Integrand size = 98, antiderivative size = 291 \[ \int \frac {-324+972 x-633 x^2-252 x^3+324 x^4+33 x^5+108 x^6-216 x^7+32 x^9}{1296-7776 x+17064 x^2-14904 x^3-179 x^4+8364 x^5-3186 x^6-1836 x^7+1329 x^8+144 x^9-216 x^{10}+16 x^{12}} \, dx=\frac {1}{8} \arctan \left (\frac {1}{3} \left (-3 \sqrt {7}+4 x\right )\right )+\frac {1}{8} \arctan \left (\frac {1}{3} \left (3 \sqrt {7}+4 x\right )\right )-\frac {1}{8} \arctan \left (\frac {1}{9} \left (8-9 \sqrt {7}+12 x\right )\right )-\frac {1}{8} \arctan \left (\frac {1}{9} \left (8+9 \sqrt {7}+12 x\right )\right )-\frac {1}{8} \arctan \left (\frac {1}{2} \left (18+2 \sqrt {7}-27 x-4 x^2-9 \sqrt {7} x^2-6 x^3\right )\right )-\frac {1}{8} \arctan \left (\frac {1}{2} \left (18-2 \sqrt {7}-27 x-4 x^2+9 \sqrt {7} x^2-6 x^3\right )\right )+\frac {1}{16} \sqrt {7} \log \left (36-108 x-12 \sqrt {7} x+89 x^2+18 \sqrt {7} x^2+18 x^3-27 x^4-4 \sqrt {7} x^4+4 x^6\right )-\frac {1}{16} \sqrt {7} \log \left (36-108 x+12 \sqrt {7} x+89 x^2-18 \sqrt {7} x^2+18 x^3-27 x^4+4 \sqrt {7} x^4+4 x^6\right ) \] Output:
1/8*arctan(-7^(1/2)+4/3*x)+1/8*arctan(7^(1/2)+4/3*x)-1/8*arctan(8/9-7^(1/2 )+4/3*x)-1/8*arctan(8/9+7^(1/2)+4/3*x)+1/8*arctan(-9-7^(1/2)+27/2*x+2*x^2+ 9/2*7^(1/2)*x^2+3*x^3)+1/8*arctan(-9+7^(1/2)+27/2*x+2*x^2-9/2*7^(1/2)*x^2+ 3*x^3)+1/16*7^(1/2)*ln(36-108*x-12*7^(1/2)*x+89*x^2+18*7^(1/2)*x^2+18*x^3- 27*x^4-4*x^4*7^(1/2)+4*x^6)-1/16*7^(1/2)*ln(36-108*x+12*7^(1/2)*x+89*x^2-1 8*7^(1/2)*x^2+18*x^3-27*x^4+4*x^4*7^(1/2)+4*x^6)
Result contains higher order function than in optimal. Order 9 vs. order 3 in optimal.
Time = 0.23 (sec) , antiderivative size = 249, normalized size of antiderivative = 0.86 \[ \int \frac {-324+972 x-633 x^2-252 x^3+324 x^4+33 x^5+108 x^6-216 x^7+32 x^9}{1296-7776 x+17064 x^2-14904 x^3-179 x^4+8364 x^5-3186 x^6-1836 x^7+1329 x^8+144 x^9-216 x^{10}+16 x^{12}} \, dx=\frac {\arctan \left (\frac {2 x}{3 \sqrt {\frac {1}{2} i \left (3 i+\sqrt {7}\right )}}\right )}{\sqrt {-6+2 i \sqrt {7}}}-\frac {\text {arctanh}\left (\frac {2 x}{3 \sqrt {\frac {1}{2} \left (3+i \sqrt {7}\right )}}\right )}{\sqrt {6+2 i \sqrt {7}}}-\frac {1}{8} \text {RootSum}\left [16-96 \text {$\#$1}+216 \text {$\#$1}^2-216 \text {$\#$1}^3+69 \text {$\#$1}^4+36 \text {$\#$1}^5-27 \text {$\#$1}^6+4 \text {$\#$1}^8\&,\frac {48 \log (x-\text {$\#$1}) \text {$\#$1}-180 \log (x-\text {$\#$1}) \text {$\#$1}^2+216 \log (x-\text {$\#$1}) \text {$\#$1}^3-81 \log (x-\text {$\#$1}) \text {$\#$1}^4-32 \log (x-\text {$\#$1}) \text {$\#$1}^5+24 \log (x-\text {$\#$1}) \text {$\#$1}^6}{-48+216 \text {$\#$1}-324 \text {$\#$1}^2+138 \text {$\#$1}^3+90 \text {$\#$1}^4-81 \text {$\#$1}^5+16 \text {$\#$1}^7}\&\right ] \] Input:
Integrate[(-324 + 972*x - 633*x^2 - 252*x^3 + 324*x^4 + 33*x^5 + 108*x^6 - 216*x^7 + 32*x^9)/(1296 - 7776*x + 17064*x^2 - 14904*x^3 - 179*x^4 + 8364 *x^5 - 3186*x^6 - 1836*x^7 + 1329*x^8 + 144*x^9 - 216*x^10 + 16*x^12),x]
Output:
ArcTan[(2*x)/(3*Sqrt[(I/2)*(3*I + Sqrt[7])])]/Sqrt[-6 + (2*I)*Sqrt[7]] - A rcTanh[(2*x)/(3*Sqrt[(3 + I*Sqrt[7])/2])]/Sqrt[6 + (2*I)*Sqrt[7]] - RootSu m[16 - 96*#1 + 216*#1^2 - 216*#1^3 + 69*#1^4 + 36*#1^5 - 27*#1^6 + 4*#1^8 & , (48*Log[x - #1]*#1 - 180*Log[x - #1]*#1^2 + 216*Log[x - #1]*#1^3 - 81* Log[x - #1]*#1^4 - 32*Log[x - #1]*#1^5 + 24*Log[x - #1]*#1^6)/(-48 + 216*# 1 - 324*#1^2 + 138*#1^3 + 90*#1^4 - 81*#1^5 + 16*#1^7) & ]/8
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.
| \(\displaystyle \int \frac {32 x^9-216 x^7+108 x^6+33 x^5+324 x^4-252 x^3-633 x^2+972 x-324}{16 x^{12}-216 x^{10}+144 x^9+1329 x^8-1836 x^7-3186 x^6+8364 x^5-179 x^4-14904 x^3+17064 x^2-7776 x+1296} \, dx\) |
| \(\Big \downarrow \) 2462 |
| \(\displaystyle \int \left (\frac {3 \left (8 x^2-27\right )}{4 \left (4 x^4-27 x^2+81\right )}-\frac {x \left (24 x^5-32 x^4-81 x^3+216 x^2-180 x+48\right )}{4 \left (4 x^8-27 x^6+36 x^5+69 x^4-216 x^3+216 x^2-96 x+16\right )}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle -12 \int \frac {x}{4 x^8-27 x^6+36 x^5+69 x^4-216 x^3+216 x^2-96 x+16}dx+45 \int \frac {x^2}{4 x^8-27 x^6+36 x^5+69 x^4-216 x^3+216 x^2-96 x+16}dx-54 \int \frac {x^3}{4 x^8-27 x^6+36 x^5+69 x^4-216 x^3+216 x^2-96 x+16}dx+\frac {81}{4} \int \frac {x^4}{4 x^8-27 x^6+36 x^5+69 x^4-216 x^3+216 x^2-96 x+16}dx+8 \int \frac {x^5}{4 x^8-27 x^6+36 x^5+69 x^4-216 x^3+216 x^2-96 x+16}dx-6 \int \frac {x^6}{4 x^8-27 x^6+36 x^5+69 x^4-216 x^3+216 x^2-96 x+16}dx-\frac {1}{8} \arctan \left (\sqrt {7}-\frac {4 x}{3}\right )+\frac {1}{8} \arctan \left (\frac {4 x}{3}+\sqrt {7}\right )+\frac {1}{16} \sqrt {7} \log \left (2 x^2-3 \sqrt {7} x+9\right )-\frac {1}{16} \sqrt {7} \log \left (2 x^2+3 \sqrt {7} x+9\right )\) |
Input:
Int[(-324 + 972*x - 633*x^2 - 252*x^3 + 324*x^4 + 33*x^5 + 108*x^6 - 216*x ^7 + 32*x^9)/(1296 - 7776*x + 17064*x^2 - 14904*x^3 - 179*x^4 + 8364*x^5 - 3186*x^6 - 1836*x^7 + 1329*x^8 + 144*x^9 - 216*x^10 + 16*x^12),x]
Output:
$Aborted
Result contains higher order function than in optimal. Order 9 vs. order 3.
