3.49.69 e5x(1+x2x2+x3(1+x)log(74)+e5+x(16x+11x26x3+x4(26x+2x2)log(74)+log2(74)))16x+11x26x3+x4(26x+2x2)log(74)+log2(74)dx

Optimal. Leaf size=27 x+e5xx1+3xx2+log(74)

________________________________________________________________________________________

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, number of rulesintegrand 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

integral=e5x(12x2+x3+x(1log(74))+e5+x(13x+x2log(74))2+log(74))(13x+x2log(74))2dx=(12e5xx2(13x+x2log(74))2+e5xx3(13x+x2log(74))2e5x(1log(74))(13x+x2log(74))2e5xx(1+log(74))(13x+x2log(74))2)dx=x2e5xx2(13x+x2log(74))2dx+(1log(74))e5xx(13x+x2log(74))2dx+(1+log(74))e5x(13x+x2log(74))2dx+e5xx3(13x+x2log(74))2dx=x2(e5x13x+x2log(74)+e5x(1+3x+log(74))(13x+x2log(74))2)dx+(1log(74))(2e5x(3+5+4log(74))(5+4log(74))(32x+5+4log(74))2+6e5x(5+4log(74))3/2(32x+5+4log(74))+2e5x(35+4log(74))(5+4log(74))(3+2x+5+4log(74))2+6e5x(5+4log(74))3/2(3+2x+5+4log(74)))dx+(1+log(74))(4e5x(5+4log(74))(32x+5+4log(74))2+4e5x(5+4log(74))3/2(32x+5+4log(74))+4e5x(5+4log(74))(3+2x+5+4log(74))2+4e5x(5+4log(74))3/2(3+2x+5+4log(74)))dx+(e5x(3+x)13x+x2log(74)+e5x(3(1log(74))+x(8+log(74)))(13x+x2log(74))2)dx=Rest of rules removed due to large latex content

________________________________________________________________________________________

Mathematica [A]  time = 2.47, size = 28, normalized size = 1.04 xe5xx13x+x2log(74)

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])

________________________________________________________________________________________

fricas [A]  time = 0.50, size = 42, normalized size = 1.56 ((x33x2+xlog(47)+x)e(x+5)x)e(x5)x23x+log(47)+1

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)

________________________________________________________________________________________

giac [B]  time = 2.42, size = 68, normalized size = 2.52 x3e53x2e5xe5log(7)+2xe5log(2)+xe52xe(x)x2e53xe5e5log(7)+2e5log(2)+e5

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)

________________________________________________________________________________________

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




method result size



norman (x3e5+x+(3ln(7)+6ln(2)+3)e5+x+(8ln(7)+2ln(2))xe5+xx)ex5x2+ln(47)3x+1 63
derivativedivides Expression too large to display 2191
default 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)

________________________________________________________________________________________

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))

________________________________________________________________________________________

mupad [F]  time = 0.00, size = -1, normalized size = -0.04 ex5(x+ex+5(ln(47)(2x26x+2)6x+ln(47)2+11x26x3+x4+1)+ln(47)(x1)2x2+x31)ln(47)(2x26x+2)6x+ln(47)2+11x26x3+x4+1dx

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)

________________________________________________________________________________________

sympy [A]  time = 0.30, size = 26, normalized size = 0.96 xxex5x23xlog(7)+1+2log(2)

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))

________________________________________________________________________________________