3.49.69
Optimal. Leaf size=27
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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, = 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
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Mathematica [A] time = 2.47, size = 28, normalized size = 1.04
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
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
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
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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
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
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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