4}\right )\right )^2} \, dx\\ &=\int \left (1-\frac {2 e^{-5-x} x^2}{\left (1-3 x+x^2-\log \left (\frac {7}{4}\right )\right )^2}+\frac {e^{-5-x} x^3}{\left (1-3 x+x^2-\log \left (\frac {7}{4}\right )\right )^2}-\frac {e^{-5-x} \left (1-\log \left (\frac {7}{4}\right )\right )}{\left (1-3 x+x^2-\log \left (\frac {7}{4}\right )\right )^2}-\frac {e^{-5-x} x \left (-1+\log \left (\frac {7}{4}\right )\right )}{\left (1-3 x+x^2-\log \left (\frac {7}{4}\right )\right )^2}\right ) \, dx\\ &=x-2 \int \frac {e^{-5-x} x^2}{\left (1-3 x+x^2-\log \left (\frac {7}{4}\right )\right )^2} \, dx+\left (1-\log \left (\frac {7}{4}\right )\right ) \int \frac {e^{-5-x} x}{\left (1-3 x+x^2-\log \left (\frac {7}{4}\right )\right )^2} \, dx+\left (-1+\log \left (\frac {7}{4}\right )\right ) \int \frac {e^{-5-x}}{\left (1-3 x+x^2-\log \left (\frac {7}{4}\right )\right )^2} \, dx+\int \frac {e^{-5-x} x^3}{\left (1-3 x+x^2-\log \left (\frac {7}{4}\right )\right )^2} \, dx\\ &=x-2 \int \left (\frac {e^{-5-x}}{1-3 x+x^2-\log \left (\frac {7}{4}\right )}+\frac {e^{-5-x} \left (-1+3 x+\log \left (\frac {7}{4}\right )\right )}{\left (1-3 x+x^2-\log \left (\frac {7}{4}\right )\right )^2}\right ) \, dx+\left (1-\log \left (\frac {7}{4}\right )\right ) \int \left (\frac {2 e^{-5-x} \left (3+\sqrt {5+4 \log \left (\frac {7}{4}\right )}\right )}{\left (5+4 \log \left (\frac {7}{4}\right )\right ) \left (3-2 x+\sqrt {5+4 \log \left (\frac {7}{4}\right )}\right )^2}+\frac {6 e^{-5-x}}{\left (5+4 \log \left (\frac {7}{4}\right )\right )^{3/2} \left (3-2 x+\sqrt {5+4 \log \left (\frac {7}{4}\right )}\right )}+\frac {2 e^{-5-x} \left (3-\sqrt {5+4 \log \left (\frac {7}{4}\right )}\right )}{\left (5+4 \log \left (\frac {7}{4}\right )\right ) \left (-3+2 x+\sqrt {5+4 \log \left (\frac {7}{4}\right )}\right )^2}+\frac {6 e^{-5-x}}{\left (5+4 \log \left (\frac {7}{4}\right )\right )^{3/2} \left (-3+2 x+\sqrt {5+4 \log \left (\frac {7}{4}\right )}\right )}\right ) \, dx+\left (-1+\log \left (\frac {7}{4}\right )\right ) \int \left (\frac {4 e^{-5-x}}{\left (5+4 \log \left (\frac {7}{4}\right )\right ) \left (3-2 x+\sqrt {5+4 \log \left (\frac {7}{4}\right )}\right )^2}+\frac {4 e^{-5-x}}{\left (5+4 \log \left (\frac {7}{4}\right )\right )^{3/2} \left (3-2 x+\sqrt {5+4 \log \left (\frac {7}{4}\right )}\right )}+\frac {4 e^{-5-x}}{\left (5+4 \log \left (\frac {7}{4}\right )\right ) \left (-3+2 x+\sqrt {5+4 \log \left (\frac {7}{4}\right )}\right )^2}+\frac {4 e^{-5-x}}{\left (5+4 \log \left (\frac {7}{4}\right )\right )^{3/2} \left (-3+2 x+\sqrt {5+4 \log \left (\frac {7}{4}\right )}\right )}\right ) \, dx+\int \left (\frac {e^{-5-x} (3+x)}{1-3 x+x^2-\log \left (\frac {7}{4}\right )}+\frac {e^{-5-x} \left (-3 \left (1-\log \left (\frac {7}{4}\right )\right )+x \left (8+\log \left (\frac {7}{4}\right )\right )\right )}{\left (1-3 x+x^2-\log \left (\frac {7}{4}\right )\right )^2}\right ) \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [A] time = 2.47, size = 28, normalized size = 1.04 \begin {gather*} x-\frac {e^{-5-x} x}{1-3 x+x^2-\log \left (\frac {7}{4}\right )} \end {gather*}