Time = 0.18 (sec) , antiderivative size = 51, normalized size of antiderivative = 0.18
| method | result | size |
| risch | \(\frac {\left (\munderset {\textit {\_R} =\operatorname {RootOf}\left (4 \textit {\_Z}^{4}-3 \textit {\_Z}^{2}+1\right )}{\sum }\textit {\_R} \ln \left (4 x^{3}+\left (16 \textit {\_R}^{3}+36 \textit {\_R}^{2}-12 \textit {\_R} -27\right ) x -24 \textit {\_R}^{2}+18\right )\right )}{4}\) | \(51\) |
| default | \(\frac {\sqrt {7}\, \ln \left (2 x^{2}-3 \sqrt {7}\, x +9\right )}{16}+\frac {\arctan \left (-\sqrt {7}+\frac {4 x}{3}\right )}{8}-\frac {\sqrt {7}\, \ln \left (2 x^{2}+3 \sqrt {7}\, x +9\right )}{16}+\frac {\arctan \left (\sqrt {7}+\frac {4 x}{3}\right )}{8}-\frac {\left (\munderset {\textit {\_R} =\operatorname {RootOf}\left (4 \textit {\_Z}^{4}-3 \textit {\_Z}^{2}+1\right )}{\sum }\textit {\_R} \ln \left (2 x^{2}+\left (12 \textit {\_R}^{3}-9 \textit {\_R} \right ) x -8 \textit {\_R}^{3}+6 \textit {\_R} \right )\right )}{4}\) | \(108\) |
Input:
int((32*x^9-216*x^7+108*x^6+33*x^5+324*x^4-252*x^3-633*x^2+972*x-324)/(16* x^12-216*x^10+144*x^9+1329*x^8-1836*x^7-3186*x^6+8364*x^5-179*x^4-14904*x^ 3+17064*x^2-7776*x+1296),x,method=_RETURNVERBOSE)
Output:
1/4*sum(_R*ln(4*x^3+(16*_R^3+36*_R^2-12*_R-27)*x-24*_R^2+18),_R=RootOf(4*_ Z^4-3*_Z^2+1))
Time = 0.10 (sec) , antiderivative size = 273, normalized size of antiderivative = 0.94 \[ \int \frac {-324+972 x-633 x^2-252 x^3+324 x^4+33 x^5+108 x^6-216 x^7+32 x^9}{1296-7776 x+17064 x^2-14904 x^3-179 x^4+8364 x^5-3186 x^6-1836 x^7+1329 x^8+144 x^9-216 x^{10}+16 x^{12}} \, dx=-\frac {1}{16} \, \sqrt {7} \log \left (4 \, x^{6} - 27 \, x^{4} + 18 \, x^{3} + 89 \, x^{2} + 2 \, \sqrt {7} {\left (2 \, x^{4} - 9 \, x^{2} + 6 \, x\right )} - 108 \, x + 36\right ) + \frac {1}{16} \, \sqrt {7} \log \left (4 \, x^{6} - 27 \, x^{4} + 18 \, x^{3} + 89 \, x^{2} - 2 \, \sqrt {7} {\left (2 \, x^{4} - 9 \, x^{2} + 6 \, x\right )} - 108 \, x + 36\right ) + \frac {1}{8} \, \arctan \left (\frac {734210}{958431} \, x^{5} + \frac {152964}{319477} \, x^{4} - \frac {3793665}{638954} \, x^{3} - \frac {45872}{319477} \, x^{2} + \frac {1}{958431} \, \sqrt {7} {\left (146916 \, x^{5} + 68808 \, x^{4} - 