\(\int \frac {19+52 x+73 x^2+58 x^3+28 x^4+8 x^5+x^6+e^x (25+60 x+76 x^2+58 x^3+28 x^4+8 x^5+x^6)}{25+60 x+76 x^2+58 x^3+28 x^4+8 x^5+x^6} \, dx\) [4463]
Optimal result
Integrand size = 91, antiderivative size = 18 \[
\int \frac {19+52 x+73 x^2+58 x^3+28 x^4+8 x^5+x^6+e^x \left (25+60 x+76 x^2+58 x^3+28 x^4+8 x^5+x^6\right )}{25+60 x+76 x^2+58 x^3+28 x^4+8 x^5+x^6} \, dx=4+e^x+x+\frac {x}{-1+x+(1+x)^4}
\]
[Out]
4+x+exp(x)+x/((1+x)^4+x-1)
Rubi [F]
\[
\int \frac {19+52 x+73 x^2+58 x^3+28 x^4+8 x^5+x^6+e^x \left (25+60 x+76 x^2+58 x^3+28 x^4+8 x^5+x^6\right )}{25+60 x+76 x^2+58 x^3+28 x^4+8 x^5+x^6} \, dx=\int \frac {19+52 x+73 x^2+58 x^3+28 x^4+8 x^5+x^6+e^x \left (25+60 x+76 x^2+58 x^3+28 x^4+8 x^5+x^6\right )}{25+60 x+76 x^2+58 x^3+28 x^4+8 x^5+x^6} \, dx
\]
[In]
Int[(19 + 52*x + 73*x^2 + 58*x^3 + 28*x^4 + 8*x^5 + x^6 + E^x*(25 + 60*x + 76*x^2 + 58*x^3 + 28*x^4 + 8*x^5 +
x^6))/(25 + 60*x + 76*x^2 + 58*x^3 + 28*x^4 + 8*x^5 + x^6),x]
[Out]
E^x + (6096*(-47 + 3*Sqrt[249])^(1/3))/(83*(4*2^(1/3) - (-94 + 6*Sqrt[249])^(2/3) + 2*(-47 + 3*Sqrt[249])^(1/3
)*(4 + 3*x))) + (342*(2/83)^(2/3)*(3*(747 - 47*Sqrt[249]))^(1/3)*(8 + 2^(1/3)*(4/(-47 + 3*Sqrt[249])^(1/3) - (
-94 + 6*Sqrt[249])^(1/3))*(4 + 3*x)))/((4 + 2^(1/3)*(-47 + 3*Sqrt[249])^(2/3))*(2^(1/3)*(4/(-47 + 3*Sqrt[249])
^(1/3) - (-94 + 6*Sqrt[249])^(1/3)) + 2*(4 + 3*x))*(4 + 8*(2/(-47 + 3*Sqrt[249]))^(2/3) + 2^(1/3)*(-47 + 3*Sqr
t[249])^(2/3) - 2^(1/3)*(4/(-47 + 3*Sqrt[249])^(1/3) - (-94 + 6*Sqrt[249])^(1/3))*(4 + 3*x) + 2*(4 + 3*x)^2))
- (936*(2/83)^(2/3)*(3*(747 - 47*Sqrt[249]))^(1/3)*(42 + ((4*2^(2/3)*(15 - Sqrt[249]) + (21 - Sqrt[249])*(-94
+ 6*Sqrt[249])^(1/3))*(4 + 3*x))/(-47 + 3*Sqrt[249])^(2/3)))/((4 + 2^(1/3)*(-47 + 3*Sqrt[249])^(2/3))*(2^(1/3)
*(4/(-47 + 3*Sqrt[249])^(1/3) - (-94 + 6*Sqrt[249])^(1/3)) + 2*(4 + 3*x))*(4 + 8*(2/(-47 + 3*Sqrt[249]))^(2/3)
+ 2^(1/3)*(-47 + 3*Sqrt[249])^(2/3) - 2^(1/3)*(4/(-47 + 3*Sqrt[249])^(1/3) - (-94 + 6*Sqrt[249])^(1/3))*(4 +
3*x) + 2*(4 + 3*x)^2)) - (1824*Sqrt[6]*(531523*2^(2/3) - 33687*2^(2/3)*Sqrt[249] + 56*(9900994 - 627450*Sqrt[2
49])^(1/3)*(47 - 3*Sqrt[249]) + 4*(11197 - 705*Sqrt[249])*(-94 + 6*Sqrt[249])^(1/3) - 658*(-104951 + 6651*Sqrt
[249])^(2/3) + 42*Sqrt[249]*(-104951 + 6651*Sqrt[249])^(2/3))*ArcTan[(4*2^(1/3) - (-94 + 6*Sqrt[249])^(2/3) -
4*(-47 + 3*Sqrt[249])^(1/3)*(4 + 3*x))/Sqrt[6*(8*2^(2/3) + 8*(-47 + 3*Sqrt[249])^(2/3) + 2^(1/3)*(-47 + 3*Sqrt
[249])^(4/3))]])/((4 - 8*(2/(-47 + 3*Sqrt[249]))^(2/3) - 2^(1/3)*(-47 + 3*Sqrt[249])^(2/3))^2*(8*2^(2/3) - 4*(
-47 + 3*Sqrt[249])^(2/3) + 2^(1/3)*(-47 + 3*Sqrt[249])^(4/3))*(8*2^(2/3) + 8*(-47 + 3*Sqrt[249])^(2/3) + 2^(1/
3)*(-47 + 3*Sqrt[249])^(4/3))^(3/2)) - (9984*Sqrt[6]*(2^(1/3)*(748851501 - 47456537*Sqrt[249])*(-47 + 3*Sqrt[2
49])^(2/3) + 8*(2225 - 141*Sqrt[249])^(1/3)*(64*2^(2/3)*(807591 - 51179*Sqrt[249]) - (122751 - 7779*Sqrt[249])
*(-47 + 3*Sqrt[249])^(2/3)) - 12*(182077962 - 11538722*Sqrt[249] + 2^(2/3)*(1930035 - 122311*Sqrt[249])*(-1049
51 + 6651*Sqrt[249])^(1/3)) + 4*(-47 + 3*Sqrt[249])^(1/3)*(2^(2/3)*(86218401 - 5463869*Sqrt[249]) + 32*(17121
- 1085*Sqrt[249])*(-104951 + 6651*Sqrt[249])^(2/3)))*ArcTan[(4*2^(1/3) - (-94 + 6*Sqrt[249])^(2/3) - 4*(-47 +
3*Sqrt[249])^(1/3)*(4 + 3*x))/Sqrt[6*(8*2^(2/3) + 8*(-47 + 3*Sqrt[249])^(2/3) + 2^(1/3)*(-47 + 3*Sqrt[249])^(4
/3))]])/((-47 + 3*Sqrt[249])^(7/3)*(4 - 8*(2/(-47 + 3*Sqrt[249]))^(2/3) - 2^(1/3)*(-47 + 3*Sqrt[249])^(2/3))^2
*(8*2^(2/3) - 4*(-47 + 3*Sqrt[249])^(2/3) + 2^(1/3)*(-47 + 3*Sqrt[249])^(4/3))*(8*2^(2/3) + 8*(-47 + 3*Sqrt[24
9])^(2/3) + 2^(1/3)*(-47 + 3*Sqrt[249])^(4/3))^(3/2)) - (1248*Sqrt[3/83]*2^(2/3)*(21*2^(2/3)*(4950497 - 313725
*Sqrt[249]) + 120*(104951 - 6651*Sqrt[249])*(-47 + 3*Sqrt[249])^(2/3) + 2*(6064041 - 384293*Sqrt[249])*(-94 +
6*Sqrt[249])^(1/3) + 2*(40917 - 2593*Sqrt[249])*(2225 - 141*Sqrt[249])^(1/3)*(-94 + 6*Sqrt[249])^(2/3))*Log[4*
2^(2/3)*(15 - Sqrt[249]) - 12*(-47 + 3*Sqrt[249])^(2/3) + (21 - Sqrt[249])*(-94 + 6*Sqrt[249])^(1/3) + 47*2^(2
/3)*x - 3*2^(2/3)*Sqrt[249]*x - 16*(-47 + 3*Sqrt[249])^(2/3)*x + 4*(2*(-47 + 3*Sqrt[249]))^(1/3)*x - 6*(-47 +
3*Sqrt[249])^(2/3)*x^2])/((-47 + 3*Sqrt[249])^(10/3)*(4 - 8*(2/(-47 + 3*Sqrt[249]))^(2/3) - 2^(1/3)*(-47 + 3*S
qrt[249])^(2/3))^2*(4 + 2^(1/3)*(-47 + 3*Sqrt[249])^(2/3))) - (228*Sqrt[3/83]*(8*(-47 + 3*Sqrt[249])^(4/3) - 2
^(1/3)*(8900 - 564*Sqrt[249] - 47*2^(1/3)*(-47 + 3*Sqrt[249])^(5/3)))*Log[4*2^(2/3)*(15 - Sqrt[249]) - 12*(-47
+ 3*Sqrt[249])^(2/3) + (21 - Sqrt[249])*(-94 + 6*Sqrt[249])^(1/3) + 47*2^(2/3)*x - 3*2^(2/3)*Sqrt[249]*x - 16
*(-47 + 3*Sqrt[249])^(2/3)*x + 4*(2*(-47 + 3*Sqrt[249]))^(1/3)*x - 6*(-47 + 3*Sqrt[249])^(2/3)*x^2])/((-47 + 3
*Sqrt[249])^(4/3)*(4 - 8*(2/(-47 + 3*Sqrt[249]))^(2/3) - 2^(1/3)*(-47 + 3*Sqrt[249])^(2/3))^2*(4 + 2^(1/3)*(-4