Integrate[(E^(-5 - x)*(-1 + x - 2*x^2 + x^3 - (-1 + x)*Log[7/4] + E^(5 + x)*(1 - 6*x + 11*x^2 - 6*x^3 + x^4 -

(2 - 6*x + 2*x^2)*Log[7/4] + Log[7/4]^2)))/(1 - 6*x + 11*x^2 - 6*x^3 + x^4 - (2 - 6*x + 2*x^2)*Log[7/4] + Log[

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fricas [A] time = 0.50, size = 42, normalized size = 1.56 \begin {gather*} \frac {{\left ({\left (x^{3} - 3 \, x^{2} + x \log \left (\frac {4}{7}\right ) + x\right )} e^{\left (x + 5\right )} - x\right )} e^{\left (-x - 5\right )}}{x^{2} - 3 \, x + \log \left (\frac {4}{7}\right ) + 1} \end {gather*}

integrate(((log(4/7)^2+(2*x^2-6*x+2)*log(4/7)+x^4-6*x^3+11*x^2-6*x+1)*exp(5+x)+(x-1)*log(4/7)+x^3-2*x^2+x-1)/(

log(4/7)^2+(2*x^2-6*x+2)*log(4/7)+x^4-6*x^3+11*x^2-6*x+1)/exp(5+x),x, algorithm="fricas")

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giac [B] time = 2.42, size = 68, normalized size = 2.52 \begin {gather*} \frac {x^{3} e^{5} - 3 \, x^{2} e^{5} - x e^{5} \log \relax (7) + 2 \, x e^{5} \log \relax (2) + x e^{5} - 2 \, x e^{\left (-x\right )}}{x^{2} e^{5} - 3 \, x e^{5} - e^{5} \log \relax (7) + 2 \, e^{5} \log \relax (2) + e^{5}} \end {gather*}

integrate(((log(4/7)^2+(2*x^2-6*x+2)*log(4/7)+x^4-6*x^3+11*x^2-6*x+1)*exp(5+x)+(x-1)*log(4/7)+x^3-2*x^2+x-1)/(

log(4/7)^2+(2*x^2-6*x+2)*log(4/7)+x^4-6*x^3+11*x^2-6*x+1)/exp(5+x),x, algorithm="giac")

(x^3*e^5 - 3*x^2*e^5 - x*e^5*log(7) + 2*x*e^5*log(2) + x*e^5 - 2*x*e^(-x))/(x^2*e^5 - 3*x*e^5 - e^5*log(7) + 2

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method	result	size

norman	$\frac {\left (x^{3} {\mathrm e}^{5+x}+\left (-3 \ln \relax (7)+6 \ln \relax (2)+3\right ) {\mathrm e}^{5+x}+\left (-8-\ln \relax (7)+2 \ln \relax (2)\right ) x \,{\mathrm e}^{5+x}-x \right ) {\mathrm e}^{-x -5}}{x^{2}+\ln \left (\frac {4}{7}\right )-3 x +1}$	$63$
derivativedivides	$\text {Expression too large to display}$	$2191$
default	$\text {Expression too large to display}$	$2191$

int(((ln(4/7)^2+(2*x^2-6*x+2)*ln(4/7)+x^4-6*x^3+11*x^2-6*x+1)*exp(5+x)+(x-1)*ln(4/7)+x^3-2*x^2+x-1)/(ln(4/7)^2

