Integrand size = 79, antiderivative size = 74 \[ \int \frac {8 \left (3-2 \sqrt {3}\right ) x+24 \sqrt {3} x^5}{-28+16 \sqrt {3}+\left (-20+20 \sqrt {3}\right ) x^2+\left (-148-22 \sqrt {3}\right ) x^4+\left (60+60 \sqrt {3}\right ) x^6-36 x^8} \, dx=\sqrt [4]{3} \text {arctanh}\left (\frac {1}{\sqrt [4]{3}}-\sqrt [4]{3} x\right )+\sqrt [4]{3} \text {arctanh}\left (\frac {1}{\sqrt [4]{3}}+\sqrt [4]{3} x\right )-\sqrt [4]{3} \text {arctanh}\left (\sqrt {\frac {1}{2}+\frac {1}{\sqrt {3}}}-\frac {x^2}{\sqrt [4]{3}}\right ) \] Output:
-3^(1/4)*arctanh(-1/3*3^(3/4)+3^(1/4)*x)+3^(1/4)*arctanh(1/3*3^(3/4)+3^(1/ 4)*x)+3^(1/4)*arctanh(-1/6*(18+12*3^(1/2))^(1/2)+1/3*3^(3/4)*x^2)
Result contains higher order function than in optimal. Order 9 vs. order 3 in optimal.
Time = 0.12 (sec) , antiderivative size = 163, normalized size of antiderivative = 2.20 \[ \int \frac {8 \left (3-2 \sqrt {3}\right ) x+24 \sqrt {3} x^5}{-28+16 \sqrt {3}+\left (-20+20 \sqrt {3}\right ) x^2+\left (-148-22 \sqrt {3}\right ) x^4+\left (60+60 \sqrt {3}\right ) x^6-36 x^8} \, dx=\text {RootSum}\left [-14+8 \sqrt {3}-10 \text {$\#$1}^2+10 \sqrt {3} \text {$\#$1}^2-74 \text {$\#$1}^4-11 \sqrt {3} \text {$\#$1}^4+30 \text {$\#$1}^6+30 \sqrt {3} \text {$\#$1}^6-18 \text {$\#$1}^8\&,\frac {3 \log (x-\text {$\#$1})-2 \sqrt {3} \log (x-\text {$\#$1})+3 \sqrt {3} \log (x-\text {$\#$1}) \text {$\#$1}^4}{-5+5 \sqrt {3}-74 \text {$\#$1}^2-11 \sqrt {3} \text {$\#$1}^2+45 \text {$\#$1}^4+45 \sqrt {3} \text {$\#$1}^4-36 \text {$\#$1}^6}\&\right ] \] Input:
Integrate[(8*(3 - 2*Sqrt[3])*x + 24*Sqrt[3]*x^5)/(-28 + 16*Sqrt[3] + (-20 + 20*Sqrt[3])*x^2 + (-148 - 22*Sqrt[3])*x^4 + (60 + 60*Sqrt[3])*x^6 - 36*x ^8),x]
Output:
RootSum[-14 + 8*Sqrt[3] - 10*#1^2 + 10*Sqrt[3]*#1^2 - 74*#1^4 - 11*Sqrt[3] *#1^4 + 30*#1^6 + 30*Sqrt[3]*#1^6 - 18*#1^8 & , (3*Log[x - #1] - 2*Sqrt[3] *Log[x - #1] + 3*Sqrt[3]*Log[x - #1]*#1^4)/(-5 + 5*Sqrt[3] - 74*#1^2 - 11* Sqrt[3]*#1^2 + 45*#1^4 + 45*Sqrt[3]*#1^4 - 36*#1^6) & ]
Time = 1.90 (sec) , antiderivative size = 101, normalized size of antiderivative = 1.36, number of steps used = 6, number of rules used = 5, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.063, Rules used = {2027, 7266, 27, 2492, 2009}
Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.