7 + 3*Sqrt[249])^(2/3))) + (1248*2^(2/3)*(34778079*2^(2/3) - Sqrt[249]*(2203971*2^(2/3) + 4*(9900994 - 627450*
Sqrt[249])^(1/3)*(867 - 55*Sqrt[249]) + 120*(2225 - 141*Sqrt[249])*(-47 + 3*Sqrt[249])^(2/3) + 257118*(-94 + 6
*Sqrt[249])^(1/3) - 16294*Sqrt[249]*(-94 + 6*Sqrt[249])^(1/3)))*Log[4*2^(1/3) - (-94 + 6*Sqrt[249])^(2/3) + 2*
(-47 + 3*Sqrt[249])^(1/3)*(4 + 3*x)])/(83*(-47 + 3*Sqrt[249])^(7/3)*(4 - 8*(2/(-47 + 3*Sqrt[249]))^(2/3) - 2^(
1/3)*(-47 + 3*Sqrt[249])^(2/3))^2*(4 + 2^(1/3)*(-47 + 3*Sqrt[249])^(2/3))) - (1368*(47 - 3*Sqrt[249])*(8 + 2^(
2/3)*(47*(-47 + 3*Sqrt[249])^(1/3) - (-94 + 6*Sqrt[249])^(2/3)))*Log[4*2^(1/3) - (-94 + 6*Sqrt[249])^(2/3) + 2
*(-47 + 3*Sqrt[249])^(1/3)*(4 + 3*x)])/((747 - 47*Sqrt[249])*(4 - 8*(2/(-47 + 3*Sqrt[249]))^(2/3) - 2^(1/3)*(-
47 + 3*Sqrt[249])^(2/3))^2*(4 + 2^(1/3)*(-47 + 3*Sqrt[249])^(2/3))) - (1314*(-47 + 3*Sqrt[249])^(2/3)*(2^(1/3)
*(4/(-47 + 3*Sqrt[249])^(1/3) - (-94 + 6*Sqrt[249])^(1/3))*PolynomialRemainder[(36*x^2)/(2^(1/3)*(4/(-47 + 3*S
qrt[249])^(1/3) - (-94 + 6*Sqrt[249])^(1/3)) + 2*(4 + 3*x))^2, (4 + 8*(2/(-47 + 3*Sqrt[249]))^(2/3) + 2^(1/3)*
(-47 + 3*Sqrt[249])^(2/3) - 2^(1/3)*(4/(-47 + 3*Sqrt[249])^(1/3) - (-94 + 6*Sqrt[249])^(1/3))*(4 + 3*x) + 2*(4
+ 3*x)^2)/18, 4/3 + x] - 4*(4 + 3*x)*PolynomialRemainder[(36*x^2)/(2^(1/3)*(4/(-47 + 3*Sqrt[249])^(1/3) - (-9
4 + 6*Sqrt[249])^(1/3)) + 2*(4 + 3*x))^2, (4 + 8*(2/(-47 + 3*Sqrt[249]))^(2/3) + 2^(1/3)*(-47 + 3*Sqrt[249])^(
2/3) - 2^(1/3)*(4/(-47 + 3*Sqrt[249])^(1/3) - (-94 + 6*Sqrt[249])^(1/3))*(4 + 3*x) + 2*(4 + 3*x)^2)/18, 4/3 +
x]))/((8*2^(2/3) + 8*(-47 + 3*Sqrt[249])^(2/3) + 2^(1/3)*(-47 + 3*Sqrt[249])^(4/3))*(4 + 8*(2/(-47 + 3*Sqrt[24
9]))^(2/3) + 2^(1/3)*(-47 + 3*Sqrt[249])^(2/3) - 2^(1/3)*(4/(-47 + 3*Sqrt[249])^(1/3) - (-94 + 6*Sqrt[249])^(1
/3))*(4 + 3*x) + 2*(4 + 3*x)^2)) - (1044*(-47 + 3*Sqrt[249])^(2/3)*(2^(1/3)*(4/(-47 + 3*Sqrt[249])^(1/3) - (-9
4 + 6*Sqrt[249])^(1/3))*PolynomialRemainder[(36*x^3)/(2^(1/3)*(4/(-47 + 3*Sqrt[249])^(1/3) - (-94 + 6*Sqrt[249
])^(1/3)) + 2*(4 + 3*x))^2, (4 + 8*(2/(-47 + 3*Sqrt[249]))^(2/3) + 2^(1/3)*(-47 + 3*Sqrt[249])^(2/3) - 2^(1/3)
*(4/(-47 + 3*Sqrt[249])^(1/3) - (-94 + 6*Sqrt[249])^(1/3))*(4 + 3*x) + 2*(4 + 3*x)^2)/18, 4/3 + x] - 4*(4 + 3*
x)*PolynomialRemainder[(36*x^3)/(2^(1/3)*(4/(-47 + 3*Sqrt[249])^(1/3) - (-94 + 6*Sqrt[249])^(1/3)) + 2*(4 + 3*
x))^2, (4 + 8*(2/(-47 + 3*Sqrt[249]))^(2/3) + 2^(1/3)*(-47 + 3*Sqrt[249])^(2/3) - 2^(1/3)*(4/(-47 + 3*Sqrt[249
])^(1/3) - (-94 + 6*Sqrt[249])^(1/3))*(4 + 3*x) + 2*(4 + 3*x)^2)/18, 4/3 + x]))/((8*2^(2/3) + 8*(-47 + 3*Sqrt[
249])^(2/3) + 2^(1/3)*(-47 + 3*Sqrt[249])^(4/3))*(4 + 8*(2/(-47 + 3*Sqrt[249]))^(2/3) + 2^(1/3)*(-47 + 3*Sqrt[
249])^(2/3) - 2^(1/3)*(4/(-47 + 3*Sqrt[249])^(1/3) - (-94 + 6*Sqrt[249])^(1/3))*(4 + 3*x) + 2*(4 + 3*x)^2)) -
(504*(-47 + 3*Sqrt[249])^(2/3)*(2^(1/3)*(4/(-47 + 3*Sqrt[249])^(1/3) - (-94 + 6*Sqrt[249])^(1/3))*PolynomialRe
mainder[(36*x^4)/(2^(1/3)*(4/(-47 + 3*Sqrt[249])^(1/3) - (-94 + 6*Sqrt[249])^(1/3)) + 2*(4 + 3*x))^2, (4 + 8*(
2/(-47 + 3*Sqrt[249]))^(2/3) + 2^(1/3)*(-47 + 3*Sqrt[249])^(2/3) - 2^(1/3)*(4/(-47 + 3*Sqrt[249])^(1/3) - (-94
+ 6*Sqrt[249])^(1/3))*(4 + 3*x) + 2*(4 + 3*x)^2)/18, 4/3 + x] - 4*(4 + 3*x)*PolynomialRemainder[(36*x^4)/(2^(
1/3)*(4/(-47 + 3*Sqrt[249])^(1/3) - (-94 + 6*Sqrt[249])^(1/3)) + 2*(4 + 3*x))^2, (4 + 8*(2/(-47 + 3*Sqrt[249])
)^(2/3) + 2^(1/3)*(-47 + 3*Sqrt[249])^(2/3) - 2^(1/3)*(4/(-47 + 3*Sqrt[249])^(1/3) - (-94 + 6*Sqrt[249])^(1/3)
)*(4 + 3*x) + 2*(4 + 3*x)^2)/18, 4/3 + x]))/((8*2^(2/3) + 8*(-47 + 3*Sqrt[249])^(2/3) + 2^(1/3)*(-47 + 3*Sqrt[
249])^(4/3))*(4 + 8*(2/(-47 + 3*Sqrt[249]))^(2/3) + 2^(1/3)*(-47 + 3*Sqrt[249])^(2/3) - 2^(1/3)*(4/(-47 + 3*Sq
rt[249])^(1/3) - (-94 + 6*Sqrt[249])^(1/3))*(4 + 3*x) + 2*(4 + 3*x)^2)) - (144*(-47 + 3*Sqrt[249])^(2/3)*(2^(1
/3)*(4/(-47 + 3*Sqrt[249])^(1/3) - (-94 + 6*Sqrt[249])^(1/3))*PolynomialRemainder[(36*x^5)/(2^(1/3)*(4/(-47 +
3*Sqrt[249])^(1/3) - (-94 + 6*Sqrt[249])^(1/3)) + 2*(4 + 3*x))^2, (4 + 8*(2/(-47 + 3*Sqrt[249]))^(2/3) + 2^(1/
3)*(-47 + 3*Sqrt[249])^(2/3) - 2^(1/3)*(4/(-47 + 3*Sqrt[249])^(1/3) - (-94 + 6*Sqrt[249])^(1/3))*(4 + 3*x) + 2
*(4 + 3*x)^2)/18, 4/3 + x] - 4*(4 + 3*x)*PolynomialRemainder[(36*x^5)/(2^(1/3)*(4/(-47 + 3*Sqrt[249])^(1/3) -
(-94 + 6*Sqrt[249])^(1/3)) + 2*(4 + 3*x))^2, (4 + 8*(2/(-47 + 3*Sqrt[249]))^(2/3) + 2^(1/3)*(-47 + 3*Sqrt[249]
)^(2/3) - 2^(1/3)*(4/(-47 + 3*Sqrt[249])^(1/3) - (-94 + 6*Sqrt[249])^(1/3))*(4 + 3*x) + 2*(4 + 3*x)^2)/18, 4/3
+ x]))/((8*2^(2/3) + 8*(-47 + 3*Sqrt[249])^(2/3) + 2^(1/3)*(-47 + 3*Sqrt[249])^(4/3))*(4 + 8*(2/(-47 + 3*Sqrt
[249]))^(2/3) + 2^(1/3)*(-47 + 3*Sqrt[249])^(2/3) - 2^(1/3)*(4/(-47 + 3*Sqrt[249])^(1/3) - (-94 + 6*Sqrt[249])