(x^3*exp(5+x)+(-3*ln(7)+6*ln(2)+3)*exp(5+x)+(-8-ln(7)+2*ln(2))*x*exp(5+x)-x)/(x^2+ln(4/7)-3*x+1)/exp(5+x)

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maxima [B] time = 0.52, size = 898, normalized size = 33.26 result too large to display

integrate(((log(4/7)^2+(2*x^2-6*x+2)*log(4/7)+x^4-6*x^3+11*x^2-6*x+1)*exp(5+x)+(x-1)*log(4/7)+x^3-2*x^2+x-1)/(

log(4/7)^2+(2*x^2-6*x+2)*log(4/7)+x^4-6*x^3+11*x^2-6*x+1)/exp(5+x),x, algorithm="maxima")

((2*x - 3)/(x^2*(4*log(4/7) - 5) - 3*x*(4*log(4/7) - 5) + 4*log(4/7)^2 - log(4/7) - 5) + 2*log((2*x - sqrt(-4*

log(4/7) + 5) - 3)/(2*x + sqrt(-4*log(4/7) + 5) - 3))/((4*log(4/7) - 5)*sqrt(-4*log(4/7) + 5)))*log(4/7)^2 + 2

*(2*(log(4/7) + 1)*log((2*x - sqrt(-4*log(4/7) + 5) - 3)/(2*x + sqrt(-4*log(4/7) + 5) - 3))/((4*log(4/7) - 5)*

sqrt(-4*log(4/7) + 5)) - (x*(2*log(4/7) - 7) + 3*log(4/7) + 3)/(x^2*(4*log(4/7) - 5) - 3*x*(4*log(4/7) - 5) +

4*log(4/7)^2 - log(4/7) - 5))*log(4/7) - 6*((3*x - 2*log(4/7) - 2)/(x^2*(4*log(4/7) - 5) - 3*x*(4*log(4/7) - 5

) + 4*log(4/7)^2 - log(4/7) - 5) + 3*log((2*x - sqrt(-4*log(4/7) + 5) - 3)/(2*x + sqrt(-4*log(4/7) + 5) - 3))/

((4*log(4/7) - 5)*sqrt(-4*log(4/7) + 5)))*log(4/7) + 2*((2*x - 3)/(x^2*(4*log(4/7) - 5) - 3*x*(4*log(4/7) - 5)

+ 4*log(4/7)^2 - log(4/7) - 5) + 2*log((2*x - sqrt(-4*log(4/7) + 5) - 3)/(2*x + sqrt(-4*log(4/7) + 5) - 3))/(

(4*log(4/7) - 5)*sqrt(-4*log(4/7) + 5)))*log(4/7) + x - x*e^(-x)/(x^2*e^5 - 3*x*e^5 - (log(7) - 2*log(2) - 1)*

e^5) - 3*(2*log(4/7)^2 - 14*log(4/7) + 11)*log((2*x - sqrt(-4*log(4/7) + 5) - 3)/(2*x + sqrt(-4*log(4/7) + 5)

- 3))/((4*log(4/7) - 5)*sqrt(-4*log(4/7) + 5)) - 27*(2*log(4/7) - 1)*log((2*x - sqrt(-4*log(4/7) + 5) - 3)/(2*

x + sqrt(-4*log(4/7) + 5) - 3))/((4*log(4/7) - 5)*sqrt(-4*log(4/7) + 5)) + 22*(log(4/7) + 1)*log((2*x - sqrt(-

4*log(4/7) + 5) - 3)/(2*x + sqrt(-4*log(4/7) + 5) - 3))/((4*log(4/7) - 5)*sqrt(-4*log(4/7) + 5)) + ((2*log(4/7