| \(\displaystyle \int \frac {24 \sqrt {3} x^5+8 \left (3-2 \sqrt {3}\right ) x}{-36 x^8+\left (60+60 \sqrt {3}\right ) x^6+\left (-148-22 \sqrt {3}\right ) x^4+\left (20 \sqrt {3}-20\right ) x^2+16 \sqrt {3}-28} \, dx\) |
| \(\Big \downarrow \) 2027 |
| \(\displaystyle \int \frac {x \left (24 \sqrt {3} x^4+8 \left (3-2 \sqrt {3}\right )\right )}{-36 x^8+\left (60+60 \sqrt {3}\right ) x^6+\left (-148-22 \sqrt {3}\right ) x^4+\left (20 \sqrt {3}-20\right ) x^2+16 \sqrt {3}-28}dx\) |
| \(\Big \downarrow \) 7266 |
| \(\displaystyle \frac {1}{2} \int -\frac {4 \left (3 \sqrt {3} x^4-2 \sqrt {3}+3\right )}{18 x^8-30 \left (1+\sqrt {3}\right ) x^6+\left (74+11 \sqrt {3}\right ) x^4+10 \left (1-\sqrt {3}\right ) x^2+2 \left (7-4 \sqrt {3}\right )}dx^2\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle -2 \int \frac {3 \sqrt {3} x^4-2 \sqrt {3}+3}{18 x^8-30 \left (1+\sqrt {3}\right ) x^6+\left (74+11 \sqrt {3}\right ) x^4+10 \left (1-\sqrt {3}\right ) x^2+2 \left (7-4 \sqrt {3}\right )}dx^2\) |
| \(\Big \downarrow \) 2492 |
| \(\displaystyle -\frac {1}{9} \int \left (\frac {3\ 3^{3/4} \left (-12 \sqrt {3} x^2-2\ 3^{3/4}+5 \sqrt {3}+15\right )}{2 \left (6 x^4-\left (5-2 \sqrt [4]{3}+5 \sqrt {3}\right ) x^2+2 \left (2-\sqrt {3}\right )\right )}-\frac {3\ 3^{3/4} \left (-12 \sqrt {3} x^2+2\ 3^{3/4}+5 \sqrt {3}+15\right )}{2 \left (6 x^4-\left (5+2 \sqrt [4]{3}+5 \sqrt {3}\right ) x^2+2 \left (2-\sqrt {3}\right )\right )}\right )dx^2\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle \frac {1}{9} \left (\frac {9}{2} \sqrt [4]{3} \log \left (6 x^4-\left (5-2 \sqrt [4]{3}+5 \sqrt {3}\right ) x^2+2 \left (2-\sqrt {3}\right )\right )-\frac {9}{2} \sqrt [4]{3} \log \left (6 x^4-\left (5+2 \sqrt [4]{3}+5 \sqrt {3}\right ) x^2+2 \left (2-\sqrt {3}\right )\right )\right )\) |
Input:
Int[(8*(3 - 2*Sqrt[3])*x + 24*Sqrt[3]*x^5)/(-28 + 16*Sqrt[3] + (-20 + 20*S qrt[3])*x^2 + (-148 - 22*Sqrt[3])*x^4 + (60 + 60*Sqrt[3])*x^6 - 36*x^8),x]
Output:
((9*3^(1/4)*Log[2*(2 - Sqrt[3]) - (5 - 2*3^(1/4) + 5*Sqrt[3])*x^2 + 6*x^4] )/2 - (9*3^(1/4)*Log[2*(2 - Sqrt[3]) - (5 + 2*3^(1/4) + 5*Sqrt[3])*x^2 + 6 *x^4])/2)/9
Int[(a_)*(Fx_), x_Symbol] :> Simp[a Int[Fx, x], x] /; FreeQ[a, x] && !Ma tchQ[Fx, (b_)*(Gx_) /; FreeQ[b, x]]
Int[(Fx_.)*((a_.)*(x_)^(r_.) + (b_.)*(x_)^(s_.))^(p_.), x_Symbol] :> Int[x^ (p*r)*(a + b*x^(s - r))^p*Fx, x] /; FreeQ[{a, b, r, s}, x] && IntegerQ[p] & & PosQ[s - r] && !(EqQ[p, 1] && EqQ[u, 1])
