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

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

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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}

result too large to display

Antiderivative was successfully verified.

[In]

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]

[Out]

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

Rule 2177

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 ===
True

Rule 2178

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

Rule 2268

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]

Rule 6688

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

Rule 6728

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]

Rule 6742

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

Rubi steps

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

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

Antiderivative was successfully verified.

[In]

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[
7/4]^2),x]

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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")

[Out]

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

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giac [B]  time = 2.42, size = 68, normalized size = 2.52 $$\begin{array}{c}\frac{x^3{e}^5-3x^2{e}^5-x{e}^5\log (7)+2x{e}^5\log (2)+x{e}^5-2x{e}^{(-x)}}{x^2{e}^5-3x{e}^5-e^5\log (7)+2e^5\log (2)+e^5}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

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")

[Out]

(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
*e^5*log(2) + e^5)

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maple [B]  time = 0.36, size = 63, normalized size = 2.33

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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
+(2*x^2-6*x+2)*ln(4/7)+x^4-6*x^3+11*x^2-6*x+1)/exp(5+x),x,method=_RETURNVERBOSE)

[Out]

(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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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")

[Out]

((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
*log(4/7) - 5)*sqrt(-4*log(4/7) + 5))

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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 +
1),x)

[Out]

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 +
1), x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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-
1)/(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)

[Out]

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

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