Integrand size = 115, antiderivative size = 84 \[ \int \frac {5000 \sqrt {5} \left (1000 \sqrt {3}-750 \sqrt {5}\right ) x+5000 \sqrt {5} \left (-5250 \sqrt {3}-3150 \sqrt {5}\right ) x^3+65625000 \sqrt {15} x^5}{-1937500+500000 \sqrt {15}+\left (3125000-625000 \sqrt {15}\right ) x^2+\left (-88750000-4062500 \sqrt {15}\right ) x^4+\left (164062500+32812500 \sqrt {15}\right ) x^6-172265625 x^8} \, dx=-\sqrt [4]{\frac {3}{5}} \text {arctanh}\left (\sqrt {\frac {1}{2}+\frac {2}{\sqrt {15}}}-\frac {7}{2} \sqrt [4]{\frac {5}{3}} x^2\right )-\sqrt [4]{\frac {3}{5}} \text {arctanh}\left (\sqrt {\frac {1}{2}+\frac {2}{\sqrt {15}}}-\frac {1}{2} 3^{3/4} \sqrt [4]{5} x^2\right ) \] Output:
1/5*3^(1/4)*5^(3/4)*arctanh(-1/30*(450+120*15^(1/2))^(1/2)+7/6*5^(1/4)*3^( 3/4)*x^2)+1/5*3^(1/4)*5^(3/4)*arctanh(-1/30*(450+120*15^(1/2))^(1/2)+1/2*5 ^(1/4)*3^(3/4)*x^2)
Result contains higher order function than in optimal. Order 9 vs. order 3 in optimal.
Time = 0.19 (sec) , antiderivative size = 194, normalized size of antiderivative = 2.31 \[ \int \frac {5000 \sqrt {5} \left (1000 \sqrt {3}-750 \sqrt {5}\right ) x+5000 \sqrt {5} \left (-5250 \sqrt {3}-3150 \sqrt {5}\right ) x^3+65625000 \sqrt {15} x^5}{-1937500+500000 \sqrt {15}+\left (3125000-625000 \sqrt {15}\right ) x^2+\left (-88750000-4062500 \sqrt {15}\right ) x^4+\left (164062500+32812500 \sqrt {15}\right ) x^6-172265625 x^8} \, dx=\text {RootSum}\left [-124+32 \sqrt {15}+200 \text {$\#$1}^2-40 \sqrt {15} \text {$\#$1}^2-5680 \text {$\#$1}^4-260 \sqrt {15} \text {$\#$1}^4+10500 \text {$\#$1}^6+2100 \sqrt {15} \text {$\#$1}^6-11025 \text {$\#$1}^8\&,\frac {-30 \log (x-\text {$\#$1})+8 \sqrt {15} \log (x-\text {$\#$1})-126 \log (x-\text {$\#$1}) \text {$\#$1}^2-42 \sqrt {15} \log (x-\text {$\#$1}) \text {$\#$1}^2+105 \sqrt {15} \log (x-\text {$\#$1}) \text {$\#$1}^4}{10-2 \sqrt {15}-568 \text {$\#$1}^2-26 \sqrt {15} \text {$\#$1}^2+1575 \text {$\#$1}^4+315 \sqrt {15} \text {$\#$1}^4-2205 \text {$\#$1}^6}\&\right ] \] Input:
Integrate[(5000*Sqrt[5]*(1000*Sqrt[3] - 750*Sqrt[5])*x + 5000*Sqrt[5]*(-52 50*Sqrt[3] - 3150*Sqrt[5])*x^3 + 65625000*Sqrt[15]*x^5)/(-1937500 + 500000 *Sqrt[15] + (3125000 - 625000*Sqrt[15])*x^2 + (-88750000 - 4062500*Sqrt[15 ])*x^4 + (164062500 + 32812500*Sqrt[15])*x^6 - 172265625*x^8),x]
Output:
RootSum[-124 + 32*Sqrt[15] + 200*#1^2 - 40*Sqrt[15]*#1^2 - 5680*#1^4 - 260 *Sqrt[15]*#1^4 + 10500*#1^6 + 2100*Sqrt[15]*#1^6 - 11025*#1^8 & , (-30*Log [x - #1] + 8*Sqrt[15]*Log[x - #1] - 126*Log[x - #1]*#1^2 - 42*Sqrt[15]*Log [x - #1]*#1^2 + 105*Sqrt[15]*Log[x - #1]*#1^4)/(10 - 2*Sqrt[15] - 568*#1^2 - 26*Sqrt[15]*#1^2 + 1575*#1^4 + 315*Sqrt[15]*#1^4 - 2205*#1^6) & ]
Leaf count is larger than twice the leaf count of optimal. \(291\) vs. \(2(84)=168\).