Int[(Px_.)*((a_) + (b_.)*(x_) + (c_.)*(x_)^2 + (d_.)*(x_)^3 + (e_.)*(x_)^4) ^(p_), x_Symbol] :> Simp[e^p Int[ExpandIntegrand[Px*(b/d + ((d + Sqrt[e*( (b^2 - 4*a*c)/a) + 8*a*d*(e/b)])/(2*e))*x + x^2)^p*(b/d + ((d - Sqrt[e*((b^ 2 - 4*a*c)/a) + 8*a*d*(e/b)])/(2*e))*x + x^2)^p, x], x], x] /; FreeQ[{a, b, c, d, e}, x] && PolyQ[Px, x] && ILtQ[p, 0] && EqQ[a*d^2 - b^2*e, 0]
Int[(u_)*(x_)^(m_.), x_Symbol] :> Simp[1/(m + 1) Subst[Int[SubstFor[x^(m + 1), u, x], x], x, x^(m + 1)], x] /; FreeQ[m, x] && NeQ[m, -1] && Function OfQ[x^(m + 1), u, x]
Time = 0.42 (sec) , antiderivative size = 47, normalized size of antiderivative = 0.64
| method | result | size |
| default | \(3^{\frac {1}{4}} \operatorname {arctanh}\left (\frac {\left (4 x^{2}-2 \sqrt {3}-2\right ) 3^{\frac {3}{4}}}{12}\right )-3^{\frac {1}{4}} \operatorname {arctanh}\left (\frac {\left (18 x^{2}-6-6 \sqrt {3}\right ) 3^{\frac {3}{4}}}{36}\right )\) | \(47\) |
Input:
int((8*(3-2*3^(1/2))*x+24*3^(1/2)*x^5)/(-28+16*3^(1/2)+(-20+20*3^(1/2))*x^ 2+(-148-22*3^(1/2))*x^4+(60+60*3^(1/2))*x^6-36*x^8),x,method=_RETURNVERBOS E)
Output:
3^(1/4)*arctanh(1/12*(4*x^2-2*3^(1/2)-2)*3^(3/4))-3^(1/4)*arctanh(1/36*(18 *x^2-6-6*3^(1/2))*3^(3/4))
Leaf count of result is larger than twice the leaf count of optimal. 200 vs. \(2 (59) = 118\).
Time = 0.09 (sec) , antiderivative size = 200, normalized size of antiderivative = 2.70 \[ \int \frac {8 \left (3-2 \sqrt {3}\right ) x+24 \sqrt {3} x^5}{-28+16 \sqrt {3}+\left (-20+20 \sqrt {3}\right ) x^2+\left (-148-22 \sqrt {3}\right ) x^4+\left (60+60 \sqrt {3}\right ) x^6-36 x^8} \, dx=\frac {1}{2} \cdot 3^{\frac {1}{4}} \log \left (\frac {324 \, x^{16} - 1080 \, x^{14} + 864 \, x^{12} - 1740 \, x^{10} + 3085 \, x^{8} - 20 \, x^{6} + 2496 \, x^{4} - 200 \, x^{2} + 8 \, \sqrt {3} {\left (9 \, x^{12} - 15 \, x^{10} + 37 \, x^{8} + 5 \, x^{6} + 7 \, x^{4}\right )} + 2 \cdot 3^{\frac {1}{4}} {\left (108 \, x^{14} - 270 \, x^{12} + 216 \, x^{10} - 445 \, x^{8} + 246 \, x^{6} - 210 \, x^{4} + 8 \, x^{2} + \sqrt {3} {\left (90 \, x^{12} - 102 \, x^{10} - 75 \, x^{8} - 244 \, x^{6} - 90 \, x^{4} + 4 \, x^{2}\right )}\right )} + 4}{324 \, x^{16} - 1080 \, x^{14} + 864 \, x^{12} - 2100 \, x^{10} + 3217 \, x^{8} - 140 \, x^{6} + 2400 \, x^{4} - 200 \, x^{2} + 4}\right ) \] Input:
integrate((8*(3-2*3^(1/2))*x+24*3^(1/2)*x^5)/(-28+16*3^(1/2)+(-20+20*3^(1/ 2))*x^2+(-148-22*3^(1/2))*x^4+(60+60*3^(1/2))*x^6-36*x^8),x, algorithm="fr icas")
Output:
1/2*3^(1/4)*log((324*x^16 - 1080*x^14 + 864*x^12 - 1740*x^10 + 3085*x^8 - 20*x^6 + 2496*x^4 - 200*x^2 + 8*sqrt(3)*(9*x^12 - 15*x^10 + 37*x^8 + 5*x^6 + 7*x^4) + 2*3^(1/4)*(108*x^14 - 270*x^12 + 216*x^10 - 445*x^8 + 246*x^6 - 210*x^4 + 8*x^2 + sqrt(3)*(90*x^12 - 102*x^10 - 75*x^8 - 244*x^6 - 90*x^ 4 + 4*x^2)) + 4)/(324*x^16 - 1080*x^14 + 864*x^12 - 2100*x^10 + 3217*x^8 - 140*x^6 + 2400*x^4 - 200*x^2 + 4))
