Integrand size = 105, antiderivative size = 75 \[ \int \frac {8 \sqrt {11}-2 \sqrt {165}-14 \sqrt {15} x+\left (-70 \sqrt {11}-14 \sqrt {165}\right ) x^2+770 x^3+245 \sqrt {11} x^4}{8 \left (-30+8 \sqrt {15}\right )+8 \left (-650+40 \sqrt {15}\right ) x^2+8 \left (3850+1015 \sqrt {15}\right ) x^4-107800 x^6} \, dx=\frac {\text {arctanh}\left (\sqrt [4]{\frac {5}{3}} \sqrt {11} x\right )}{8 \sqrt [4]{3} 5^{3/4}}-\frac {\text {arctanh}\left (\sqrt {\frac {1}{2}+\frac {2}{\sqrt {15}}}-\frac {7}{2} \sqrt [4]{\frac {5}{3}} x^2\right )}{16 \sqrt [4]{3} 5^{3/4}} \] Output:
1/120*arctanh(1/3*5^(1/4)*3^(3/4)*11^(1/2)*x)*3^(3/4)*5^(1/4)+1/240*arctan h(-1/30*(450+120*15^(1/2))^(1/2)+7/6*5^(1/4)*3^(3/4)*x^2)*3^(3/4)*5^(1/4)
Result contains higher order function than in optimal. Order 9 vs. order 3 in optimal.
Time = 0.23 (sec) , antiderivative size = 208, normalized size of antiderivative = 2.77 \[ \int \frac {8 \sqrt {11}-2 \sqrt {165}-14 \sqrt {15} x+\left (-70 \sqrt {11}-14 \sqrt {165}\right ) x^2+770 x^3+245 \sqrt {11} x^4}{8 \left (-30+8 \sqrt {15}\right )+8 \left (-650+40 \sqrt {15}\right ) x^2+8 \left (3850+1015 \sqrt {15}\right ) x^4-107800 x^6} \, dx=-\frac {1}{80} \text {RootSum}\left [-30+8 \sqrt {15}-650 \text {$\#$1}^2+40 \sqrt {15} \text {$\#$1}^2+3850 \text {$\#$1}^4+1015 \sqrt {15} \text {$\#$1}^4-13475 \text {$\#$1}^6\&,\frac {8 \sqrt {11} \log (x-\text {$\#$1})-2 \sqrt {165} \log (x-\text {$\#$1})-14 \sqrt {15} \log (x-\text {$\#$1}) \text {$\#$1}-70 \sqrt {11} \log (x-\text {$\#$1}) \text {$\#$1}^2-14 \sqrt {165} \log (x-\text {$\#$1}) \text {$\#$1}^2+770 \log (x-\text {$\#$1}) \text {$\#$1}^3+245 \sqrt {11} \log (x-\text {$\#$1}) \text {$\#$1}^4}{130 \text {$\#$1}-8 \sqrt {15} \text {$\#$1}-1540 \text {$\#$1}^3-406 \sqrt {15} \text {$\#$1}^3+8085 \text {$\#$1}^5}\&\right ] \] Input:
Integrate[(8*Sqrt[11] - 2*Sqrt[165] - 14*Sqrt[15]*x + (-70*Sqrt[11] - 14*S qrt[165])*x^2 + 770*x^3 + 245*Sqrt[11]*x^4)/(8*(-30 + 8*Sqrt[15]) + 8*(-65 0 + 40*Sqrt[15])*x^2 + 8*(3850 + 1015*Sqrt[15])*x^4 - 107800*x^6),x]
Output:
-1/80*RootSum[-30 + 8*Sqrt[15] - 650*#1^2 + 40*Sqrt[15]*#1^2 + 3850*#1^4 + 1015*Sqrt[15]*#1^4 - 13475*#1^6 & , (8*Sqrt[11]*Log[x - #1] - 2*Sqrt[165] *Log[x - #1] - 14*Sqrt[15]*Log[x - #1]*#1 - 70*Sqrt[11]*Log[x - #1]*#1^2 - 14*Sqrt[165]*Log[x - #1]*#1^2 + 770*Log[x - #1]*#1^3 + 245*Sqrt[11]*Log[x - #1]*#1^4)/(130*#1 - 8*Sqrt[15]*#1 - 1540*#1^3 - 406*Sqrt[15]*#1^3 + 808 5*#1^5) & ]
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.