^(1/3))*(4 + 3*x) + 2*(4 + 3*x)^2)) - (18*(-47 + 3*Sqrt[249])^(2/3)*(2^(1/3)*(4/(-47 + 3*Sqrt[249])^(1/3) - (-
94 + 6*Sqrt[249])^(1/3))*PolynomialRemainder[(36*x^6)/(2^(1/3)*(4/(-47 + 3*Sqrt[249])^(1/3) - (-94 + 6*Sqrt[24
9])^(1/3)) + 2*(4 + 3*x))^2, (4 + 8*(2/(-47 + 3*Sqrt[249]))^(2/3) + 2^(1/3)*(-47 + 3*Sqrt[249])^(2/3) - 2^(1/3
)*(4/(-47 + 3*Sqrt[249])^(1/3) - (-94 + 6*Sqrt[249])^(1/3))*(4 + 3*x) + 2*(4 + 3*x)^2)/18, 4/3 + x] - 4*(4 + 3
*x)*PolynomialRemainder[(36*x^6)/(2^(1/3)*(4/(-47 + 3*Sqrt[249])^(1/3) - (-94 + 6*Sqrt[249])^(1/3)) + 2*(4 + 3
*x))^2, (4 + 8*(2/(-47 + 3*Sqrt[249]))^(2/3) + 2^(1/3)*(-47 + 3*Sqrt[249])^(2/3) - 2^(1/3)*(4/(-47 + 3*Sqrt[24
9])^(1/3) - (-94 + 6*Sqrt[249])^(1/3))*(4 + 3*x) + 2*(4 + 3*x)^2)/18, 4/3 + x]))/((8*2^(2/3) + 8*(-47 + 3*Sqrt
[249])^(2/3) + 2^(1/3)*(-47 + 3*Sqrt[249])^(4/3))*(4 + 8*(2/(-47 + 3*Sqrt[249]))^(2/3) + 2^(1/3)*(-47 + 3*Sqrt
[249])^(2/3) - 2^(1/3)*(4/(-47 + 3*Sqrt[249])^(1/3) - (-94 + 6*Sqrt[249])^(1/3))*(4 + 3*x) + 2*(4 + 3*x)^2)) +
((15768*I)*(-47 + 3*Sqrt[249])^(4/3)*(8*2^(1/3) + (-47 + 3*Sqrt[249])^(4/3) + 4*(-94 + 6*Sqrt[249])^(2/3))*Sq
rt[3/(4*(-47 + 3*Sqrt[249])^(4/3) + 2^(1/3)*(2225 - 141*Sqrt[249] + 4*2^(1/3)*(-47 + 3*Sqrt[249])^(2/3)))]*Def
er[Subst][Defer[Int][PolynomialQuotient[(-4/3 + 3*2^(2/3)*x)^2/((4*2^(1/3) - (-94 + 6*Sqrt[249])^(2/3))/(6*(-4
7 + 3*Sqrt[249])^(1/3)) + 3*2^(2/3)*x)^2, (4 + 8*(2/(-47 + 3*Sqrt[249]))^(2/3) + 2^(1/3)*(-47 + 3*Sqrt[249])^(
2/3))/18 - (4/(-47 + 3*Sqrt[249])^(1/3) - (-94 + 6*Sqrt[249])^(1/3))*x + 18*2^(1/3)*x^2, 3*2^(2/3)*x]/(141*2^(
2/3) - 9*2^(2/3)*Sqrt[249] + 12*(2*(-47 + 3*Sqrt[249]))^(1/3) + (6*I)*Sqrt[3*(2225*2^(1/3) - 141*2^(1/3)*Sqrt[
249] + 4*(-47 + 3*Sqrt[249])^(4/3) + 4*(2*(-47 + 3*Sqrt[249]))^(2/3))] - 108*(2*(-47 + 3*Sqrt[249]))^(2/3)*x),
x], x, (4 + 3*x)/(9*2^(2/3))])/(8*2^(2/3) + 8*(-47 + 3*Sqrt[249])^(2/3) + 2^(1/3)*(-47 + 3*Sqrt[249])^(4/3))
+ ((15768*I)*(-47 + 3*Sqrt[249])^(4/3)*(8*2^(1/3) + (-47 + 3*Sqrt[249])^(4/3) + 4*(-94 + 6*Sqrt[249])^(2/3))*S
qrt[3/(4*(-47 + 3*Sqrt[249])^(4/3) + 2^(1/3)*(2225 - 141*Sqrt[249] + 4*2^(1/3)*(-47 + 3*Sqrt[249])^(2/3)))]*De
fer[Subst][Defer[Int][PolynomialQuotient[(-4/3 + 3*2^(2/3)*x)^2/((4*2^(1/3) - (-94 + 6*Sqrt[249])^(2/3))/(6*(-
47 + 3*Sqrt[249])^(1/3)) + 3*2^(2/3)*x)^2, (4 + 8*(2/(-47 + 3*Sqrt[249]))^(2/3) + 2^(1/3)*(-47 + 3*Sqrt[249])^
(2/3))/18 - (4/(-47 + 3*Sqrt[249])^(1/3) - (-94 + 6*Sqrt[249])^(1/3))*x + 18*2^(1/3)*x^2, 3*2^(2/3)*x]/(-141*2
^(2/3) + 9*2^(2/3)*Sqrt[249] - 12*(2*(-47 + 3*Sqrt[249]))^(1/3) + (6*I)*Sqrt[3*(2225*2^(1/3) - 141*2^(1/3)*Sqr
t[249] + 4*(-47 + 3*Sqrt[249])^(4/3) + 4*(2*(-47 + 3*Sqrt[249]))^(2/3))] + 108*(2*(-47 + 3*Sqrt[249]))^(2/3)*x
), x], x, (4 + 3*x)/(9*2^(2/3))])/(8*2^(2/3) + 8*(-47 + 3*Sqrt[249])^(2/3) + 2^(1/3)*(-47 + 3*Sqrt[249])^(4/3)
) + ((12528*I)*(-47 + 3*Sqrt[249])^(4/3)*(8*2^(1/3) + (-47 + 3*Sqrt[249])^(4/3) + 4*(-94 + 6*Sqrt[249])^(2/3))
*Sqrt[3/(4*(-47 + 3*Sqrt[249])^(4/3) + 2^(1/3)*(2225 - 141*Sqrt[249] + 4*2^(1/3)*(-47 + 3*Sqrt[249])^(2/3)))]*
Defer[Subst][Defer[Int][PolynomialQuotient[(-4/3 + 3*2^(2/3)*x)^3/((4*2^(1/3) - (-94 + 6*Sqrt[249])^(2/3))/(6*
(-47 + 3*Sqrt[249])^(1/3)) + 3*2^(2/3)*x)^2, (4 + 8*(2/(-47 + 3*Sqrt[249]))^(2/3) + 2^(1/3)*(-47 + 3*Sqrt[249]
)^(2/3))/18 - (4/(-47 + 3*Sqrt[249])^(1/3) - (-94 + 6*Sqrt[249])^(1/3))*x + 18*2^(1/3)*x^2, 3*2^(2/3)*x]/(141*
2^(2/3) - 9*2^(2/3)*Sqrt[249] + 12*(2*(-47 + 3*Sqrt[249]))^(1/3) + (6*I)*Sqrt[3*(2225*2^(1/3) - 141*2^(1/3)*Sq
rt[249] + 4*(-47 + 3*Sqrt[249])^(4/3) + 4*(2*(-47 + 3*Sqrt[249]))^(2/3))] - 108*(2*(-47 + 3*Sqrt[249]))^(2/3)*
x), x], x, (4 + 3*x)/(9*2^(2/3))])/(8*2^(2/3) + 8*(-47 + 3*Sqrt[249])^(2/3) + 2^(1/3)*(-47 + 3*Sqrt[249])^(4/3
)) + ((12528*I)*(-47 + 3*Sqrt[249])^(4/3)*(8*2^(1/3) + (-47 + 3*Sqrt[249])^(4/3) + 4*(-94 + 6*Sqrt[249])^(2/3)
)*Sqrt[3/(4*(-47 + 3*Sqrt[249])^(4/3) + 2^(1/3)*(2225 - 141*Sqrt[249] + 4*2^(1/3)*(-47 + 3*Sqrt[249])^(2/3)))]
*Defer[Subst][Defer[Int][PolynomialQuotient[(-4/3 + 3*2^(2/3)*x)^3/((4*2^(1/3) - (-94 + 6*Sqrt[249])^(2/3))/(6
*(-47 + 3*Sqrt[249])^(1/3)) + 3*2^(2/3)*x)^2, (4 + 8*(2/(-47 + 3*Sqrt[249]))^(2/3) + 2^(1/3)*(-47 + 3*Sqrt[249
])^(2/3))/18 - (4/(-47 + 3*Sqrt[249])^(1/3) - (-94 + 6*Sqrt[249])^(1/3))*x + 18*2^(1/3)*x^2, 3*2^(2/3)*x]/(-14
1*2^(2/3) + 9*2^(2/3)*Sqrt[249] - 12*(2*(-47 + 3*Sqrt[249]))^(1/3) + (6*I)*Sqrt[3*(2225*2^(1/3) - 141*2^(1/3)*
Sqrt[249] + 4*(-47 + 3*Sqrt[249])^(4/3) + 4*(2*(-47 + 3*Sqrt[249]))^(2/3))] + 108*(2*(-47 + 3*Sqrt[249]))^(2/3
)*x), x], x, (4 + 3*x)/(9*2^(2/3))])/(8*2^(2/3) + 8*(-47 + 3*Sqrt[249])^(2/3) + 2^(1/3)*(-47 + 3*Sqrt[249])^(4
/3)) + ((6048*I)*(-47 + 3*Sqrt[249])^(4/3)*(8*2^(1/3) + (-47 + 3*Sqrt[249])^(4/3) + 4*(-94 + 6*Sqrt[249])^(2/3
))*Sqrt[3/(4*(-47 + 3*Sqrt[249])^(4/3) + 2^(1/3)*(2225 - 141*Sqrt[249] + 4*2^(1/3)*(-47 + 3*Sqrt[249])^(2/3)))