)^2 - 32*log(4/7) + 47)*x + 9*log(4/7)^2 - 9*log(4/7) - 18)/(x^2*(4*log(4/7) - 5) - 3*x*(4*log(4/7) - 5) + 4*l

og(4/7)^2 - log(4/7) - 5) - 11*(x*(2*log(4/7) - 7) + 3*log(4/7) + 3)/(x^2*(4*log(4/7) - 5) - 3*x*(4*log(4/7) -

5) + 4*log(4/7)^2 - log(4/7) - 5) + 6*(9*x*(log(4/7) - 2) - 2*log(4/7)^2 + 5*log(4/7) + 7)/(x^2*(4*log(4/7) -

5) - 3*x*(4*log(4/7) - 5) + 4*log(4/7)^2 - log(4/7) - 5) - 6*(3*x - 2*log(4/7) - 2)/(x^2*(4*log(4/7) - 5) - 3

*x*(4*log(4/7) - 5) + 4*log(4/7)^2 - log(4/7) - 5) + (2*x - 3)/(x^2*(4*log(4/7) - 5) - 3*x*(4*log(4/7) - 5) +

4*log(4/7)^2 - log(4/7) - 5) - 16*log((2*x - sqrt(-4*log(4/7) + 5) - 3)/(2*x + sqrt(-4*log(4/7) + 5) - 3))/((4

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mupad [F] time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int \frac {{\mathrm {e}}^{-x-5}\,\left (x+{\mathrm {e}}^{x+5}\,\left (\ln \left (\frac {4}{7}\right )\,\left (2\,x^2-6\,x+2\right )-6\,x+{\ln \left (\frac {4}{7}\right )}^2+11\,x^2-6\,x^3+x^4+1\right )+\ln \left (\frac {4}{7}\right )\,\left (x-1\right )-2\,x^2+x^3-1\right )}{\ln \left (\frac {4}{7}\right )\,\left (2\,x^2-6\,x+2\right )-6\,x+{\ln \left (\frac {4}{7}\right )}^2+11\,x^2-6\,x^3+x^4+1} \,d x \end {gather*}

int((exp(- x - 5)*(x + exp(x + 5)*(log(4/7)*(2*x^2 - 6*x + 2) - 6*x + log(4/7)^2 + 11*x^2 - 6*x^3 + x^4 + 1) +

log(4/7)*(x - 1) - 2*x^2 + x^3 - 1))/(log(4/7)*(2*x^2 - 6*x + 2) - 6*x + log(4/7)^2 + 11*x^2 - 6*x^3 + x^4 +

int((exp(- x - 5)*(x + exp(x + 5)*(log(4/7)*(2*x^2 - 6*x + 2) - 6*x + log(4/7)^2 + 11*x^2 - 6*x^3 + x^4 + 1) +

log(4/7)*(x - 1) - 2*x^2 + x^3 - 1))/(log(4/7)*(2*x^2 - 6*x + 2) - 6*x + log(4/7)^2 + 11*x^2 - 6*x^3 + x^4 +

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sympy [A] time = 0.30, size = 26, normalized size = 0.96 \begin {gather*} x - \frac {x e^{- x - 5}}{x^{2} - 3 x - \log {\relax (7 )} + 1 + 2 \log {\relax (2 )}} \end {gather*}

integrate(((ln(4/7)**2+(2*x**2-6*x+2)*ln(4/7)+x**4-6*x**3+11*x**2-6*x+1)*exp(5+x)+(x-1)*ln(4/7)+x**3-2*x**2+x-

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3.49.69 \(\int \frac {e^{-5-x} (-1+x-2 x^2+x^3-(-1+x) \log (\frac {7}{4})+e^{5+x} (1-6 x+11 x^2-6 x^3+x^4-(2-6 x+2 x^2) \log (\frac {7}{4})+\log ^2(\frac {7}{4})))}{1-6 x+11 x^2-6 x^3+x^4-(2-6 x+2 x^2) \log (\frac {7}{4})+\log ^2(\frac {7}{4})} \, dx\)