| \(\displaystyle \int \frac {245 \sqrt {11} x^4+770 x^3+\left (-70 \sqrt {11}-14 \sqrt {165}\right ) x^2-14 \sqrt {15} x-2 \sqrt {165}+8 \sqrt {11}}{-107800 x^6+8 \left (3850+1015 \sqrt {15}\right ) x^4+8 \left (40 \sqrt {15}-650\right ) x^2+8 \left (8 \sqrt {15}-30\right )} \, dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \frac {-245 \sqrt {11} x^4-770 x^3+14 \sqrt {55} \left (\sqrt {3}+\sqrt {5}\right ) x^2+14 \sqrt {15} x-2 \sqrt {11} \left (4-\sqrt {15}\right )}{8 \left (13475 x^6-3850 \left (1+\frac {29 \sqrt {\frac {3}{5}}}{22}\right ) x^4+650 \left (1-\frac {4 \sqrt {\frac {3}{5}}}{13}\right ) x^2+30 \left (1-\frac {4}{\sqrt {15}}\right )\right )}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {1}{8} \int -\frac {245 \sqrt {11} x^4+770 x^3-14 \sqrt {55} \left (\sqrt {3}+\sqrt {5}\right ) x^2-14 \sqrt {15} x+2 \sqrt {11} \left (4-\sqrt {15}\right )}{13475 x^6-35 \left (110+29 \sqrt {15}\right ) x^4+10 \left (65-4 \sqrt {15}\right ) x^2+2 \left (15-4 \sqrt {15}\right )}dx\) |
| \(\Big \downarrow \) 25 |
| \(\displaystyle -\frac {1}{8} \int \frac {245 \sqrt {11} x^4+770 x^3-14 \sqrt {55} \left (\sqrt {3}+\sqrt {5}\right ) x^2-14 \sqrt {15} x+2 \sqrt {11} \left (4-\sqrt {15}\right )}{13475 x^6-35 \left (110+29 \sqrt {15}\right ) x^4+10 \left (65-4 \sqrt {15}\right ) x^2+2 \left (15-4 \sqrt {15}\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -\frac {1}{8} \int \left (\frac {245 \sqrt {11} x^4}{13475 x^6-3850 \left (1+\frac {29 \sqrt {\frac {3}{5}}}{22}\right ) x^4+650 \left (1-\frac {4 \sqrt {\frac {3}{5}}}{13}\right ) x^2+30 \left (1-\frac {4}{\sqrt {15}}\right )}+\frac {770 x^3}{13475 x^6-3850 \left (1+\frac {29 \sqrt {\frac {3}{5}}}{22}\right ) x^4+650 \left (1-\frac {4 \sqrt {\frac {3}{5}}}{13}\right ) x^2+30 \left (1-\frac {4}{\sqrt {15}}\right )}+\frac {14 \sqrt {55} \left (-\sqrt {3}-\sqrt {5}\right ) x^2}{13475 x^6-3850 \left (1+\frac {29 \sqrt {\frac {3}{5}}}{22}\right ) x^4+650 \left (1-\frac {4 \sqrt {\frac {3}{5}}}{13}\right ) x^2+30 \left (1-\frac {4}{\sqrt {15}}\right )}+\frac {14 \sqrt {15} x}{-13475 x^6+3850 \left (1+\frac {29 \sqrt {\frac {3}{5}}}{22}\right ) x^4-650 \left (1-\frac {4 \sqrt {\frac {3}{5}}}{13}\right ) x^2-30 \left (1-\frac {4}{\sqrt {15}}\right )}+\frac {2 \sqrt {11} \left (4-\sqrt {15}\right )}{13475 x^6-3850 \left (1+\frac {29 \sqrt {\frac {3}{5}}}{22}\right ) x^4+650 \left (1-\frac {4 \sqrt {\frac {3}{5}}}{13}\right ) x^2+30 \left (1-\frac {4}{\sqrt {15}}\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -\frac {1}{8} \int \frac {245 \sqrt {11} x^4+770 x^3-14 \sqrt {55} \left (\sqrt {3}+\sqrt {5}\right ) x^2-14 \sqrt {15} x+2 \sqrt {11} \left (4-\sqrt {15}\right )}{13475 x^6-35 \left (110+29 \sqrt {15}\right ) x^4-10 \left (-65+4 \sqrt {15}\right ) x^2+30 \left (1-\frac {4}{\sqrt {15}}\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -\frac {1}{8} \int \left (\frac {245 \sqrt {11} x^4}{13475 x^6-3850 \left (1+\frac {29 \sqrt {\frac {3}{5}}}{22}\right ) x^4+650 \left (1-\frac {4 \sqrt {\frac {3}{5}}}{13}\right ) x^2+30 \left (1-\frac {4}{\sqrt {15}}\right )}+\frac {770 x^3}{13475 x^6-3850 \left (1+\frac {29 \sqrt {\frac {3}{5}}}{22}\right ) x^4+650 \left (1-\frac {4 \sqrt {\frac {3}{5}}}{13}\right ) x^2+30 \left (1-\frac {4}{\sqrt {15}}\right )}+\frac {14 \sqrt {55} \left (-\sqrt {3}-\sqrt {5}\right ) x^2}{13475 x^6-3850 \left (1+\frac {29 \sqrt {\frac {3}{5}}}{22}\right ) x^4+650 \left (1-\frac {4 \sqrt {\frac {3}{5}}}{13}\right ) x^2+30 \left (1-\frac {4}{\sqrt {15}}\right )}+\frac {14 \sqrt {15} x}{-13475 x^6+3850 \left (1+\frac {29 \sqrt {\frac {3}{5}}}{22}\right ) x^4-650 \left (1-\frac {4 \sqrt {\frac {3}{5}}}{13}\right ) x^2-30 \left (1-\frac {4}{\sqrt {15}}\right )}+\frac {2 \sqrt {11} \left (4-\sqrt {15}\right )}{13475 x^6-3850 \left (1+\frac {29 \sqrt {\frac {3}{5}}}{22}\right ) x^4+650 \left (1-\frac {4 \sqrt {\frac {3}{5}}}{13}\right ) x^2+30 \left (1-\frac {4}{\sqrt {15}}\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -\frac {1}{8} \int \frac {245 \sqrt {11} x^4+770 x^3-14 \sqrt {55} \left (\sqrt {3}+\sqrt {5}\right ) x^2-14 \sqrt {15} x+2 \sqrt {11} \left (4-\sqrt {15}\right )}{13475 x^6-35 \left (110+29 \sqrt {15}\right ) x^4-10 \left (-65+4 \sqrt {15}\right ) x^2+30 \left (1-\frac {4}{\sqrt {15}}\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -\frac {1}{8} \int \left (\frac {245 \sqrt {11} x^4}{13475 x^6-3850 \left (1+\frac {29 \sqrt {\frac {3}{5}}}{22}\right ) x^4+650 \left (1-\frac {4 \sqrt {\frac {3}{5}}}{13}\right ) x^2+30 \left (1-\frac {4}{\sqrt {15}}\right )}+\frac {770 x^3}{13475 x^6-3850 \left (1+\frac {29 \sqrt {\frac {3}{5}}}{22}\right ) x^4+650 \left (1-\frac {4 \sqrt {\frac {3}{5}}}{13}\right ) x^2+30 \left (1-\frac {4}{\sqrt {15}}\right )}+\frac {14 \sqrt {55} \left (-\sqrt {3}-\sqrt {5}\right ) x^2}{13475 x^6-3850 \left (1+\frac {29 \sqrt {\frac {3}{5}}}{22}\right ) x^4+650 \left (1-\frac {4 \sqrt {\frac {3}{5}}}{13}\right ) x^2+30 \left (1-\frac {4}{\sqrt {15}}\right )}+\frac {14 \sqrt {15} x}{-13475 x^6+3850 \left (1+\frac {29 \sqrt {\frac {3}{5}}}{22}\right ) x^4-650 \left (1-\frac {4 \sqrt {\frac {3}{5}}}{13}\right ) x^2-30 \left (1-\frac {4}{\sqrt {15}}\right )}+\frac {2 \sqrt {11} \left (4-\sqrt {15}\right )}{13475 x^6-3850 \left (1+\frac {29 \sqrt {\frac {3}{5}}}{22}\right ) x^4+650 \left (1-\frac {4 \sqrt {\frac {3}{5}}}{13}\right ) x^2+30 \left (1-\frac {4}{\sqrt {15}}\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -\frac {1}{8} \int \frac {245 \sqrt {11} x^4+770 x^3-14 \sqrt {55} \left (\sqrt {3}+\sqrt {5}\right ) x^2-14 \sqrt {15} x+2 \sqrt {11} \left (4-\sqrt {15}\right )}{13475 x^6-35 \left (110+29 \sqrt {15}\right ) x^4-10 \left (-65+4 \sqrt {15}\right ) x^2+30 \left (1-\frac {4}{\sqrt {15}}\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -\frac {1}{8} \int \left (\frac {245 \sqrt {11} x^4}{13475 x^6-3850 \left (1+\frac {29 \sqrt {\frac {3}{5}}}{22}\right ) x^4+650 \left (1-\frac {4 \sqrt {\frac {3}{5}}}{13}\right ) x^2+30 \left (1-\frac {4}{\sqrt {15}}\right )}+\frac {770 x^3}{13475 x^6-3850 \left (1+\frac {29 \sqrt {\frac {3}{5}}}{22}\right ) x^4+650 \left (1-\frac {4 \sqrt {\frac {3}{5}}}{13}\right ) x^2+30 \left (1-\frac {4}{\sqrt {15}}\right )}+\frac {14 \sqrt {55} \left (-\sqrt {3}-\sqrt {5}\right ) x^2}{13475 x^6-3850 \left (1+\frac {29 \sqrt {\frac {3}{5}}}{22}\right ) x^4+650 \left (1-\frac {4 \sqrt {\frac {3}{5}}}{13}\right ) x^2+30 \left (1-\frac {4}{\sqrt {15}}\right )}+\frac {14 \sqrt {15} x}{-13475 x^6+3850 \left (1+\frac {29 \sqrt {\frac {3}{5}}}{22}\right ) x^4-650 \left (1-\frac {4 \sqrt {\frac {3}{5}}}{13}\right ) x^2-30 \left (1-\frac {4}{\sqrt {15}}\right )}+\frac {2 \sqrt {11} \left (4-\sqrt {15}\right )}{13475 x^6-3850 \left (1+\frac {29 \sqrt {\frac {3}{5}}}{22}\right ) x^4+650 \left (1-\frac {4 \sqrt {\frac {3}{5}}}{13}\right ) x^2+30 \left (1-\frac {4}{\sqrt {15}}\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -\frac {1}{8} \int \frac {245 \sqrt {11} x^4+770 x^3-14 \sqrt {55} \left (\sqrt {3}+\sqrt {5}\right ) x^2-14 \sqrt {15} x+2 \sqrt {11} \left (4-\sqrt {15}\right )}{13475 x^6-35 \left (110+29 \sqrt {15}\right ) x^4-10 \left (-65+4 \sqrt {15}\right ) x^2+30 \left (1-\frac {4}{\sqrt {15}}\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -\frac {1}{8} \int \left (\frac {245 \sqrt {11} x^4}{13475 x^6-3850 \left (1+\frac {29 \sqrt {\frac {3}{5}}}{22}\right ) x^4+650 \left (1-\frac {4 \sqrt {\frac {3}{5}}}{13}\right ) x^2+30 \left (1-\frac {4}{\sqrt {15}}\right )}+\frac {770 x^3}{13475 x^6-3850 \left (1+\frac {29 \sqrt {\frac {3}{5}}}{22}\right ) x^4+650 \left (1-\frac {4 \sqrt {\frac {3}{5}}}{13}\right ) x^2+30 \left (1-\frac {4}{\sqrt {15}}\right )}+\frac {14 \sqrt {55} \left (-\sqrt {3}-\sqrt {5}\right ) x^2}{13475 x^6-3850 \left (1+\frac {29 \sqrt {\frac {3}{5}}}{22}\right ) x^4+650 \left (1-\frac {4 \sqrt {\frac {3}{5}}}{13}\right ) x^2+30 \left (1-\frac {4}{\sqrt {15}}\right )}+\frac {14 \sqrt {15} x}{-13475 x^6+3850 \left (1+\frac {29 \sqrt {\frac {3}{5}}}{22}\right ) x^4-650 \left (1-\frac {4 \sqrt {\frac {3}{5}}}{13}\right ) x^2-30 \left (1-\frac {4}{\sqrt {15}}\right )}+\frac {2 \sqrt {11} \left (4-\sqrt {15}\right )}{13475 x^6-3850 \left (1+\frac {29 \sqrt {\frac {3}{5}}}{22}\right ) x^4+650 \left (1-\frac {4 \sqrt {\frac {3}{5}}}{13}\right ) x^2+30 \left (1-\frac {4}{\sqrt {15}}\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -\frac {1}{8} \int \frac {245 \sqrt {11} x^4+770 x^3-14 \sqrt {55} \left (\sqrt {3}+\sqrt {5}\right ) x^2-14 \sqrt {15} x+2 \sqrt {11} \left (4-\sqrt {15}\right )}{13475 x^6-35 \left (110+29 \sqrt {15}\right ) x^4-10 \left (-65+4 \sqrt {15}\right ) x^2+30 \left (1-\frac {4}{\sqrt {15}}\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -\frac {1}{8} \int \left (\frac {245 \sqrt {11} x^4}{13475 x^6-3850 \left (1+\frac {29 \sqrt {\frac {3}{5}}}{22}\right ) x^4+650 \left (1-\frac {4 \sqrt {\frac {3}{5}}}{13}\right ) x^2+30 \left (1-\frac {4}{\sqrt {15}}\right )}+\frac {770 x^3}{13475 x^6-3850 \left (1+\frac {29 \sqrt {\frac {3}{5}}}{22}\right ) x^4+650 \left (1-\frac {4 \sqrt {\frac {3}{5}}}{13}\right ) x^2+30 \left (1-\frac {4}{\sqrt {15}}\right )}+\frac {14 \sqrt {55} \left (-\sqrt {3}-\sqrt {5}\right ) x^2}{13475 x^6-3850 \left (1+\frac {29 \sqrt {\frac {3}{5}}}{22}\right ) x^4+650 \left (1-\frac {4 \sqrt {\frac {3}{5}}}{13}\right ) x^2+30 \left (1-\frac {4}{\sqrt {15}}\right )}+\frac {14 \sqrt {15} x}{-13475 x^6+3850 \left (1+\frac {29 \sqrt {\frac {3}{5}}}{22}\right ) x^4-650 \left (1-\frac {4 \sqrt {\frac {3}{5}}}{13}\right ) x^2-30 \left (1-\frac {4}{\sqrt {15}}\right )}+\frac {2 \sqrt {11} \left (4-\sqrt {15}\right )}{13475 x^6-3850 \left (1+\frac {29 \sqrt {\frac {3}{5}}}{22}\right ) x^4+650 \left (1-\frac {4 \sqrt {\frac {3}{5}}}{13}\right ) x^2+30 \left (1-\frac {4}{\sqrt {15}}\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -\frac {1}{8} \int \frac {245 \sqrt {11} x^4+770 x^3-14 \sqrt {55} \left (\sqrt {3}+\sqrt {5}\right ) x^2-14 \sqrt {15} x+2 \sqrt {11} \left (4-\sqrt {15}\right )}{13475 x^6-35 \left (110+29 \sqrt {15}\right ) x^4-10 \left (-65+4 \sqrt {15}\right ) x^2+30 \left (1-\frac {4}{\sqrt {15}}\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -\frac {1}{8} \int \left (\frac {245 \sqrt {11} x^4}{13475 x^6-3850 \left (1+\frac {29 \sqrt {\frac {3}{5}}}{22}\right ) x^4+650 \left (1-\frac {4 \sqrt {\frac {3}{5}}}{13}\right ) x^2+30 \left (1-\frac {4}{\sqrt {15}}\right )}+\frac {770 x^3}{13475 x^6-3850 \left (1+\frac {29 \sqrt {\frac {3}{5}}}{22}\right ) x^4+650 \left (1-\frac {4 \sqrt {\frac {3}{5}}}{13}\right ) x^2+30 \left (1-\frac {4}{\sqrt {15}}\right )}+\frac {14 \sqrt {55} \left (-\sqrt {3}-\sqrt {5}\right ) x^2}{13475 x^6-3850 \left (1+\frac {29 \sqrt {\frac {3}{5}}}{22}\right ) x^4+650 \left (1-\frac {4 \sqrt {\frac {3}{5}}}{13}\right ) x^2+30 \left (1-\frac {4}{\sqrt {15}}\right )}+\frac {14 \sqrt {15} x}{-13475 x^6+3850 \left (1+\frac {29 \sqrt {\frac {3}{5}}}{22}\right ) x^4-650 \left (1-\frac {4 \sqrt {\frac {3}{5}}}{13}\right ) x^2-30 \left (1-\frac {4}{\sqrt {15}}\right )}+\frac {2 \sqrt {11} \left (4-\sqrt {15}\right )}{13475 x^6-3850 \left (1+\frac {29 \sqrt {\frac {3}{5}}}{22}\right ) x^4+650 \left (1-\frac {4 \sqrt {\frac {3}{5}}}{13}\right ) x^2+30 \left (1-\frac {4}{\sqrt {15}}\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -\frac {1}{8} \int \frac {245 \sqrt {11} x^4+770 x^3-14 \sqrt {55} \left (\sqrt {3}+\sqrt {5}\right ) x^2-14 \sqrt {15} x+2 \sqrt {11} \left (4-\sqrt {15}\right )}{13475 x^6-35 \left (110+29 \sqrt {15}\right ) x^4-10 \left (-65+4 \sqrt {15}\right ) x^2+30 \left (1-\frac {4}{\sqrt {15}}\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -\frac {1}{8} \int \left (\frac {245 \sqrt {11} x^4}{13475 x^6-3850 \left (1+\frac {29 \sqrt {\frac {3}{5}}}{22}\right ) x^4+650 \left (1-\frac {4 \sqrt {\frac {3}{5}}}{13}\right ) x^2+30 \left (1-\frac {4}{\sqrt {15}}\right )}+\frac {770 x^3}{13475 x^6-3850 \left (1+\frac {29 \sqrt {\frac {3}{5}}}{22}\right ) x^4+650 \left (1-\frac {4 \sqrt {\frac {3}{5}}}{13}\right ) x^2+30 \left (1-\frac {4}{\sqrt {15}}\right )}+\frac {14 \sqrt {55} \left (-\sqrt {3}-\sqrt {5}\right ) x^2}{13475 