1698677 \, x^{3} - 131112 \, x^{2} + 6488874 \, x - 3023445\right )} + \frac {41819189}{1916862} \, x - \frac {3597777}{319477}\right ) - \frac {1}{8} \, \arctan \left (-\frac {734210}{958431} \, x^{5} - \frac {152964}{319477} \, x^{4} + \frac {3793665}{638954} \, x^{3} + \frac {45872}{319477} \, x^{2} + \frac {1}{958431} \, \sqrt {7} {\left (146916 \, x^{5} + 68808 \, x^{4} - 1698677 \, x^{3} - 131112 \, x^{2} + 6488874 \, x - 3023445\right )} - \frac {41819189}{1916862} \, x + \frac {3597777}{319477}\right ) - \frac {1}{8} \, \arctan \left (\frac {32}{551} \, x^{2} + \frac {1}{167284151} \, \sqrt {7} {\left (21859272 \, x^{2} + 15419184 \, x - 57758867\right )} + \frac {24192}{303601} \, x + \frac {57564432}{167284151}\right ) + \frac {1}{8} \, \arctan \left (-\frac {32}{551} \, x^{2} + \frac {1}{167284151} \, \sqrt {7} {\left (21859272 \, x^{2} + 15419184 \, x - 57758867\right )} - \frac {24192}{303601} \, x - \frac {57564432}{167284151}\right ) \] Input:
integrate((32*x^9-216*x^7+108*x^6+33*x^5+324*x^4-252*x^3-633*x^2+972*x-324 )/(16*x^12-216*x^10+144*x^9+1329*x^8-1836*x^7-3186*x^6+8364*x^5-179*x^4-14 904*x^3+17064*x^2-7776*x+1296),x, algorithm="fricas")
Output:
-1/16*sqrt(7)*log(4*x^6 - 27*x^4 + 18*x^3 + 89*x^2 + 2*sqrt(7)*(2*x^4 - 9* x^2 + 6*x) - 108*x + 36) + 1/16*sqrt(7)*log(4*x^6 - 27*x^4 + 18*x^3 + 89*x ^2 - 2*sqrt(7)*(2*x^4 - 9*x^2 + 6*x) - 108*x + 36) + 1/8*arctan(734210/958 431*x^5 + 152964/319477*x^4 - 3793665/638954*x^3 - 45872/319477*x^2 + 1/95 8431*sqrt(7)*(146916*x^5 + 68808*x^4 - 1698677*x^3 - 131112*x^2 + 6488874* x - 3023445) + 41819189/1916862*x - 3597777/319477) - 1/8*arctan(-734210/9 58431*x^5 - 152964/319477*x^4 + 3793665/638954*x^3 + 45872/319477*x^2 + 1/ 958431*sqrt(7)*(146916*x^5 + 68808*x^4 - 1698677*x^3 - 131112*x^2 + 648887 4*x - 3023445) - 41819189/1916862*x + 3597777/319477) - 1/8*arctan(32/551* x^2 + 1/167284151*sqrt(7)*(21859272*x^2 + 15419184*x - 57758867) + 24192/3 03601*x + 57564432/167284151) + 1/8*arctan(-32/551*x^2 + 1/167284151*sqrt( 7)*(21859272*x^2 + 15419184*x - 57758867) - 24192/303601*x - 57564432/1672 84151)
Leaf count of result is larger than twice the leaf count of optimal. 634 vs. \(2 (260) = 520\).