Timed out. \[ \int \frac {8 \left (3-2 \sqrt {3}\right ) x+24 \sqrt {3} x^5}{-28+16 \sqrt {3}+\left (-20+20 \sqrt {3}\right ) x^2+\left (-148-22 \sqrt {3}\right ) x^4+\left (60+60 \sqrt {3}\right ) x^6-36 x^8} \, dx=\text {Timed out} \] Input:
integrate((8*(3-2*3**(1/2))*x+24*3**(1/2)*x**5)/(-28+16*3**(1/2)+(-20+20*3 **(1/2))*x**2+(-148-22*3**(1/2))*x**4+(60+60*3**(1/2))*x**6-36*x**8),x)
Output:
Timed out
\[ \int \frac {8 \left (3-2 \sqrt {3}\right ) x+24 \sqrt {3} x^5}{-28+16 \sqrt {3}+\left (-20+20 \sqrt {3}\right ) x^2+\left (-148-22 \sqrt {3}\right ) x^4+\left (60+60 \sqrt {3}\right ) x^6-36 x^8} \, dx=\int { -\frac {4 \, {\left (3 \, \sqrt {3} x^{5} - x {\left (2 \, \sqrt {3} - 3\right )}\right )}}{18 \, x^{8} - 30 \, x^{6} {\left (\sqrt {3} + 1\right )} + x^{4} {\left (11 \, \sqrt {3} + 74\right )} - 10 \, x^{2} {\left (\sqrt {3} - 1\right )} - 8 \, \sqrt {3} + 14} \,d x } \] Input:
integrate((8*(3-2*3^(1/2))*x+24*3^(1/2)*x^5)/(-28+16*3^(1/2)+(-20+20*3^(1/ 2))*x^2+(-148-22*3^(1/2))*x^4+(60+60*3^(1/2))*x^6-36*x^8),x, algorithm="ma xima")
Output:
-4*integrate((3*sqrt(3)*x^5 - x*(2*sqrt(3) - 3))/(18*x^8 - 30*x^6*(sqrt(3) + 1) + x^4*(11*sqrt(3) + 74) - 10*x^2*(sqrt(3) - 1) - 8*sqrt(3) + 14), x)
Exception generated. \[ \int \frac {8 \left (3-2 \sqrt {3}\right ) x+24 \sqrt {3} x^5}{-28+16 \sqrt {3}+\left (-20+20 \sqrt {3}\right ) x^2+\left (-148-22 \sqrt {3}\right ) x^4+\left (60+60 \sqrt {3}\right ) x^6-36 x^8} \, dx=\text {Exception raised: TypeError} \] Input:
integrate((8*(3-2*3^(1/2))*x+24*3^(1/2)*x^5)/(-28+16*3^(1/2)+(-20+20*3^(1/ 2))*x^2+(-148-22*3^(1/2))*x^4+(60+60*3^(1/2))*x^6-36*x^8),x, algorithm="gi ac")
Output:
Exception raised: TypeError >> an error occurred running a Giac command:IN PUT:sage2:=int(sage0,sageVARx):;OUTPUT:Unable to find common minimal polyn omial Error: Bad Argument ValueUnable to find common minimal polynomial Er ror: Bad
Time = 12.38 (sec) , antiderivative size = 1086, normalized size of antiderivative = 14.68 \[ \int \frac {8 \left (3-2 \sqrt {3}\right ) x+24 \sqrt {3} x^5}{-28+16 \sqrt {3}+\left (-20+20 \sqrt {3}\right ) x^2+\left (-148-22 \sqrt {3}\right ) x^4+\left (60+60 \sqrt {3}\right ) x^6-36 x^8} \, dx=\text {Too large to display} \] Input:
int((24*3^(1/2)*x^5 - 8*x*(2*3^(1/2) - 3))/(x^2*(20*3^(1/2) - 20) + x^6*(6 0*3^(1/2) + 60) - x^4*(22*3^(1/2) + 148) + 16*3^(1/2) - 36*x^8 - 28),x)
Output:
symsum(log(87551280*root(1449600*3^(1/2)*z^4 - 2534448*z^4 + 1267224*3^(1/ 2)*z^2 - 2174400*z^2 + 271800*3^(1/2) - 475209, z, k) - 50276880*3^(1/2)*r oot(1449600*3^(1/2)*z^4 - 2534448*z^4 + 1267224*3^(1/2)*z^2 - 2174400*z^2 + 271800*3^(1/2) - 475209, z, k) - 1944000*3^(1/2) - 329319432*3^(1/2)*roo t(1449600*3^(1/2)*z^4 - 2534448*z^4 + 1267224*3^(1/2)*z^2 - 2174400*z^2 + 271800*3^(1/2) - 475209, z, k)^2 - 233470080*3^(1/2)*root(1449600*3^(1/2)* z^4 - 2534448*z^4 + 1267224*3^(1/2)*z^2 - 2174400*z^2 + 271800*3^(1/2) - 4 75209, z, k)^3 - 1548784624*3^(1/2)*root(1449600*3^(1/2)*z^4 - 2534448*z^4 + 1267224*3^(1/2)*z^2 - 2174400*z^2 + 271800*3^(1/2) - 475209, z, k)^4 - 268143360*3^(1/2)*root(1449600*3^(1/2)*z^4 - 2534448*z^4 + 1267224*3^(1/2) *z^2 - 2174400*z^2 + 271800*3^(1/2) - 475209, z, k)^5 - 1708447104*3^(1/2) *root(1449600*3^(1/2)*z^4 - 2534448*z^4 + 1267224*3^(1/2)*z^2 - 2174400*z^ 2 + 271800*3^(1/2) - 475209, z, k)^6 - 125503551*root(1449600*3^(1/2)*z^4 - 2534448*z^4 + 1267224*3^(1/2)*z^2 - 2174400*z^2 + 271800*3^(1/2) - 47520 9, z, k)*x^2 + 8650260*3^(1/2)*x^2 + 592458234*root(1449600*3^(1/2)*z^4 - 2534448*z^4 + 1267224*3^(1/2)*z^2 - 2174400*z^2 + 271800*3^(1/2) - 475209, z, k)^2 + 402215040*root(1449600*3^(1/2)*z^4 - 2534448*z^4 + 1267224*3^(1 /2)*z^2 - 2174400*z^2 + 271800*3^(1/2) - 475209, z, k)^3 + 2580641856*root (1449600*3^(1/2)*z^4 - 2534448*z^4 + 1267224*3^(1/2)*z^2 - 2174400*z^2 + 2 71800*3^(1/2) - 475209, z, k)^4 + 466940160*root(1449600*3^(1/2)*z^4 - ...
\[ \int \frac {8 \left (3-2 \sqrt {3}\right ) x+24 \sqrt {3} x^5}{-28+16 \sqrt {3}+\left (-20+20 \sqrt {3}\right ) x^2+\left (-148-22 \sqrt {3}\right ) x^4+\left (60+60 \sqrt {3}\right ) x^6-36 x^8} \, dx=-216 \sqrt {3}\, \left (\int \frac {x^{13}}{324 x^{16}-1080 x^{14}+864 x^{12}-2100 x^{10}+3217 x^{8}-140 x^{6}+2400 x^{4}-200 x^{2}+4}d x \right )+360 \sqrt {3}\, \left (\int \frac {x^{11}}{324 x^{16}-1080 x^{14}+864 x^{12}-2100 x^{10}+3217 x^{8}-140 x^{6}+2400 x^{4}-200 x^{2}+4}d x \right )-744 \sqrt {3}\, \left (\int \frac {x^{9}}{324 x^{16}-1080 x^{14}+864 x^{12}-2100 x^{10}+3217 x^{8}-140 x^{6}+2400 x^{4}-200 x^{2}+4}d x \right )-720 \sqrt {3}\, \left (\int \frac {x^{7}}{324 x^{16}-1080 x^{14}+864 x^{12}-2100 x^{10}+3217 x^{8}-140 x^{6}+2400 x^{4}-200 x^{2}+4}d x \right )+556 \sqrt {3}\, \left (\int \frac {x^{5}}{324 x^{16}-1080 x^{14}+864 x^{12}-2100 x^{10}+3217 x^{8}-140 x^{6}+2400 x^{4}-200 x^{2}+4}d x \right )-40 \sqrt {3}\, \left (\int \frac {x^{3}}{324 x^{16}-1080 x^{14}+864 x^{12}-2100 x^{10}+3217 x^{8}-140 x^{6}+2400 x^{4}-200 x^{2}+4}d x \right )+16 \sqrt {3}\, \left (\int \frac {x}{324 x^{16}-1080 x^{14}+864 x^{12}-2100 x^{10}+3217 x^{8}-140 x^{6}+2400 x^{4}-200 x^{2}+4}d x \right )-1080 \left (\int \frac {x^{11}}{324 x^{16}-1080 x^{14}+864 x^{12}-2100 x^{10}+3217 x^{8}-140 x^{6}+2400 x^{4}-200 x^{2}+4}d x \right )+180 \left (\int \frac {x^{9}}{324 x^{16}-1080 x^{14}+864 x^{12}-2100 x^{10}+3217 x^{8}-140 x^{6}+2400 x^{4}-200 x^{2}+4}d x \right )+720 \left (\int \frac {x^{7}}{324 x^{16}-1080 x^{14}+864 x^{12}-2100 x^{10}+3217 x^{8}-140 x^{6}+2400 x^{4}-200 x^{2}+4}d x \right )-1440 \left (\int \frac {x^{5}}{324 x^{16}-1080 x^{14}+864 x^{12}-2100 x^{10}+3217 x^{8}-140 x^{6}+2400 x^{4}-200 x^{2}+4}d x \right )+120 \left (\int \frac {x^{3}}{324 x^{16}-1080 x^{14}+864 x^{12}-2100 x^{10}+3217 x^{8}-140 x^{6}+2400 x^{4}-200 x^{2}+4}d x \right )+24 \left (\int \frac {x}{324 x^{16}-1080 x^{14}+864 x^{12}-2100 x^{10}+3217 x^{8}-140 x^{6}+2400 x^{4}-200 x^{2}+4}d x \right ) \] Input:
int((8*(3-2*3^(1/2))*x+24*3^(1/2)*x^5)/(-28+16*3^(1/2)+(-20+20*3^(1/2))*x^ 2+(-148-22*3^(1/2))*x^4+(60+60*3^(1/2))*x^6-36*x^8),x)
Output:
4*( - 54*sqrt(3)*int(x**13/(324*x**16 - 1080*x**14 + 864*x**12 - 2100*x**1 0 + 3217*x**8 - 140*x**6 + 2400*x**4 - 200*x**2 + 4),x) + 90*sqrt(3)*int(x **11/(324*x**16 - 1080*x**14 + 864*x**12 - 2100*x**10 + 3217*x**8 - 140*x* *6 + 2400*x**4 - 200*x**2 + 4),x) - 186*sqrt(3)*int(x**9/(324*x**16 - 1080 *x**14 + 864*x**12 - 2100*x**10 + 3217*x**8 - 140*x**6 + 2400*x**4 - 200*x **2 + 4),x) - 180*sqrt(3)*int(x**7/(324*x**16 - 1080*x**14 + 864*x**12 - 2 100*x**10 + 3217*x**8 - 140*x**6 + 2400*x**4 - 200*x**2 + 4),x) + 139*sqrt (3)*int(x**5/(324*x**16 - 1080*x**14 + 864*x**12 - 2100*x**10 + 3217*x**8 - 140*x**6 + 2400*x**4 - 200*x**2 + 4),x) - 10*sqrt(3)*int(x**3/(324*x**16 - 1080*x**14 + 864*x**12 - 2100*x**10 + 3217*x**8 - 140*x**6 + 2400*x**4 - 200*x**2 + 4),x) + 4*sqrt(3)*int(x/(324*x**16 - 1080*x**14 + 864*x**12 - 2100*x**10 + 3217*x**8 - 140*x**6 + 2400*x**4 - 200*x**2 + 4),x) - 270*in t(x**11/(324*x**16 - 1080*x**14 + 864*x**12 - 2100*x**10 + 3217*x**8 - 140 *x**6 + 2400*x**4 - 200*x**2 + 4),x) + 45*int(x**9/(324*x**16 - 1080*x**14 + 864*x**12 - 2100*x**10 + 3217*x**8 - 140*x**6 + 2400*x**4 - 200*x**2 + 4),x) + 180*int(x**7/(324*x**16 - 1080*x**14 + 864*x**12 - 2100*x**10 + 32 17*x**8 - 140*x**6 + 2400*x**4 - 200*x**2 + 4),x) - 360*int(x**5/(324*x**1 6 - 1080*x**14 + 864*x**12 - 2100*x**10 + 3217*x**8 - 140*x**6 + 2400*x**4 - 200*x**2 + 4),x) + 30*int(x**3/(324*x**16 - 1080*x**14 + 864*x**12 - 21 00*x**10 + 3217*x**8 - 140*x**6 + 2400*x**4 - 200*x**2 + 4),x) + 6*int(...