]*Defer[Subst][Defer[Int][PolynomialQuotient[(-4/3 + 3*2^(2/3)*x)^4/((4*2^(1/3) - (-94 + 6*Sqrt[249])^(2/3))/(
6*(-47 + 3*Sqrt[249])^(1/3)) + 3*2^(2/3)*x)^2, (4 + 8*(2/(-47 + 3*Sqrt[249]))^(2/3) + 2^(1/3)*(-47 + 3*Sqrt[24
9])^(2/3))/18 - (4/(-47 + 3*Sqrt[249])^(1/3) - (-94 + 6*Sqrt[249])^(1/3))*x + 18*2^(1/3)*x^2, 3*2^(2/3)*x]/(14
1*2^(2/3) - 9*2^(2/3)*Sqrt[249] + 12*(2*(-47 + 3*Sqrt[249]))^(1/3) + (6*I)*Sqrt[3*(2225*2^(1/3) - 141*2^(1/3)*
Sqrt[249] + 4*(-47 + 3*Sqrt[249])^(4/3) + 4*(2*(-47 + 3*Sqrt[249]))^(2/3))] - 108*(2*(-47 + 3*Sqrt[249]))^(2/3
)*x), x], x, (4 + 3*x)/(9*2^(2/3))])/(8*2^(2/3) + 8*(-47 + 3*Sqrt[249])^(2/3) + 2^(1/3)*(-47 + 3*Sqrt[249])^(4
/3)) + ((6048*I)*(-47 + 3*Sqrt[249])^(4/3)*(8*2^(1/3) + (-47 + 3*Sqrt[249])^(4/3) + 4*(-94 + 6*Sqrt[249])^(2/3
))*Sqrt[3/(4*(-47 + 3*Sqrt[249])^(4/3) + 2^(1/3)*(2225 - 141*Sqrt[249] + 4*2^(1/3)*(-47 + 3*Sqrt[249])^(2/3)))
]*Defer[Subst][Defer[Int][PolynomialQuotient[(-4/3 + 3*2^(2/3)*x)^4/((4*2^(1/3) - (-94 + 6*Sqrt[249])^(2/3))/(
6*(-47 + 3*Sqrt[249])^(1/3)) + 3*2^(2/3)*x)^2, (4 + 8*(2/(-47 + 3*Sqrt[249]))^(2/3) + 2^(1/3)*(-47 + 3*Sqrt[24
9])^(2/3))/18 - (4/(-47 + 3*Sqrt[249])^(1/3) - (-94 + 6*Sqrt[249])^(1/3))*x + 18*2^(1/3)*x^2, 3*2^(2/3)*x]/(-1
41*2^(2/3) + 9*2^(2/3)*Sqrt[249] - 12*(2*(-47 + 3*Sqrt[249]))^(1/3) + (6*I)*Sqrt[3*(2225*2^(1/3) - 141*2^(1/3)
*Sqrt[249] + 4*(-47 + 3*Sqrt[249])^(4/3) + 4*(2*(-47 + 3*Sqrt[249]))^(2/3))] + 108*(2*(-47 + 3*Sqrt[249]))^(2/
3)*x), x], x, (4 + 3*x)/(9*2^(2/3))])/(8*2^(2/3) + 8*(-47 + 3*Sqrt[249])^(2/3) + 2^(1/3)*(-47 + 3*Sqrt[249])^(
4/3)) + ((1728*I)*(-47 + 3*Sqrt[249])^(4/3)*(8*2^(1/3) + (-47 + 3*Sqrt[249])^(4/3) + 4*(-94 + 6*Sqrt[249])^(2/
3))*Sqrt[3/(4*(-47 + 3*Sqrt[249])^(4/3) + 2^(1/3)*(2225 - 141*Sqrt[249] + 4*2^(1/3)*(-47 + 3*Sqrt[249])^(2/3))
)]*Defer[Subst][Defer[Int][PolynomialQuotient[(-4/3 + 3*2^(2/3)*x)^5/((4*2^(1/3) - (-94 + 6*Sqrt[249])^(2/3))/
(6*(-47 + 3*Sqrt[249])^(1/3)) + 3*2^(2/3)*x)^2, (4 + 8*(2/(-47 + 3*Sqrt[249]))^(2/3) + 2^(1/3)*(-47 + 3*Sqrt[2
49])^(2/3))/18 - (4/(-47 + 3*Sqrt[249])^(1/3) - (-94 + 6*Sqrt[249])^(1/3))*x + 18*2^(1/3)*x^2, 3*2^(2/3)*x]/(1
41*2^(2/3) - 9*2^(2/3)*Sqrt[249] + 12*(2*(-47 + 3*Sqrt[249]))^(1/3) + (6*I)*Sqrt[3*(2225*2^(1/3) - 141*2^(1/3)
*Sqrt[249] + 4*(-47 + 3*Sqrt[249])^(4/3) + 4*(2*(-47 + 3*Sqrt[249]))^(2/3))] - 108*(2*(-47 + 3*Sqrt[249]))^(2/
3)*x), x], x, (4 + 3*x)/(9*2^(2/3))])/(8*2^(2/3) + 8*(-47 + 3*Sqrt[249])^(2/3) + 2^(1/3)*(-47 + 3*Sqrt[249])^(
4/3)) + ((1728*I)*(-47 + 3*Sqrt[249])^(4/3)*(8*2^(1/3) + (-47 + 3*Sqrt[249])^(4/3) + 4*(-94 + 6*Sqrt[249])^(2/
3))*Sqrt[3/(4*(-47 + 3*Sqrt[249])^(4/3) + 2^(1/3)*(2225 - 141*Sqrt[249] + 4*2^(1/3)*(-47 + 3*Sqrt[249])^(2/3))
)]*Defer[Subst][Defer[Int][PolynomialQuotient[(-4/3 + 3*2^(2/3)*x)^5/((4*2^(1/3) - (-94 + 6*Sqrt[249])^(2/3))/
(6*(-47 + 3*Sqrt[249])^(1/3)) + 3*2^(2/3)*x)^2, (4 + 8*(2/(-47 + 3*Sqrt[249]))^(2/3) + 2^(1/3)*(-47 + 3*Sqrt[2
49])^(2/3))/18 - (4/(-47 + 3*Sqrt[249])^(1/3) - (-94 + 6*Sqrt[249])^(1/3))*x + 18*2^(1/3)*x^2, 3*2^(2/3)*x]/(-
141*2^(2/3) + 9*2^(2/3)*Sqrt[249] - 12*(2*(-47 + 3*Sqrt[249]))^(1/3) + (6*I)*Sqrt[3*(2225*2^(1/3) - 141*2^(1/3
)*Sqrt[249] + 4*(-47 + 3*Sqrt[249])^(4/3) + 4*(2*(-47 + 3*Sqrt[249]))^(2/3))] + 108*(2*(-47 + 3*Sqrt[249]))^(2
/3)*x), x], x, (4 + 3*x)/(9*2^(2/3))])/(8*2^(2/3) + 8*(-47 + 3*Sqrt[249])^(2/3) + 2^(1/3)*(-47 + 3*Sqrt[249])^
(4/3)) + ((216*I)*(-47 + 3*Sqrt[249])^(4/3)*(8*2^(1/3) + (-47 + 3*Sqrt[249])^(4/3) + 4*(-94 + 6*Sqrt[249])^(2/
3))*Sqrt[3/(4*(-47 + 3*Sqrt[249])^(4/3) + 2^(1/3)*(2225 - 141*Sqrt[249] + 4*2^(1/3)*(-47 + 3*Sqrt[249])^(2/3))
)]*Defer[Subst][Defer[Int][PolynomialQuotient[(-4/3 + 3*2^(2/3)*x)^6/((4*2^(1/3) - (-94 + 6*Sqrt[249])^(2/3))/
(6*(-47 + 3*Sqrt[249])^(1/3)) + 3*2^(2/3)*x)^2, (4 + 8*(2/(-47 + 3*Sqrt[249]))^(2/3) + 2^(1/3)*(-47 + 3*Sqrt[2
49])^(2/3))/18 - (4/(-47 + 3*Sqrt[249])^(1/3) - (-94 + 6*Sqrt[249])^(1/3))*x + 18*2^(1/3)*x^2, 3*2^(2/3)*x]/(1
41*2^(2/3) - 9*2^(2/3)*Sqrt[249] + 12*(2*(-47 + 3*Sqrt[249]))^(1/3) + (6*I)*Sqrt[3*(2225*2^(1/3) - 141*2^(1/3)
*Sqrt[249] + 4*(-47 + 3*Sqrt[249])^(4/3) + 4*(2*(-47 + 3*Sqrt[249]))^(2/3))] - 108*(2*(-47 + 3*Sqrt[249]))^(2/
3)*x), x], x, (4 + 3*x)/(9*2^(2/3))])/(8*2^(2/3) + 8*(-47 + 3*Sqrt[249])^(2/3) + 2^(1/3)*(-47 + 3*Sqrt[249])^(
4/3)) + ((216*I)*(-47 + 3*Sqrt[249])^(4/3)*(8*2^(1/3) + (-47 + 3*Sqrt[249])^(4/3) + 4*(-94 + 6*Sqrt[249])^(2/3
))*Sqrt[3/(4*(-47 + 3*Sqrt[249])^(4/3) + 2^(1/3)*(2225 - 141*Sqrt[249] + 4*2^(1/3)*(-47 + 3*Sqrt[249])^(2/3)))
]*Defer[Subst][Defer[Int][PolynomialQuotient[(-4/3 + 3*2^(2/3)*x)^6/((4*2^(1/3) - (-94 + 6*Sqrt[249])^(2/3))/(
6*(-47 + 3*Sqrt[249])^(1/3)) + 3*2^(2/3)*x)^2, (4 + 8*(2/(-47 + 3*Sqrt[249]))^(2/3) + 2^(1/3)*(-47 + 3*Sqrt[24