Time = 3.21 (sec) , antiderivative size = 291, normalized size of antiderivative = 3.46, number of steps used = 6, number of rules used = 5, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.043, Rules used = {2028, 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.
| \(\displaystyle \int \frac {65625000 \sqrt {15} x^5+5000 \sqrt {5} \left (-5250 \sqrt {3}-3150 \sqrt {5}\right ) x^3+5000 \sqrt {5} \left (1000 \sqrt {3}-750 \sqrt {5}\right ) x}{-172265625 x^8+\left (164062500+32812500 \sqrt {15}\right ) x^6+\left (-88750000-4062500 \sqrt {15}\right ) x^4+\left (3125000-625000 \sqrt {15}\right ) x^2+500000 \sqrt {15}-1937500} \, dx\) |
| \(\Big \downarrow \) 2028 |
| \(\displaystyle \int \frac {x \left (65625000 \sqrt {15} x^4+5000 \sqrt {5} \left (-5250 \sqrt {3}-3150 \sqrt {5}\right ) x^2+5000 \sqrt {5} \left (1000 \sqrt {3}-750 \sqrt {5}\right )\right )}{-172265625 x^8+\left (164062500+32812500 \sqrt {15}\right ) x^6+\left (-88750000-4062500 \sqrt {15}\right ) x^4+\left (3125000-625000 \sqrt {15}\right ) x^2+500000 \sqrt {15}-1937500}dx\) |
| \(\Big \downarrow \) 7266 |
| \(\displaystyle \frac {1}{2} \int \frac {40 \left (-105 \sqrt {15} x^4+42 \left (3+\sqrt {15}\right ) x^2+2 \left (15-4 \sqrt {15}\right )\right )}{11025 x^8-2100 \left (5+\sqrt {15}\right ) x^6+20 \left (284+13 \sqrt {15}\right ) x^4-40 \left (5-\sqrt {15}\right ) x^2+4 \left (31-8 \sqrt {15}\right )}dx^2\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle 20 \int \frac {-105 \sqrt {15} x^4+42 \left (3+\sqrt {15}\right ) x^2+2 \left (15-4 \sqrt {15}\right )}{11025 x^8-2100 \left (5+\sqrt {15}\right ) x^6+20 \left (284+13 \sqrt {15}\right ) x^4-40 \left (5-\sqrt {15}\right ) x^2+4 \left (31-8 \sqrt {15}\right )}dx^2\) |
| \(\Big \downarrow \) 2492 |
| \(\displaystyle \frac {4 \int \left (\frac {2205 \sqrt [4]{15} \left (\sqrt {3}+\sqrt {5}-5 \sqrt [4]{15}\right )}{2 \left (105 x^4-2 \left (25-4 \sqrt [4]{3} 5^{3/4}+5 \sqrt {15}\right ) x^2+2 \left (4-\sqrt {15}\right )\right )}-\frac {2205 \sqrt [4]{15} \left (\sqrt {3}+\sqrt {5}+5 \sqrt [4]{15}\right )}{2 \left (105 x^4-2 \left (25+4 \sqrt [4]{3} 5^{3/4}+5 \sqrt {15}\right ) x^2+2 \left (4-\sqrt {15}\right )\right )}\right )dx^2}{2205}\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle \frac {4 \left (\frac {441 \sqrt [4]{3} 5^{3/4} \left (\sqrt {3}+\sqrt {5}-5 \sqrt [4]{15}\right ) \text {arctanh}\left (\frac {-21 \sqrt {5} x^2-4 \sqrt [4]{15}+5 \sqrt {5}+5 \sqrt {3}}{2 \sqrt {8-10\ 3^{3/4} \sqrt [4]{5}-10 \sqrt [4]{3} 5^{3/4}+27 \sqrt {15}}}\right )}{4 \sqrt {8-10\ 3^{3/4} \sqrt [4]{5}-10 \sqrt [4]{3} 5^{3/4}+27 \sqrt {15}}}-\frac {441 \sqrt [4]{3} 5^{3/4} \left (\sqrt {3}+\sqrt {5}+5 \sqrt [4]{15}\right ) \text {arctanh}\left (\frac {-21 \sqrt {5} x^2+4 \sqrt [4]{15}+5 \sqrt {5}+5 \sqrt {3}}{2 \sqrt {8+10\ 3^{3/4} \sqrt [4]{5}+10 \sqrt [4]{3} 5^{3/4}+27 \sqrt {15}}}\right )}{4 \sqrt {8+10\ 3^{3/4} \sqrt [4]{5}+10 \sqrt [4]{3} 5^{3/4}+27 \sqrt {15}}}\right )}{2205}\) |