Time = 0.81 (sec) , antiderivative size = 634, normalized size of antiderivative = 2.18 \[ \int \frac {-324+972 x-633 x^2-252 x^3+324 x^4+33 x^5+108 x^6-216 x^7+32 x^9}{1296-7776 x+17064 x^2-14904 x^3-179 x^4+8364 x^5-3186 x^6-1836 x^7+1329 x^8+144 x^9-216 x^{10}+16 x^{12}} \, dx =\text {Too large to display} \] Input:
integrate((32*x**9-216*x**7+108*x**6+33*x**5+324*x**4-252*x**3-633*x**2+97 2*x-324)/(16*x**12-216*x**10+144*x**9+1329*x**8-1836*x**7-3186*x**6+8364*x **5-179*x**4-14904*x**3+17064*x**2-7776*x+1296),x)
Output:
sqrt(7)*log(x**6 + x**4*(-27/4 - sqrt(7)) + 9*x**3/2 + x**2*(9*sqrt(7)/2 + 89/4) + x*(-27 - 3*sqrt(7)) + 9)/16 - sqrt(7)*log(x**6 + x**4*(-27/4 + sq rt(7)) + 9*x**3/2 + x**2*(89/4 - 9*sqrt(7)/2) + x*(-27 + 3*sqrt(7)) + 9)/1 6 + atan(x**2*(44280*sqrt(7)/(-376177 + 83952*sqrt(7)) - 54944/(-376177 + 83952*sqrt(7))) + x*(9003712080*sqrt(7)/(-123787337137 + 30197125134*sqrt( 7)) - 9619833888/(-123787337137 + 30197125134*sqrt(7))) + 133745022/(-1875 77335 + 28630458*sqrt(7)) - 74617651*sqrt(7)/(-187577335 + 28630458*sqrt(7 )))/8 + atan(x**2*(54944/(83952*sqrt(7) + 376177) + 44280*sqrt(7)/(83952*s qrt(7) + 376177)) + x*(9619833888/(30197125134*sqrt(7) + 123787337137) + 9 003712080*sqrt(7)/(30197125134*sqrt(7) + 123787337137)) - 74617651*sqrt(7) /(28630458*sqrt(7) + 187577335) - 133745022/(28630458*sqrt(7) + 187577335) )/8 + atan(x**5*(13736/(-3210 + 15093*sqrt(7)) + 11070*sqrt(7)/(-3210 + 15 093*sqrt(7))) + x**4*(27472*sqrt(7)/(10494*sqrt(7) + 312673) + 154980/(104 94*sqrt(7) + 312673)) + x**3*(-79688899*sqrt(7)/(-15153168 + 17945118*sqrt (7)) - 132666462/(-15153168 + 17945118*sqrt(7))) + x**2*(-1500618680/(3500 7088 + 1561829283*sqrt(7)) - 229043664*sqrt(7)/(35007088 + 1561829283*sqrt (7))) + x*(183771619031726/(-3419774020020 + 5451936535422*sqrt(7)) + 9578 9159022429*sqrt(7)/(-3419774020020 + 5451936535422*sqrt(7))) - 25714393*sq rt(7)/(-2525528 + 2990853*sqrt(7)) - 37603017/(-2525528 + 2990853*sqrt(7)) )/8 + atan(x**5*(-13736/(3210 + 15093*sqrt(7)) + 11070*sqrt(7)/(3210 + ...
\[ \int \frac {-324+972 x-633 x^2-252 x^3+324 x^4+33 x^5+108 x^6-216 x^7+32 x^9}{1296-7776 x+17064 x^2-14904 x^3-179 x^4+8364 x^5-3186 x^6-1836 x^7+1329 x^8+144 x^9-216 x^{10}+16 x^{12}} \, dx=\int { \frac {32 \, x^{9} - 216 \, x^{7} + 108 \, x^{6} + 33 \, x^{5} + 324 \, x^{4} - 252 \, x^{3} - 633 \, x^{2} + 972 \, x - 324}{16 \, x^{12} - 216 \, x^{10} + 144 \, x^{9} + 1329 \, x^{8} - 1836 \, x^{7} - 3186 \, x^{6} + 8364 \, x^{5} - 179 \, x^{4} - 14904 \, x^{3} + 17064 \, x^{2} - 7776 \, x + 1296} \,d x } \] Input:
integrate((32*x^9-216*x^7+108*x^6+33*x^5+324*x^4-252*x^3-633*x^2+972*x-324 )/(16*x^12-216*x^10+144*x^9+1329*x^8-1836*x^7-3186*x^6+8364*x^5-179*x^4-14 904*x^3+17064*x^2-7776*x+1296),x, algorithm="maxima")