9])^(2/3))/18 - (4/(-47 + 3*Sqrt[249])^(1/3) - (-94 + 6*Sqrt[249])^(1/3))*x + 18*2^(1/3)*x^2, 3*2^(2/3)*x]/(-1
41*2^(2/3) + 9*2^(2/3)*Sqrt[249] - 12*(2*(-47 + 3*Sqrt[249]))^(1/3) + (6*I)*Sqrt[3*(2225*2^(1/3) - 141*2^(1/3)
*Sqrt[249] + 4*(-47 + 3*Sqrt[249])^(4/3) + 4*(2*(-47 + 3*Sqrt[249]))^(2/3))] + 108*(2*(-47 + 3*Sqrt[249]))^(2/
3)*x), x], x, (4 + 3*x)/(9*2^(2/3))])/(8*2^(2/3) + 8*(-47 + 3*Sqrt[249])^(2/3) + 2^(1/3)*(-47 + 3*Sqrt[249])^(
4/3)) + ((94608*I)*2^(2/3)*(47 - 3*Sqrt[249])^2*Sqrt[3/(4*(-47 + 3*Sqrt[249])^(4/3) + 2^(1/3)*(2225 - 141*Sqrt
[249] + 4*2^(1/3)*(-47 + 3*Sqrt[249])^(2/3)))]*Defer[Subst][Defer[Int][PolynomialRemainder[(-4/3 + 3*2^(2/3)*x
)^2/((4*2^(1/3) - (-94 + 6*Sqrt[249])^(2/3))/(6*(-47 + 3*Sqrt[249])^(1/3)) + 3*2^(2/3)*x)^2, (4 + 8*(2/(-47 +
3*Sqrt[249]))^(2/3) + 2^(1/3)*(-47 + 3*Sqrt[249])^(2/3))/18 - (4/(-47 + 3*Sqrt[249])^(1/3) - (-94 + 6*Sqrt[249
])^(1/3))*x + 18*2^(1/3)*x^2, 3*2^(2/3)*x]/(141*2^(2/3) - 9*2^(2/3)*Sqrt[249] + 12*(2*(-47 + 3*Sqrt[249]))^(1/
3) + (6*I)*Sqrt[3*(2225*2^(1/3) - 141*2^(1/3)*Sqrt[249] + 4*(-47 + 3*Sqrt[249])^(4/3) + 4*(2*(-47 + 3*Sqrt[249
]))^(2/3))] - 108*(2*(-47 + 3*Sqrt[249]))^(2/3)*x), x], x, (4 + 3*x)/(9*2^(2/3))])/(8*2^(2/3) + 8*(-47 + 3*Sqr
t[249])^(2/3) + 2^(1/3)*(-47 + 3*Sqrt[249])^(4/3)) + ((94608*I)*2^(2/3)*(47 - 3*Sqrt[249])^2*Sqrt[3/(4*(-47 +
3*Sqrt[249])^(4/3) + 2^(1/3)*(2225 - 141*Sqrt[249] + 4*2^(1/3)*(-47 + 3*Sqrt[249])^(2/3)))]*Defer[Subst][Defer
[Int][PolynomialRemainder[(-4/3 + 3*2^(2/3)*x)^2/((4*2^(1/3) - (-94 + 6*Sqrt[249])^(2/3))/(6*(-47 + 3*Sqrt[249
])^(1/3)) + 3*2^(2/3)*x)^2, (4 + 8*(2/(-47 + 3*Sqrt[249]))^(2/3) + 2^(1/3)*(-47 + 3*Sqrt[249])^(2/3))/18 - (4/
(-47 + 3*Sqrt[249])^(1/3) - (-94 + 6*Sqrt[249])^(1/3))*x + 18*2^(1/3)*x^2, 3*2^(2/3)*x]/(-141*2^(2/3) + 9*2^(2
/3)*Sqrt[249] - 12*(2*(-47 + 3*Sqrt[249]))^(1/3) + (6*I)*Sqrt[3*(2225*2^(1/3) - 141*2^(1/3)*Sqrt[249] + 4*(-47
+ 3*Sqrt[249])^(4/3) + 4*(2*(-47 + 3*Sqrt[249]))^(2/3))] + 108*(2*(-47 + 3*Sqrt[249]))^(2/3)*x), x], x, (4 +
3*x)/(9*2^(2/3))])/(8*2^(2/3) + 8*(-47 + 3*Sqrt[249])^(2/3) + 2^(1/3)*(-47 + 3*Sqrt[249])^(4/3)) + ((75168*I)*
2^(2/3)*(47 - 3*Sqrt[249])^2*Sqrt[3/(4*(-47 + 3*Sqrt[249])^(4/3) + 2^(1/3)*(2225 - 141*Sqrt[249] + 4*2^(1/3)*(
-47 + 3*Sqrt[249])^(2/3)))]*Defer[Subst][Defer[Int][PolynomialRemainder[(-4/3 + 3*2^(2/3)*x)^3/((4*2^(1/3) - (
-94 + 6*Sqrt[249])^(2/3))/(6*(-47 + 3*Sqrt[249])^(1/3)) + 3*2^(2/3)*x)^2, (4 + 8*(2/(-47 + 3*Sqrt[249]))^(2/3)
+ 2^(1/3)*(-47 + 3*Sqrt[249])^(2/3))/18 - (4/(-47 + 3*Sqrt[249])^(1/3) - (-94 + 6*Sqrt[249])^(1/3))*x + 18*2^
(1/3)*x^2, 3*2^(2/3)*x]/(141*2^(2/3) - 9*2^(2/3)*Sqrt[249] + 12*(2*(-47 + 3*Sqrt[249]))^(1/3) + (6*I)*Sqrt[3*(
2225*2^(1/3) - 141*2^(1/3)*Sqrt[249] + 4*(-47 + 3*Sqrt[249])^(4/3) + 4*(2*(-47 + 3*Sqrt[249]))^(2/3))] - 108*(
2*(-47 + 3*Sqrt[249]))^(2/3)*x), x], x, (4 + 3*x)/(9*2^(2/3))])/(8*2^(2/3) + 8*(-47 + 3*Sqrt[249])^(2/3) + 2^(
1/3)*(-47 + 3*Sqrt[249])^(4/3)) + ((75168*I)*2^(2/3)*(47 - 3*Sqrt[249])^2*Sqrt[3/(4*(-47 + 3*Sqrt[249])^(4/3)
+ 2^(1/3)*(2225 - 141*Sqrt[249] + 4*2^(1/3)*(-47 + 3*Sqrt[249])^(2/3)))]*Defer[Subst][Defer[Int][PolynomialRem
ainder[(-4/3 + 3*2^(2/3)*x)^3/((4*2^(1/3) - (-94 + 6*Sqrt[249])^(2/3))/(6*(-47 + 3*Sqrt[249])^(1/3)) + 3*2^(2/
3)*x)^2, (4 + 8*(2/(-47 + 3*Sqrt[249]))^(2/3) + 2^(1/3)*(-47 + 3*Sqrt[249])^(2/3))/18 - (4/(-47 + 3*Sqrt[249])
^(1/3) - (-94 + 6*Sqrt[249])^(1/3))*x + 18*2^(1/3)*x^2, 3*2^(2/3)*x]/(-141*2^(2/3) + 9*2^(2/3)*Sqrt[249] - 12*
(2*(-47 + 3*Sqrt[249]))^(1/3) + (6*I)*Sqrt[3*(2225*2^(1/3) - 141*2^(1/3)*Sqrt[249] + 4*(-47 + 3*Sqrt[249])^(4/
3) + 4*(2*(-47 + 3*Sqrt[249]))^(2/3))] + 108*(2*(-47 + 3*Sqrt[249]))^(2/3)*x), x], x, (4 + 3*x)/(9*2^(2/3))])/
(8*2^(2/3) + 8*(-47 + 3*Sqrt[249])^(2/3) + 2^(1/3)*(-47 + 3*Sqrt[249])^(4/3)) + ((36288*I)*2^(2/3)*(47 - 3*Sqr
t[249])^2*Sqrt[3/(4*(-47 + 3*Sqrt[249])^(4/3) + 2^(1/3)*(2225 - 141*Sqrt[249] + 4*2^(1/3)*(-47 + 3*Sqrt[249])^
(2/3)))]*Defer[Subst][Defer[Int][PolynomialRemainder[(-4/3 + 3*2^(2/3)*x)^4/((4*2^(1/3) - (-94 + 6*Sqrt[249])^
(2/3))/(6*(-47 + 3*Sqrt[249])^(1/3)) + 3*2^(2/3)*x)^2, (4 + 8*(2/(-47 + 3*Sqrt[249]))^(2/3) + 2^(1/3)*(-47 + 3
*Sqrt[249])^(2/3))/18 - (4/(-47 + 3*Sqrt[249])^(1/3) - (-94 + 6*Sqrt[249])^(1/3))*x + 18*2^(1/3)*x^2, 3*2^(2/3
)*x]/(141*2^(2/3) - 9*2^(2/3)*Sqrt[249] + 12*(2*(-47 + 3*Sqrt[249]))^(1/3) + (6*I)*Sqrt[3*(2225*2^(1/3) - 141*
2^(1/3)*Sqrt[249] + 4*(-47 + 3*Sqrt[249])^(4/3) + 4*(2*(-47 + 3*Sqrt[249]))^(2/3))] - 108*(2*(-47 + 3*Sqrt[249
]))^(2/3)*x), x], x, (4 + 3*x)/(9*2^(2/3))])/(8*2^(2/3) + 8*(-47 + 3*Sqrt[249])^(2/3) + 2^(1/3)*(-47 + 3*Sqrt[
249])^(4/3)) + ((36288*I)*2^(2/3)*(47 - 3*Sqrt[249])^2*Sqrt[3/(4*(-47 + 3*Sqrt[249])^(4/3) + 2^(1/3)*(2225 - 1
41*Sqrt[249] + 4*2^(1/3)*(-47 + 3*Sqrt[249])^(2/3)))]*Defer[Subst][Defer[Int][PolynomialRemainder[(-4/3 + 3*2^