Input:
Int[(5000*Sqrt[5]*(1000*Sqrt[3] - 750*Sqrt[5])*x + 5000*Sqrt[5]*(-5250*Sqr t[3] - 3150*Sqrt[5])*x^3 + 65625000*Sqrt[15]*x^5)/(-1937500 + 500000*Sqrt[ 15] + (3125000 - 625000*Sqrt[15])*x^2 + (-88750000 - 4062500*Sqrt[15])*x^4 + (164062500 + 32812500*Sqrt[15])*x^6 - 172265625*x^8),x]
Output:
(4*((441*3^(1/4)*5^(3/4)*(Sqrt[3] + Sqrt[5] - 5*15^(1/4))*ArcTanh[(5*Sqrt[ 3] + 5*Sqrt[5] - 4*15^(1/4) - 21*Sqrt[5]*x^2)/(2*Sqrt[8 - 10*3^(3/4)*5^(1/ 4) - 10*3^(1/4)*5^(3/4) + 27*Sqrt[15]])])/(4*Sqrt[8 - 10*3^(3/4)*5^(1/4) - 10*3^(1/4)*5^(3/4) + 27*Sqrt[15]]) - (441*3^(1/4)*5^(3/4)*(Sqrt[3] + Sqrt [5] + 5*15^(1/4))*ArcTanh[(5*Sqrt[3] + 5*Sqrt[5] + 4*15^(1/4) - 21*Sqrt[5] *x^2)/(2*Sqrt[8 + 10*3^(3/4)*5^(1/4) + 10*3^(1/4)*5^(3/4) + 27*Sqrt[15]])] )/(4*Sqrt[8 + 10*3^(3/4)*5^(1/4) + 10*3^(1/4)*5^(3/4) + 27*Sqrt[15]])))/22 05
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_.) + (c_.)*(x_)^(t_.))^(p_.), x_Symbol] :> Int[x^(p*r)*(a + b*x^(s - r) + c*x^(t - r))^p*Fx, x] /; FreeQ[ {a, b, c, r, s, t}, x] && IntegerQ[p] && PosQ[s - r] && PosQ[t - r] && !(E qQ[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 = 0.70 (sec) , antiderivative size = 60, normalized size of antiderivative = 0.71
| method | result | size |
| default | \(\frac {15^{\frac {1}{4}} \sqrt {5}\, \operatorname {arctanh}\left (\frac {\left (90 x^{2}-6 \sqrt {15}-30\right ) \sqrt {5}\, 15^{\frac {3}{4}}}{900}\right )}{5}+\frac {15^{\frac {1}{4}} \sqrt {5}\, \operatorname {arctanh}\left (\frac {\left (490 x^{2}-14 \sqrt {15}-70\right ) \sqrt {5}\, 15^{\frac {3}{4}}}{2100}\right )}{5}\) | \(60\) |
Input:
int((5000*5^(1/2)*(1000*3^(1/2)-750*5^(1/2))*x+5000*5^(1/2)*(-5250*3^(1/2) -3150*5^(1/2))*x^3+65625000*15^(1/2)*x^5)/(-1937500+500000*15^(1/2)+(31250 00-625000*15^(1/2))*x^2+(-88750000-4062500*15^(1/2))*x^4+(164062500+328125 00*15^(1/2))*x^6-172265625*x^8),x,method=_RETURNVERBOSE)
Output:
1/5*15^(1/4)*5^(1/2)*arctanh(1/900*(90*x^2-6*15^(1/2)-30)*5^(1/2)*15^(3/4) )+1/5*15^(1/4)*5^(1/2)*arctanh(1/2100*(490*x^2-14*15^(1/2)-70)*5^(1/2)*15^ (3/4))
Timed out. \[ \int \frac {5000 \sqrt {5} \left (1000 \sqrt {3}-750 \sqrt {5}\right ) x+5000 \sqrt {5} \left (-5250 \sqrt {3}-3150 \sqrt {5}\right ) x^3+65625000 \sqrt {15} x^5}{-1937500+500000 \sqrt {15}+\left (3125000-625000 \sqrt {15}\right ) x^2+\left (-88750000-4062500 \sqrt {15}\right ) x^4+\left (164062500+32812500 \sqrt {15}\right ) x^6-172265625 x^8} \, dx=\text {Timed out} \] Input:
integrate((5000*5^(1/2)*(1000*3^(1/2)-750*5^(1/2))*x+5000*5^(1/2)*(-5250*3 ^(1/2)-3150*5^(1/2))*x^3+65625000*15^(1/2)*x^5)/(-1937500+500000*15^(1/2)+ (3125000-625000*15^(1/2))*x^2+(-88750000-4062500*15^(1/2))*x^4+(164062500+ 32812500*15^(1/2))*x^6-172265625*x^8),x, algorithm="fricas")
Output:
Timed out
Timed out. \[ \int \frac {5000 \sqrt {5} \left (1000 \sqrt {3}-750 \sqrt {5}\right ) x+5000 \sqrt {5} \left (-5250 \sqrt {3}-3150 \sqrt {5}\right ) x^3+65625000 \sqrt {15} x^5}{-1937500+500000 \sqrt {15}+\left (3125000-625000 \sqrt {15}\right ) x^2+\left (-88750000-4062500 \sqrt {15}\right ) x^4+\left (164062500+32812500 \sqrt {15}\right ) x^6-172265625 x^8} \, dx=\text {Timed out} \] Input:
integrate((5000*5**(1/2)*(1000*3**(1/2)-750*5**(1/2))*x+5000*5**(1/2)*(-52 50*3**(1/2)-3150*5**(1/2))*x**3+65625000*15**(1/2)*x**5)/(-1937500+500000* 15**(1/2)+(3125000-625000*15**(1/2))*x**2+(-88750000-4062500*15**(1/2))*x* *4+(164062500+32812500*15**(1/2))*x**6-172265625*x**8),x)
Output:
Timed out
\[ \int \frac {5000 \sqrt {5} \left (1000 \sqrt {3}-750 \sqrt {5}\right ) x+5000 \sqrt {5} \left (-5250 \sqrt {3}-3150 \sqrt {5}\right ) x^3+65625000 \sqrt {15} x^5}{-1937500+500000 \sqrt {15}+\left (3125000-625000 \sqrt {15}\right ) x^2+\left (-88750000-4062500 \sqrt {15}\right ) x^4+\left (164062500+32812500 \sqrt {15}\right ) x^6-172265625 x^8} \, dx=\int { -\frac {8 \, {\left (525 \, \sqrt {15} x^{5} - 42 \, \sqrt {5} x^{3} {\left (3 \, \sqrt {5} + 5 \, \sqrt {3}\right )} - 10 \, \sqrt {5} x {\left (3 \, \sqrt {5} - 4 \, \sqrt {3}\right )}\right )}}{11025 \, x^{8} - 2100 \, x^{6} {\left (\sqrt {15} + 5\right )} + 20 \, x^{4} {\left (13 \, \sqrt {15} + 284\right )} + 40 \, x^{2} {\left (\sqrt {15} - 5\right )} - 32 \, \sqrt {15} + 124} \,d x } \] Input:
integrate((5000*5^(1/2)*(1000*3^(1/2)-750*5^(1/2))*x+5000*5^(1/2)*(-5250*3 ^(1/2)-3150*5^(1/2))*x^3+65625000*15^(1/2)*x^5)/(-1937500+500000*15^(1/2)+ (3125000-625000*15^(1/2))*x^2+(-88750000-4062500*15^(1/2))*x^4+(164062500+ 32812500*15^(1/2))*x^6-172265625*x^8),x, algorithm="maxima")
Output:
-8*integrate((525*sqrt(15)*x^5 - 42*sqrt(5)*x^3*(3*sqrt(5) + 5*sqrt(3)) - 10*sqrt(5)*x*(3*sqrt(5) - 4*sqrt(3)))/(11025*x^8 - 2100*x^6*(sqrt(15) + 5) + 20*x^4*(13*sqrt(15) + 284) + 40*x^2*(sqrt(15) - 5) - 32*sqrt(15) + 124) , x)
Exception generated. \[ \int \frac {5000 \sqrt {5} \left (1000 \sqrt {3}-750 \sqrt {5}\right ) x+5000 \sqrt {5} \left (-5250 \sqrt {3}-3150 \sqrt {5}\right ) x^3+65625000 \sqrt {15} x^5}{-1937500+500000 \sqrt {15}+\left (3125000-625000 \sqrt {15}\right ) x^2+\left (-88750000-4062500 \sqrt {15}\right ) x^4+\left (164062500+32812500 \sqrt {15}\right ) x^6-172265625 x^8} \, dx=\text {Exception raised: TypeError} \] Input:
integrate((5000*5^(1/2)*(1000*3^(1/2)-750*5^(1/2))*x+5000*5^(1/2)*(-5250*3 ^(1/2)-3150*5^(1/2))*x^3+65625000*15^(1/2)*x^5)/(-1937500+500000*15^(1/2)+ (3125000-625000*15^(1/2))*x^2+(-88750000-4062500*15^(1/2))*x^4+(164062500+ 32812500*15^(1/2))*x^6-172265625*x^8),x, algorithm="giac")
Output:
Exception raised: TypeError >> an error occurred running a Giac command:IN PUT:sage2:=int(sage0,sageVARx):;OUTPUT: *** Warning: increasing stack s ize to 4096000.Francis algorithm failure for[-1.0,0.0,infinity,infinity,in finity]pr
Time = 12.59 (sec) , antiderivative size = 1086, normalized size of antiderivative = 12.93 \[ \int \frac {5000 \sqrt {5} \left (1000 \sqrt {3}-750 \sqrt {5}\right ) x+5000 \sqrt {5} \left (-5250 \sqrt {3}-3150 \sqrt {5}\right ) x^3+65625000 \sqrt {15} x^5}{-1937500+500000 \sqrt {15}+\left (3125000-625000 \sqrt {15}\right ) x^2+\left (-88750000-4062500 \sqrt {15}\right ) x^4+\left (164062500+32812500 \sqrt {15}\right ) x^6-172265625 x^8} \, dx=\text {Too large to display} \] Input:
int(-(65625000*15^(1/2)*x^5 + 5000*5^(1/2)*x*(1000*3^(1/2) - 750*5^(1/2)) - 5000*5^(1/2)*x^3*(5250*3^(1/2) + 3150*5^(1/2)))/(x^2*(625000*15^(1/2) - 3125000) + x^4*(4062500*15^(1/2) + 88750000) - 500000*15^(1/2) - x^6*(3281 2500*15^(1/2) + 164062500) + 172265625*x^8 + 1937500),x)
Output:
symsum(log(14413269276*root(18530304000*15^(1/2)*z^4 - 71793623040*z^4 + 7 179362304*15^(1/2)*z^2 - 27795456000*z^2 + 694886400*15^(1/2) - 2692260864 , z, k) - 3705932916*15^(1/2)*root(18530304000*15^(1/2)*z^4 - 71793623040* z^4 + 7179362304*15^(1/2)*z^2 - 27795456000*z^2 + 694886400*15^(1/2) - 269 2260864, z, k) - 150361596*15^(1/2) - 24252197760*15^(1/2)*root(1853030400 0*15^(1/2)*z^4 - 71793623040*z^4 + 7179362304*15^(1/2)*z^2 - 27795456000*z ^2 + 694886400*15^(1/2) - 2692260864, z, k)^2 - 38435384736*15^(1/2)*root( 18530304000*15^(1/2)*z^4 - 71793623040*z^4 + 7179362304*15^(1/2)*z^2 - 277 95456000*z^2 + 694886400*15^(1/2) - 2692260864, z, k)^3 - 238264183984*15^ (1/2)*root(18530304000*15^(1/2)*z^4 - 71793623040*z^4 + 7179362304*15^(1/2 )*z^2 - 27795456000*z^2 + 694886400*15^(1/2) - 2692260864, z, k)^4 - 98824 877760*15^(1/2)*root(18530304000*15^(1/2)*z^4 - 71793623040*z^4 + 71793623 04*15^(1/2)*z^2 - 27795456000*z^2 + 694886400*15^(1/2) - 2692260864, z, k) ^5 - 604371210240*15^(1/2)*root(18530304000*15^(1/2)*z^4 - 71793623040*z^4 + 7179362304*15^(1/2)*z^2 - 27795456000*z^2 + 694886400*15^(1/2) - 269226 0864, z, k)^6 + 117295652025*root(18530304000*15^(1/2)*z^4 - 71793623040*z ^4 + 7179362304*15^(1/2)*z^2 - 27795456000*z^2 + 694886400*15^(1/2) - 2692 260864, z, k)*x^2 - 3456415935*15^(1/2)*x^2 + 93859916874*root(18530304000 *15^(1/2)*z^4 - 71793623040*z^4 + 7179362304*15^(1/2)*z^2 - 27795456000*z^ 2 + 694886400*15^(1/2) - 2692260864, z, k)^2 + 148237316640*root(185303...