Output:
integrate((32*x^9 - 216*x^7 + 108*x^6 + 33*x^5 + 324*x^4 - 252*x^3 - 633*x ^2 + 972*x - 324)/(16*x^12 - 216*x^10 + 144*x^9 + 1329*x^8 - 1836*x^7 - 31 86*x^6 + 8364*x^5 - 179*x^4 - 14904*x^3 + 17064*x^2 - 7776*x + 1296), x)
Time = 0.17 (sec) , antiderivative size = 235, normalized size of antiderivative = 0.81 \[ \int \frac {-324+972 x-633 x^2-252 x^3+324 x^4+33 x^5+108 x^6-216 x^7+32 x^9}{1296-7776 x+17064 x^2-14904 x^3-179 x^4+8364 x^5-3186 x^6-1836 x^7+1329 x^8+144 x^9-216 x^{10}+16 x^{12}} \, dx=\frac {1}{16} \, \sqrt {7} \log \left ({\left (4 \, x^{2} + 3 \, \sqrt {7} x - 2 \, \sqrt {7}\right )}^{2} + {\left (3 \, x - 2\right )}^{2}\right ) - \frac {1}{16} \, \sqrt {7} \log \left ({\left (4 \, x^{2} - 3 \, \sqrt {7} x + 2 \, \sqrt {7}\right )}^{2} + {\left (3 \, x - 2\right )}^{2}\right ) - \frac {1}{16} \, \sqrt {7} \log \left (x^{2} + \frac {3}{2} \, \sqrt {14} \left (\frac {1}{4}\right )^{\frac {1}{4}} x + \frac {9}{2}\right ) + \frac {1}{16} \, \sqrt {7} \log \left (x^{2} - \frac {3}{2} \, \sqrt {14} \left (\frac {1}{4}\right )^{\frac {1}{4}} x + \frac {9}{2}\right ) + \frac {1}{8} \, \arctan \left (3 \, x^{3} + \frac {1}{2} \, x^{2} {\left (9 \, \sqrt {7} + 4\right )} + \frac {27}{2} \, x - \sqrt {7} - 9\right ) + \frac {1}{8} \, \arctan \left (3 \, x^{3} - \frac {1}{2} \, x^{2} {\left (9 \, \sqrt {7} - 4\right )} + \frac {27}{2} \, x + \sqrt {7} - 9\right ) + \frac {1}{8} \, \arctan \left (\frac {2}{3} \, \sqrt {2} \left (\frac {1}{4}\right )^{\frac {3}{4}} {\left (4 \, x + 3 \, \sqrt {14} \left (\frac {1}{4}\right )^{\frac {1}{4}}\right )}\right ) + \frac {1}{8} \, \arctan \left (\frac {2}{3} \, \sqrt {2} \left (\frac {1}{4}\right )^{\frac {3}{4}} {\left (4 \, x - 3 \, \sqrt {14} \left (\frac {1}{4}\right )^{\frac {1}{4}}\right )}\right ) - \frac {1}{8} \, \arctan \left (\frac {4}{3} \, x + \sqrt {7} + \frac {8}{9}\right ) - \frac {1}{8} \, \arctan \left (\frac {4}{3} \, x - \sqrt {7} + \frac {8}{9}\right ) \] Input:
integrate((32*x^9-216*x^7+108*x^6+33*x^5+324*x^4-252*x^3-633*x^2+972*x-324 )/(16*x^12-216*x^10+144*x^9+1329*x^8-1836*x^7-3186*x^6+8364*x^5-179*x^4-14 904*x^3+17064*x^2-7776*x+1296),x, algorithm="giac")
Output:
1/16*sqrt(7)*log((4*x^2 + 3*sqrt(7)*x - 2*sqrt(7))^2 + (3*x - 2)^2) - 1/16 *sqrt(7)*log((4*x^2 - 3*sqrt(7)*x + 2*sqrt(7))^2 + (3*x - 2)^2) - 1/16*sqr t(7)*log(x^2 + 3/2*sqrt(14)*(1/4)^(1/4)*x + 9/2) + 1/16*sqrt(7)*log(x^2 - 3/2*sqrt(14)*(1/4)^(1/4)*x + 9/2) + 1/8*arctan(3*x^3 + 1/2*x^2*(9*sqrt(7) + 4) + 27/2*x - sqrt(7) - 9) + 1/8*arctan(3*x^3 - 1/2*x^2*(9*sqrt(7) - 4) + 27/2*x + sqrt(7) - 9) + 1/8*arctan(2/3*sqrt(2)*(1/4)^(3/4)*(4*x + 3*sqrt (14)*(1/4)^(1/4))) + 1/8*arctan(2/3*sqrt(2)*(1/4)^(3/4)*(4*x - 3*sqrt(14)* (1/4)^(1/4))) - 1/8*arctan(4/3*x + sqrt(7) + 8/9) - 1/8*arctan(4/3*x - sqr t(7) + 8/9)