(2/3)*x)^4/((4*2^(1/3) - (-94 + 6*Sqrt[249])^(2/3))/(6*(-47 + 3*Sqrt[249])^(1/3)) + 3*2^(2/3)*x)^2, (4 + 8*(2/
(-47 + 3*Sqrt[249]))^(2/3) + 2^(1/3)*(-47 + 3*Sqrt[249])^(2/3))/18 - (4/(-47 + 3*Sqrt[249])^(1/3) - (-94 + 6*S
qrt[249])^(1/3))*x + 18*2^(1/3)*x^2, 3*2^(2/3)*x]/(-141*2^(2/3) + 9*2^(2/3)*Sqrt[249] - 12*(2*(-47 + 3*Sqrt[24
9]))^(1/3) + (6*I)*Sqrt[3*(2225*2^(1/3) - 141*2^(1/3)*Sqrt[249] + 4*(-47 + 3*Sqrt[249])^(4/3) + 4*(2*(-47 + 3*
Sqrt[249]))^(2/3))] + 108*(2*(-47 + 3*Sqrt[249]))^(2/3)*x), x], x, (4 + 3*x)/(9*2^(2/3))])/(8*2^(2/3) + 8*(-47
+ 3*Sqrt[249])^(2/3) + 2^(1/3)*(-47 + 3*Sqrt[249])^(4/3)) + ((10368*I)*2^(2/3)*(47 - 3*Sqrt[249])^2*Sqrt[3/(4
*(-47 + 3*Sqrt[249])^(4/3) + 2^(1/3)*(2225 - 141*Sqrt[249] + 4*2^(1/3)*(-47 + 3*Sqrt[249])^(2/3)))]*Defer[Subs
t][Defer[Int][PolynomialRemainder[(-4/3 + 3*2^(2/3)*x)^5/((4*2^(1/3) - (-94 + 6*Sqrt[249])^(2/3))/(6*(-47 + 3*
Sqrt[249])^(1/3)) + 3*2^(2/3)*x)^2, (4 + 8*(2/(-47 + 3*Sqrt[249]))^(2/3) + 2^(1/3)*(-47 + 3*Sqrt[249])^(2/3))/
18 - (4/(-47 + 3*Sqrt[249])^(1/3) - (-94 + 6*Sqrt[249])^(1/3))*x + 18*2^(1/3)*x^2, 3*2^(2/3)*x]/(141*2^(2/3) -
9*2^(2/3)*Sqrt[249] + 12*(2*(-47 + 3*Sqrt[249]))^(1/3) + (6*I)*Sqrt[3*(2225*2^(1/3) - 141*2^(1/3)*Sqrt[249] +
4*(-47 + 3*Sqrt[249])^(4/3) + 4*(2*(-47 + 3*Sqrt[249]))^(2/3))] - 108*(2*(-47 + 3*Sqrt[249]))^(2/3)*x), x], x
, (4 + 3*x)/(9*2^(2/3))])/(8*2^(2/3) + 8*(-47 + 3*Sqrt[249])^(2/3) + 2^(1/3)*(-47 + 3*Sqrt[249])^(4/3)) + ((10
368*I)*2^(2/3)*(47 - 3*Sqrt[249])^2*Sqrt[3/(4*(-47 + 3*Sqrt[249])^(4/3) + 2^(1/3)*(2225 - 141*Sqrt[249] + 4*2^
(1/3)*(-47 + 3*Sqrt[249])^(2/3)))]*Defer[Subst][Defer[Int][PolynomialRemainder[(-4/3 + 3*2^(2/3)*x)^5/((4*2^(1
/3) - (-94 + 6*Sqrt[249])^(2/3))/(6*(-47 + 3*Sqrt[249])^(1/3)) + 3*2^(2/3)*x)^2, (4 + 8*(2/(-47 + 3*Sqrt[249])
)^(2/3) + 2^(1/3)*(-47 + 3*Sqrt[249])^(2/3))/18 - (4/(-47 + 3*Sqrt[249])^(1/3) - (-94 + 6*Sqrt[249])^(1/3))*x
+ 18*2^(1/3)*x^2, 3*2^(2/3)*x]/(-141*2^(2/3) + 9*2^(2/3)*Sqrt[249] - 12*(2*(-47 + 3*Sqrt[249]))^(1/3) + (6*I)*
Sqrt[3*(2225*2^(1/3) - 141*2^(1/3)*Sqrt[249] + 4*(-47 + 3*Sqrt[249])^(4/3) + 4*(2*(-47 + 3*Sqrt[249]))^(2/3))]
+ 108*(2*(-47 + 3*Sqrt[249]))^(2/3)*x), x], x, (4 + 3*x)/(9*2^(2/3))])/(8*2^(2/3) + 8*(-47 + 3*Sqrt[249])^(2/
3) + 2^(1/3)*(-47 + 3*Sqrt[249])^(4/3)) + ((1296*I)*2^(2/3)*(47 - 3*Sqrt[249])^2*Sqrt[3/(4*(-47 + 3*Sqrt[249])
^(4/3) + 2^(1/3)*(2225 - 141*Sqrt[249] + 4*2^(1/3)*(-47 + 3*Sqrt[249])^(2/3)))]*Defer[Subst][Defer[Int][Polyno
mialRemainder[(-4/3 + 3*2^(2/3)*x)^6/((4*2^(1/3) - (-94 + 6*Sqrt[249])^(2/3))/(6*(-47 + 3*Sqrt[249])^(1/3)) +
3*2^(2/3)*x)^2, (4 + 8*(2/(-47 + 3*Sqrt[249]))^(2/3) + 2^(1/3)*(-47 + 3*Sqrt[249])^(2/3))/18 - (4/(-47 + 3*Sqr
t[249])^(1/3) - (-94 + 6*Sqrt[249])^(1/3))*x + 18*2^(1/3)*x^2, 3*2^(2/3)*x]/(141*2^(2/3) - 9*2^(2/3)*Sqrt[249]
+ 12*(2*(-47 + 3*Sqrt[249]))^(1/3) + (6*I)*Sqrt[3*(2225*2^(1/3) - 141*2^(1/3)*Sqrt[249] + 4*(-47 + 3*Sqrt[249
])^(4/3) + 4*(2*(-47 + 3*Sqrt[249]))^(2/3))] - 108*(2*(-47 + 3*Sqrt[249]))^(2/3)*x), x], x, (4 + 3*x)/(9*2^(2/
3))])/(8*2^(2/3) + 8*(-47 + 3*Sqrt[249])^(2/3) + 2^(1/3)*(-47 + 3*Sqrt[249])^(4/3)) + ((1296*I)*2^(2/3)*(47 -
3*Sqrt[249])^2*Sqrt[3/(4*(-47 + 3*Sqrt[249])^(4/3) + 2^(1/3)*(2225 - 141*Sqrt[249] + 4*2^(1/3)*(-47 + 3*Sqrt[2
49])^(2/3)))]*Defer[Subst][Defer[Int][PolynomialRemainder[(-4/3 + 3*2^(2/3)*x)^6/((4*2^(1/3) - (-94 + 6*Sqrt[2
49])^(2/3))/(6*(-47 + 3*Sqrt[249])^(1/3)) + 3*2^(2/3)*x)^2, (4 + 8*(2/(-47 + 3*Sqrt[249]))^(2/3) + 2^(1/3)*(-4
7 + 3*Sqrt[249])^(2/3))/18 - (4/(-47 + 3*Sqrt[249])^(1/3) - (-94 + 6*Sqrt[249])^(1/3))*x + 18*2^(1/3)*x^2, 3*2
^(2/3)*x]/(-141*2^(2/3) + 9*2^(2/3)*Sqrt[249] - 12*(2*(-47 + 3*Sqrt[249]))^(1/3) + (6*I)*Sqrt[3*(2225*2^(1/3)
- 141*2^(1/3)*Sqrt[249] + 4*(-47 + 3*Sqrt[249])^(4/3) + 4*(2*(-47 + 3*Sqrt[249]))^(2/3))] + 108*(2*(-47 + 3*Sq
rt[249]))^(2/3)*x), x], x, (4 + 3*x)/(9*2^(2/3))])/(8*2^(2/3) + 8*(-47 + 3*Sqrt[249])^(2/3) + 2^(1/3)*(-47 + 3
*Sqrt[249])^(4/3))
Rubi steps \begin{align*}
\text {integral}& = \int \frac {19+52 x+73 x^2+58 x^3+28 x^4+8 x^5+x^6+e^x \left (5+6 x+4 x^2+x^3\right )^2}{\left (5+6 x+4 x^2+x^3\right )^2} \, dx \\ & = \int \left (e^x+\frac {19}{\left (5+6 x+4 x^2+x^3\right )^2}+\frac {52 x}{\left (5+6 x+4 x^2+x^3\right )^2}+\frac {73 x^2}{\left (5+6 x+4 x^2+x^3\right )^2}+\frac {58 x^3}{\left (5+6 x+4 x^2+x^3\right )^2}+\frac {28 x^4}{\left (5+6 x+4 x^2+x^3\right )^2}+\frac {8 x^5}{\left (5+6 x+4 x^2+x^3\right )^2}+\frac {x^6}{\left (5+6 x+4 x^2+x^3\right )^2}\right ) \, dx \\ & = 8 \int \frac {x^5}{\left (5+6 x+4 x^2+x^3\right )^2} \, dx+19 \int \frac {1}{\left (5+6 x+4 x^2+x^3\right )^2} \, dx+28 \int \frac {x^4}{\left (5+6 x+4 x^2+x^3\right )^2} \, dx+52 \int \frac {x}{\left (5+6 x+4 x^2+x^3\right )^2} \, dx+58 \int \frac {x^3}{\left (5+6 x+4 x^2+x^3\right )^2} \, dx+73 \int \frac {x^2}{\left (5+6 x+4 x^2+x^3\right )^2} \, dx+\int e^x \, dx+\int \frac {x^6}{\left (5+6 x+4 x^2+x^3\right )^2} \, dx \\ & = e^x+8 \text {Subst}\left (\int \frac {\left (-\frac {4}{3}+x\right )^5}{\left (\frac {47}{27}+\frac {2 x}{3}+x^3\right )^2} \, dx,x,\frac {4}{3}+x\right )+19 \text {Subst}\left (\int \frac {1}{\left (\frac {47}{27}+\frac {2 x}{3}+x^3\right )^2} \, dx,x,\frac {4}{3}+x\right )+28 \text {Subst}\left (\int \frac {\left (-\frac {4}{3}+x\right )^4}{\left (\frac {47}{27}+\frac {2 x}{3}+x^3\right )^2} \, dx,x,\frac {4}{3}+x\right )+52 \text {Subst}\left (\int \frac {-\frac {4}{3}+x}{\left (\frac {47}{27}+\frac {2 x}{3}+x^3\right )^2} \, dx,x,\frac {4}{3}+x\right )+58 \text {Subst}\left (\int \frac {\left (-\frac {4}{3}+x\right )^3}{\left (\frac {47}{27}+\frac {2 x}{3}+x^3\right )^2} \, dx,x,\frac {4}{3}+x\right )+73 \text {Subst}\left (\int \frac {\left (-\frac {4}{3}+x\right )^2}{\left (\frac {47}{27}+\frac {2 x}{3}+x^3\right )^2} \, dx,x,\frac {4}{3}+x\right )+\text {Subst}\left (\int \frac {\left (-\frac {4}{3}+x\right )^6}{\left (\frac {47}{27}+\frac {2 x}{3}+x^3\right )^2} \, dx,x,\frac {4}{3}+x\right ) \\ & = e^x+8 \text {Subst}\left (\int \frac {\left (-\frac {4}{3}+x\right )^5}{\left (\frac {\frac {4}{\sqrt [3]{-47+3 \sqrt {249}}}-\sqrt [3]{-94+6 \sqrt {249}}}{3\ 2^{2/3}}+x\right )^2 \left (\frac {1}{18} \left (4+8 \left (\frac {2}{-47+3 \sqrt {249}}\right )^{2/3}+\sqrt [3]{2} \left (-47+3 \sqrt {249}\right )^{2/3}\right )-\frac {\left (\frac {4}{\sqrt [3]{-47+3 \sqrt {249}}}-\sqrt [3]{-94+6 \sqrt {249}}\right ) x}{3\ 2^{2/3}}+x^2\right )^2} \, dx,x,\frac {4}{3}+x\right )+19 \text {Subst}\left (\int \frac {1}{\left (\frac {\frac {4}{\sqrt [3]{-47+3 \sqrt {249}}}-\sqrt [3]{-94+6 \sqrt {249}}}{3\ 2^{2/3}}+x\right )^2 \left (\frac {1}{18} \left (4+8 \left (\frac {2}{-47+3 \sqrt {249}}\right )^{2/3}+\sqrt [3]{2} \left (-47+3 \sqrt {249}\right )^{2/3}\right )-\frac {\left (\frac {4}{\sqrt [3]{-47+3 \sqrt {249}}}-\sqrt [3]{-94+6 \sqrt {249}}\right ) x}{3\ 2^{2/3}}+x^2\right )^2} \, dx,x,\frac {4}{3}+x\right )+28 \text {Subst}\left (\int \frac {\left (-\frac {4}{3}+x\right )^4}{\left (\frac {\frac {4}{\sqrt [3]{-47+3 \sqrt {249}}}-\sqrt [3]{-94+6 \sqrt {249}}}{3\ 2^{2/3}}+x\right )^2 \left (\frac {1}{18} \left (4+8 \left (\frac {2}{-47+3 \sqrt {249}}\right )^{2/3}+\sqrt [3]{2} \left (-47+3 \sqrt {249}\right )^{2/3}\right )-\frac {\left (\frac {4}{\sqrt [3]{-47+3 \sqrt {249}}}-\sqrt [3]{-94+6 \sqrt {249}}\right ) x}{3\ 2^{2/3}}+x^2\right )^2} \, dx,x,\frac {4}{3}+x\right )+52 \text {Subst}\left (\int \frac {-\frac {4}{3}+x}{\left (\frac {\frac {4}{\sqrt [3]{-47+3 \sqrt {249}}}-\sqrt [3]{-94+6 \sqrt {249}}}{3\ 2^{2/3}}+x\right )^2 \left (\frac {1}{18} \left (4+8 \left (\frac {2}{-47+3 \sqrt {249}}\right )^{2/3}+\sqrt [3]{2} \left (-47+3 \sqrt {249}\right )^{2/3}\right )-\frac {\left (\frac {4}{\sqrt [3]{-47+3 \sqrt {249}}}-\sqrt [3]{-94+6 \sqrt {249}}\right ) x}{3\ 2^{2/3}}+x^2\right )^2} \, dx,x,\frac {4}{3}+x\right )+58 \text {Subst}\left (\int \frac {\left (-\frac {4}{3}+x\right )^3}{\left (\frac {\frac {4}{\sqrt [3]{-47+3 \sqrt {249}}}-\sqrt [3]{-94+6 \sqrt {249}}}{3\ 2^{2/3}}+x\right )^2 \left (\frac {1}{18} \left (4+8 \left (\frac {2}{-47+3 \sqrt {249}}\right )^{2/3}+\sqrt [3]{2} \left (-47+3 \sqrt {249}\right )^{2/3}\right )-\frac {\left (\frac {4}{\sqrt [3]{-47+3 \sqrt {249}}}-\sqrt [3]{-94+6 \sqrt {249}}\right ) x}{3\ 2^{2/3}}+x^2\right )^2} \, dx,x,\frac {4}{3}+x\right )+73 \text {Subst}\left (\int \frac {\left (-\frac {4}{3}+x\right )^2}{\left (\frac {\frac {4}{\sqrt [3]{-47+3 \sqrt {249}}}-\sqrt [3]{-94+6 \sqrt {249}}}{3\ 2^{2/3}}+x\right )^2 \left (\frac {1}{18} \left (4+8 \left (\frac {2}{-47+3 \sqrt {249}}\right )^{2/3}+\sqrt [3]{2} \left (-47+3 \sqrt {249}\right )^{2/3}\right )-\frac {\left (\frac {4}{\sqrt [3]{-47+3 \sqrt {249}}}-\sqrt [3]{-94+6 \sqrt {249}}\right ) x}{3\ 2^{2/3}}+x^2\right )^2} \, dx,x,\frac {4}{3}+x\right )+\text {Subst}\left (\int \frac {\left (-\frac {4}{3}+x\right )^6}{\left (\frac {\frac {4}{\sqrt [3]{-47+3 \sqrt {249}}}-\sqrt [3]{-94+6 \sqrt {249}}}{3\ 2^{2/3}}+x\right )^2 \left (\frac {1}{18} \left (4+8 \left (\frac {2}{-47+3 \sqrt {249}}\right )^{2/3}+\sqrt [3]{2} \left (-47+3 \sqrt {249}\right )^{2/3}\right )-\frac {\left (\frac {4}{\sqrt [3]{-47+3 \sqrt {249}}}-\sqrt [3]{-94+6 \sqrt {249}}\right ) x}{3\ 2^{2/3}}+x^2\right )^2} \, dx,x,\frac {4}{3}+x\right ) \\ & = \text {Too large to display} \\
\end{align*}
Mathematica [A] (verified)
Time = 2.25 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.11
\[