\[ \int \frac {5000 \sqrt {5} \left (1000 \sqrt {3}-750 \sqrt {5}\right ) x+5000 \sqrt {5} \left (-5250 \sqrt {3}-3150 \sqrt {5}\right ) x^3+65625000 \sqrt {15} x^5}{-1937500+500000 \sqrt {15}+\left (3125000-625000 \sqrt {15}\right ) x^2+\left (-88750000-4062500 \sqrt {15}\right ) x^4+\left (164062500+32812500 \sqrt {15}\right ) x^6-172265625 x^8} \, dx =\text {Too large to display} \] Input:
int((5000*5^(1/2)*(1000*3^(1/2)-750*5^(1/2))*x+5000*5^(1/2)*(-5250*3^(1/2) -3150*5^(1/2))*x^3+65625000*15^(1/2)*x^5)/(-1937500+500000*15^(1/2)+(31250 00-625000*15^(1/2))*x^2+(-88750000-4062500*15^(1/2))*x^4+(164062500+328125 00*15^(1/2))*x^6-172265625*x^8),x)
Output:
40*( - 1157625*sqrt(15)*int(x**13/(121550625*x**16 - 231525000*x**14 + 169 344000*x**12 - 107310000*x**10 + 40702600*x**8 - 7204000*x**6 + 1674240*x* *4 - 11200*x**2 + 16),x) + 1565550*sqrt(15)*int(x**11/(121550625*x**16 - 2 31525000*x**14 + 169344000*x**12 - 107310000*x**10 + 40702600*x**8 - 72040 00*x**6 + 1674240*x**4 - 11200*x**2 + 16),x) - 861000*sqrt(15)*int(x**9/(1 21550625*x**16 - 231525000*x**14 + 169344000*x**12 - 107310000*x**10 + 407 02600*x**8 - 7204000*x**6 + 1674240*x**4 - 11200*x**2 + 16),x) + 373800*sq rt(15)*int(x**7/(121550625*x**16 - 231525000*x**14 + 169344000*x**12 - 107 310000*x**10 + 40702600*x**8 - 7204000*x**6 + 1674240*x**4 - 11200*x**2 + 16),x) - 79700*sqrt(15)*int(x**5/(121550625*x**16 - 231525000*x**14 + 1693 44000*x**12 - 107310000*x**10 + 40702600*x**8 - 7204000*x**6 + 1674240*x** 4 - 11200*x**2 + 16),x) + 9640*sqrt(15)*int(x**3/(121550625*x**16 - 231525 000*x**14 + 169344000*x**12 - 107310000*x**10 + 40702600*x**8 - 7204000*x* *6 + 1674240*x**4 - 11200*x**2 + 16),x) - 32*sqrt(15)*int(x/(121550625*x** 16 - 231525000*x**14 + 169344000*x**12 - 107310000*x**10 + 40702600*x**8 - 7204000*x**6 + 1674240*x**4 - 11200*x**2 + 16),x) - 1918350*int(x**11/(12 1550625*x**16 - 231525000*x**14 + 169344000*x**12 - 107310000*x**10 + 4070 2600*x**8 - 7204000*x**6 + 1674240*x**4 - 11200*x**2 + 16),x) + 740250*int (x**9/(121550625*x**16 - 231525000*x**14 + 169344000*x**12 - 107310000*x** 10 + 40702600*x**8 - 7204000*x**6 + 1674240*x**4 - 11200*x**2 + 16),x) ...