Time = 11.65 (sec) , antiderivative size = 969, normalized size of antiderivative = 3.33 \[ \int \frac {-324+972 x-633 x^2-252 x^3+324 x^4+33 x^5+108 x^6-216 x^7+32 x^9}{1296-7776 x+17064 x^2-14904 x^3-179 x^4+8364 x^5-3186 x^6-1836 x^7+1329 x^8+144 x^9-216 x^{10}+16 x^{12}} \, dx=\text {Too large to display} \] Input:
int(-(972*x - 633*x^2 - 252*x^3 + 324*x^4 + 33*x^5 + 108*x^6 - 216*x^7 + 3 2*x^9 - 324)/(7776*x - 17064*x^2 + 14904*x^3 + 179*x^4 - 8364*x^5 + 3186*x ^6 + 1836*x^7 - 1329*x^8 - 144*x^9 + 216*x^10 - 16*x^12 - 1296),x)
Output:
atan((7^(1/2)*213884473604285216343651705i)/(274877906944*((7^(1/2)*820603 575457046818277723757i)/1099511627776 - (7^(1/2)*x*19807378627488637830822 20367i)/2199023255552 - (10146925135157220838351778085*x)/2199023255552 + (7^(1/2)*x^3*820547225863110549450077193i)/2199023255552 + (27336547637054 0132942968227*x^3)/2199023255552 + 2461472628807522841867291887/1099511627 776)) - (2080518451758147892639296267*x)/(1099511627776*((7^(1/2)*82060357 5457046818277723757i)/1099511627776 - (7^(1/2)*x*1980737862748863783082220 367i)/2199023255552 - (10146925135157220838351778085*x)/2199023255552 + (7 ^(1/2)*x^3*820547225863110549450077193i)/2199023255552 + (2733654763705401 32942968227*x^3)/2199023255552 + 2461472628807522841867291887/109951162777 6)) + 574689121320992720156864883/(274877906944*((7^(1/2)*8206035754570468 18277723757i)/1099511627776 - (7^(1/2)*x*1980737862748863783082220367i)/21 99023255552 - (10146925135157220838351778085*x)/2199023255552 + (7^(1/2)*x ^3*820547225863110549450077193i)/2199023255552 + (273365476370540132942968 227*x^3)/2199023255552 + 2461472628807522841867291887/1099511627776)) + (3 7812674788830274344172119*x^3)/(549755813888*((7^(1/2)*8206035754570468182 77723757i)/1099511627776 - (7^(1/2)*x*1980737862748863783082220367i)/21990 23255552 - (10146925135157220838351778085*x)/2199023255552 + (7^(1/2)*x^3* 820547225863110549450077193i)/2199023255552 + (273365476370540132942968227 *x^3)/2199023255552 + 2461472628807522841867291887/1099511627776)) - (7...
\[ \int \frac {-324+972 x-633 x^2-252 x^3+324 x^4+33 x^5+108 x^6-216 x^7+32 x^9}{1296-7776 x+17064 x^2-14904 x^3-179 x^4+8364 x^5-3186 x^6-1836 x^7+1329 x^8+144 x^9-216 x^{10}+16 x^{12}} \, dx=32 \left (\int \frac {x^{9}}{16 x^{12}-216 x^{10}+144 x^{9}+1329 x^{8}-1836 x^{7}-3186 x^{6}+8364 x^{5}-179 x^{4}-14904 x^{3}+17064 x^{2}-7776 x +1296}d x \right )-216 \left (\int \frac {x^{7}}{16 x^{12}-216 x^{10}+144 x^{9}+1329 x^{8}-1836 x^{7}-3186 x^{6}+8364 x^{5}-179 x^{4}-14904 x^{3}+17064 x^{2}-7776 x +1296}d x \right )+108 \left (\int \frac {x^{6}}{16 x^{12}-216 x^{10}+144 x^{9}+1329 x^{8}-1836 x^{7}-3186 x^{6}+8364 x^{5}-179 x^{4}-14904 x^{3}+17064 x^{2}-7776 x +1296}d x \right )+33 \left (\int \frac {x^{5}}{16 x^{12}-216 x^{10}+144 x^{9}+1329 x^{8}-1836 x^{7}-3186 x^{6}+8364 x^{5}-179 x^{4}-14904 x^{3}+17064 x^{2}-7776 x +1296}d x \right )+324 \left (\int \frac {x^{4}}{16 x^{12}-216 x^{10}+144 x^{9}+1329 x^{8}-1836 x^{7}-3186 x^{6}+8364 x^{5}-179 x^{4}-14904 x^{3}+17064 x^{2}-7776 x +1296}d x \right )-252 \left (\int \frac {x^{3}}{16 x^{12}-216 x^{10}+144 x^{9}+1329 x^{8}-1836 x^{7}-3186 x^{6}+8364 x^{5}-179 x^{4}-14904 x^{3}+17064 x^{2}-7776 x +1296}d x \right )-633 \left (\int \frac {x^{2}}{16 x^{12}-216 x^{10}+144 x^{9}+1329 x^{8}-1836 x^{7}-3186 x^{6}+8364 x^{5}-179 x^{4}-14904 x^{3}+17064 x^{2}-7776 x +1296}d x \right )+972 \left (\int \frac {x}{16 x^{12}-216 x^{10}+144 x^{9}+1329 x^{8}-1836 x^{7}-3186 x^{6}+8364 x^{5}-179 x^{4}-14904 x^{3}+17064 x^{2}-7776 x +1296}d x \right )-324 \left (\int \frac {1}{16 x^{12}-216 x^{10}+144 x^{9}+1329 x^{8}-1836 x^{7}-3186 x^{6}+8364 x^{5}-179 x^{4}-14904 x^{3}+17064 x^{2}-7776 x +1296}d x \right ) \] Input:
int((32*x^9-216*x^7+108*x^6+33*x^5+324*x^4-252*x^3-633*x^2+972*x-324)/(16* x^12-216*x^10+144*x^9+1329*x^8-1836*x^7-3186*x^6+8364*x^5-179*x^4-14904*x^ 3+17064*x^2-7776*x+1296),x)
Output:
32*int(x**9/(16*x**12 - 216*x**10 + 144*x**9 + 1329*x**8 - 1836*x**7 - 318 6*x**6 + 8364*x**5 - 179*x**4 - 14904*x**3 + 17064*x**2 - 7776*x + 1296),x ) - 216*int(x**7/(16*x**12 - 216*x**10 + 144*x**9 + 1329*x**8 - 1836*x**7 - 3186*x**6 + 8364*x**5 - 179*x**4 - 14904*x**3 + 17064*x**2 - 7776*x + 12 96),x) + 108*int(x**6/(16*x**12 - 216*x**10 + 144*x**9 + 1329*x**8 - 1836* x**7 - 3186*x**6 + 8364*x**5 - 179*x**4 - 14904*x**3 + 17064*x**2 - 7776*x + 1296),x) + 33*int(x**5/(16*x**12 - 216*x**10 + 144*x**9 + 1329*x**8 - 1 836*x**7 - 3186*x**6 + 8364*x**5 - 179*x**4 - 14904*x**3 + 17064*x**2 - 77 76*x + 1296),x) + 324*int(x**4/(16*x**12 - 216*x**10 + 144*x**9 + 1329*x** 8 - 1836*x**7 - 3186*x**6 + 8364*x**5 - 179*x**4 - 14904*x**3 + 17064*x**2 - 7776*x + 1296),x) - 252*int(x**3/(16*x**12 - 216*x**10 + 144*x**9 + 132 9*x**8 - 1836*x**7 - 3186*x**6 + 8364*x**5 - 179*x**4 - 14904*x**3 + 17064 *x**2 - 7776*x + 1296),x) - 633*int(x**2/(16*x**12 - 216*x**10 + 144*x**9 + 1329*x**8 - 1836*x**7 - 3186*x**6 + 8364*x**5 - 179*x**4 - 14904*x**3 + 17064*x**2 - 7776*x + 1296),x) + 972*int(x/(16*x**12 - 216*x**10 + 144*x** 9 + 1329*x**8 - 1836*x**7 - 3186*x**6 + 8364*x**5 - 179*x**4 - 14904*x**3 + 17064*x**2 - 7776*x + 1296),x) - 324*int(1/(16*x**12 - 216*x**10 + 144*x **9 + 1329*x**8 - 1836*x**7 - 3186*x**6 + 8364*x**5 - 179*x**4 - 14904*x** 3 + 17064*x**2 - 7776*x + 1296),x)