\int \frac {19+52 x+73 x^2+58 x^3+28 x^4+8 x^5+x^6+e^x \left (25+60 x+76 x^2+58 x^3+28 x^4+8 x^5+x^6\right )}{25+60 x+76 x^2+58 x^3+28 x^4+8 x^5+x^6} \, dx=e^x+x+\frac {1}{5+6 x+4 x^2+x^3}
\]
[In]
Integrate[(19 + 52*x + 73*x^2 + 58*x^3 + 28*x^4 + 8*x^5 + x^6 + E^x*(25 + 60*x + 76*x^2 + 58*x^3 + 28*x^4 + 8*
x^5 + x^6))/(25 + 60*x + 76*x^2 + 58*x^3 + 28*x^4 + 8*x^5 + x^6),x]
[Out]
E^x + x + (5 + 6*x + 4*x^2 + x^3)^(-1)
Maple [A] (verified)
Time = 0.12 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.11
| | |
| method | result | size |
| | |
| risch |
\(x +\frac {1}{x^{3}+4 x^{2}+6 x +5}+{\mathrm e}^{x}\) |
\(20\) |
| parts |
\(x +\frac {1}{x^{3}+4 x^{2}+6 x +5}+{\mathrm e}^{x}\) |
\(20\) |
| norman |
\(\frac {x^{4}-19 x -10 x^{2}+{\mathrm e}^{x} x^{3}+6 \,{\mathrm e}^{x} x +4 \,{\mathrm e}^{x} x^{2}+5 \,{\mathrm e}^{x}-19}{x^{3}+4 x^{2}+6 x +5}\) |
\(52\) |
| parallelrisch |
\(\frac {x^{4}-19 x -10 x^{2}+{\mathrm e}^{x} x^{3}+6 \,{\mathrm e}^{x} x +4 \,{\mathrm e}^{x} x^{2}+5 \,{\mathrm e}^{x}-19}{x^{3}+4 x^{2}+6 x +5}\) |
\(52\) |
| default |
\(\text {Expression too large to display}\) |
\(1065\) |
| | |
|
|
|
|
[In]
int(((x^6+8*x^5+28*x^4+58*x^3+76*x^2+60*x+25)*exp(x)+x^6+8*x^5+28*x^4+58*x^3+73*x^2+52*x+19)/(x^6+8*x^5+28*x^4
+58*x^3+76*x^2+60*x+25),x,method=_RETURNVERBOSE)
[Out]
x+1/(x^3+4*x^2+6*x+5)+exp(x)
Fricas [B] (verification not implemented)
Leaf count of result is larger than twice the leaf count of optimal. 50 vs. \(2 (17) = 34\).
Time = 0.26 (sec) , antiderivative size = 50, normalized size of antiderivative = 2.78
\[
\int \frac {19+52 x+73 x^2+58 x^3+28 x^4+8 x^5+x^6+e^x \left (25+60 x+76 x^2+58 x^3+28 x^4+8 x^5+x^6\right )}{25+60 x+76 x^2+58 x^3+28 x^4+8 x^5+x^6} \, dx=\frac {x^{4} + 4 \, x^{3} + 6 \, x^{2} + {\left (x^{3} + 4 \, x^{2} + 6 \, x + 5\right )} e^{x} + 5 \, x + 1}{x^{3} + 4 \, x^{2} + 6 \, x + 5}
\]
[In]
integrate(((x^6+8*x^5+28*x^4+58*x^3+76*x^2+60*x+25)*exp(x)+x^6+8*x^5+28*x^4+58*x^3+73*x^2+52*x+19)/(x^6+8*x^5+
28*x^4+58*x^3+76*x^2+60*x+25),x, algorithm="fricas")
[Out]
(x^4 + 4*x^3 + 6*x^2 + (x^3 + 4*x^2 + 6*x + 5)*e^x + 5*x + 1)/(x^3 + 4*x^2 + 6*x + 5)
Sympy [A] (verification not implemented)
Time = 0.08 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.06
\[
\int \frac {19+52 x+73 x^2+58 x^3+28 x^4+8 x^5+x^6+e^x \left (25+60 x+76 x^2+58 x^3+28 x^4+8 x^5+x^6\right )}{25+60 x+76 x^2+58 x^3+28 x^4+8 x^5+x^6} \, dx=x + e^{x} + \frac {1}{x^{3} + 4 x^{2} + 6 x + 5}
\]
[In]
integrate(((x**6+8*x**5+28*x**4+58*x**3+76*x**2+60*x+25)*exp(x)+x**6+8*x**5+28*x**4+58*x**3+73*x**2+52*x+19)/(
x**6+8*x**5+28*x**4+58*x**3+76*x**2+60*x+25),x)
[Out]
x + exp(x) + 1/(x**3 + 4*x**2 + 6*x + 5)
Maxima [B] (verification not implemented)
Leaf count of result is larger than twice the leaf count of optimal. 50 vs. \(2 (17) = 34\).
Time = 0.20 (sec) , antiderivative size = 50, normalized size of antiderivative = 2.78
\[
\int \frac {19+52 x+73 x^2+58 x^3+28 x^4+8 x^5+x^6+e^x \left (25+60 x+76 x^2+58 x^3+28 x^4+8 x^5+x^6\right )}{25+60 x+76 x^2+58 x^3+28 x^4+8 x^5+x^6} \, dx=\frac {x^{4} + 4 \, x^{3} + 6 \, x^{2} + {\left (x^{3} + 4 \, x^{2} + 6 \, x + 5\right )} e^{x} + 5 \, x + 1}{x^{3} + 4 \, x^{2} + 6 \, x + 5}
\]
[In]
integrate(((x^6+8*x^5+28*x^4+58*x^3+76*x^2+60*x+25)*exp(x)+x^6+8*x^5+28*x^4+58*x^3+73*x^2+52*x+19)/(x^6+8*x^5+
28*x^4+58*x^3+76*x^2+60*x+25),x, algorithm="maxima")
[Out]
(x^4 + 4*x^3 + 6*x^2 + (x^3 + 4*x^2 + 6*x + 5)*e^x + 5*x + 1)/(x^3 + 4*x^2 + 6*x + 5)
Giac [B] (verification not implemented)
Leaf count of result is larger than twice the leaf count of optimal. 56 vs. \(2 (17) = 34\).
Time = 0.27 (sec) , antiderivative size = 56, normalized size of antiderivative = 3.11
\[
\int \frac {19+52 x+73 x^2+58 x^3+28 x^4+8 x^5+x^6+e^x \left (25+60 x+76 x^2+58 x^3+28 x^4+8 x^5+x^6\right )}{25+60 x+76 x^2+58 x^3+28 x^4+8 x^5+x^6} \, dx=\frac {x^{4} + x^{3} e^{x} + 4 \, x^{3} + 4 \, x^{2} e^{x} + 6 \, x^{2} + 6 \, x e^{x} + 5 \, x + 5 \, e^{x} + 1}{x^{3} + 4 \, x^{2} + 6 \, x + 5}
\]
[In]
integrate(((x^6+8*x^5+28*x^4+58*x^3+76*x^2+60*x+25)*exp(x)+x^6+8*x^5+28*x^4+58*x^3+73*x^2+52*x+19)/(x^6+8*x^5+
28*x^4+58*x^3+76*x^2+60*x+25),x, algorithm="giac")
[Out]
(x^4 + x^3*e^x + 4*x^3 + 4*x^2*e^x + 6*x^2 + 6*x*e^x + 5*x + 5*e^x + 1)/(x^3 + 4*x^2 + 6*x + 5)
Mupad [B] (verification not implemented)
Time = 0.22 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.06
\[
\int \frac {19+52 x+73 x^2+58 x^3+28 x^4+8 x^5+x^6+e^x \left (25+60 x+76 x^2+58 x^3+28 x^4+8 x^5+x^6\right )}{25+60 x+76 x^2+58 x^3+28 x^4+8 x^5+x^6} \, dx=x+{\mathrm {e}}^x+\frac {1}{x^3+4\,x^2+6\,x+5}
\]
[In]
int((52*x + exp(x)*(60*x + 76*x^2 + 58*x^3 + 28*x^4 + 8*x^5 + x^6 + 25) + 73*x^2 + 58*x^3 + 28*x^4 + 8*x^5 + x
^6 + 19)/(60*x + 76*x^2 + 58*x^3 + 28*x^4 + 8*x^5 + x^6 + 25),x)
[Out]
x + exp(x) + 1/(6*x + 4*x^2 + x^3 + 5)