x^6-3850 \left (1+\frac {29 \sqrt {\frac {3}{5}}}{22}\right ) x^4+650 \left (1-\frac {4 \sqrt {\frac {3}{5}}}{13}\right ) x^2+30 \left (1-\frac {4}{\sqrt {15}}\right )}+\frac {14 \sqrt {15} x}{-13475 x^6+3850 \left (1+\frac {29 \sqrt {\frac {3}{5}}}{22}\right ) x^4-650 \left (1-\frac {4 \sqrt {\frac {3}{5}}}{13}\right ) x^2-30 \left (1-\frac {4}{\sqrt {15}}\right )}+\frac {2 \sqrt {11} \left (4-\sqrt {15}\right )}{13475 x^6-3850 \left (1+\frac {29 \sqrt {\frac {3}{5}}}{22}\right ) x^4+650 \left (1-\frac {4 \sqrt {\frac {3}{5}}}{13}\right ) x^2+30 \left (1-\frac {4}{\sqrt {15}}\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -\frac {1}{8} \int \frac {245 \sqrt {11} x^4+770 x^3-14 \sqrt {55} \left (\sqrt {3}+\sqrt {5}\right ) x^2-14 \sqrt {15} x+2 \sqrt {11} \left (4-\sqrt {15}\right )}{13475 x^6-35 \left (110+29 \sqrt {15}\right ) x^4-10 \left (-65+4 \sqrt {15}\right ) x^2+30 \left (1-\frac {4}{\sqrt {15}}\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -\frac {1}{8} \int \left (\frac {245 \sqrt {11} x^4}{13475 x^6-3850 \left (1+\frac {29 \sqrt {\frac {3}{5}}}{22}\right ) x^4+650 \left (1-\frac {4 \sqrt {\frac {3}{5}}}{13}\right ) x^2+30 \left (1-\frac {4}{\sqrt {15}}\right )}+\frac {770 x^3}{13475 x^6-3850 \left (1+\frac {29 \sqrt {\frac {3}{5}}}{22}\right ) x^4+650 \left (1-\frac {4 \sqrt {\frac {3}{5}}}{13}\right ) x^2+30 \left (1-\frac {4}{\sqrt {15}}\right )}+\frac {14 \sqrt {55} \left (-\sqrt {3}-\sqrt {5}\right ) x^2}{13475 x^6-3850 \left (1+\frac {29 \sqrt {\frac {3}{5}}}{22}\right ) x^4+650 \left (1-\frac {4 \sqrt {\frac {3}{5}}}{13}\right ) x^2+30 \left (1-\frac {4}{\sqrt {15}}\right )}+\frac {14 \sqrt {15} x}{-13475 x^6+3850 \left (1+\frac {29 \sqrt {\frac {3}{5}}}{22}\right ) x^4-650 \left (1-\frac {4 \sqrt {\frac {3}{5}}}{13}\right ) x^2-30 \left (1-\frac {4}{\sqrt {15}}\right )}+\frac {2 \sqrt {11} \left (4-\sqrt {15}\right )}{13475 x^6-3850 \left (1+\frac {29 \sqrt {\frac {3}{5}}}{22}\right ) x^4+650 \left (1-\frac {4 \sqrt {\frac {3}{5}}}{13}\right ) x^2+30 \left (1-\frac {4}{\sqrt {15}}\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -\frac {1}{8} \int \frac {245 \sqrt {11} x^4+770 x^3-14 \sqrt {55} \left (\sqrt {3}+\sqrt {5}\right ) x^2-14 \sqrt {15} x+2 \sqrt {11} \left (4-\sqrt {15}\right )}{13475 x^6-35 \left (110+29 \sqrt {15}\right ) x^4-10 \left (-65+4 \sqrt {15}\right ) x^2+30 \left (1-\frac {4}{\sqrt {15}}\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -\frac {1}{8} \int \left (\frac {245 \sqrt {11} x^4}{13475 x^6-3850 \left (1+\frac {29 \sqrt {\frac {3}{5}}}{22}\right ) x^4+650 \left (1-\frac {4 \sqrt {\frac {3}{5}}}{13}\right ) x^2+30 \left (1-\frac {4}{\sqrt {15}}\right )}+\frac {770 x^3}{13475 x^6-3850 \left (1+\frac {29 \sqrt {\frac {3}{5}}}{22}\right ) x^4+650 \left (1-\frac {4 \sqrt {\frac {3}{5}}}{13}\right ) x^2+30 \left (1-\frac {4}{\sqrt {15}}\right )}+\frac {14 \sqrt {55} \left (-\sqrt {3}-\sqrt {5}\right ) x^2}{13475 x^6-3850 \left (1+\frac {29 \sqrt {\frac {3}{5}}}{22}\right ) x^4+650 \left (1-\frac {4 \sqrt {\frac {3}{5}}}{13}\right ) x^2+30 \left (1-\frac {4}{\sqrt {15}}\right )}+\frac {14 \sqrt {15} x}{-13475 x^6+3850 \left (1+\frac {29 \sqrt {\frac {3}{5}}}{22}\right ) x^4-650 \left (1-\frac {4 \sqrt {\frac {3}{5}}}{13}\right ) x^2-30 \left (1-\frac {4}{\sqrt {15}}\right )}+\frac {2 \sqrt {11} \left (4-\sqrt {15}\right )}{13475 x^6-3850 \left (1+\frac {29 \sqrt {\frac {3}{5}}}{22}\right ) x^4+650 \left (1-\frac {4 \sqrt {\frac {3}{5}}}{13}\right ) x^2+30 \left (1-\frac {4}{\sqrt {15}}\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -\frac {1}{8} \int \frac {245 \sqrt {11} x^4+770 x^3-14 \sqrt {55} \left (\sqrt {3}+\sqrt {5}\right ) x^2-14 \sqrt {15} x+2 \sqrt {11} \left (4-\sqrt {15}\right )}{13475 x^6-35 \left (110+29 \sqrt {15}\right ) x^4-10 \left (-65+4 \sqrt {15}\right ) x^2+30 \left (1-\frac {4}{\sqrt {15}}\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -\frac {1}{8} \int \left (\frac {245 \sqrt {11} x^4}{13475 x^6-3850 \left (1+\frac {29 \sqrt {\frac {3}{5}}}{22}\right ) x^4+650 \left (1-\frac {4 \sqrt {\frac {3}{5}}}{13}\right ) x^2+30 \left (1-\frac {4}{\sqrt {15}}\right )}+\frac {770 x^3}{13475 x^6-3850 \left (1+\frac {29 \sqrt {\frac {3}{5}}}{22}\right ) x^4+650 \left (1-\frac {4 \sqrt {\frac {3}{5}}}{13}\right ) x^2+30 \left (1-\frac {4}{\sqrt {15}}\right )}+\frac {14 \sqrt {55} \left (-\sqrt {3}-\sqrt {5}\right ) x^2}{13475 x^6-3850 \left (1+\frac {29 \sqrt {\frac {3}{5}}}{22}\right ) x^4+650 \left (1-\frac {4 \sqrt {\frac {3}{5}}}{13}\right ) x^2+30 \left (1-\frac {4}{\sqrt {15}}\right )}+\frac {14 \sqrt {15} x}{-13475 x^6+3850 \left (1+\frac {29 \sqrt {\frac {3}{5}}}{22}\right ) x^4-650 \left (1-\frac {4 \sqrt {\frac {3}{5}}}{13}\right ) x^2-30 \left (1-\frac {4}{\sqrt {15}}\right )}+\frac {2 \sqrt {11} \left (4-\sqrt {15}\right )}{13475 x^6-3850 \left (1+\frac {29 \sqrt {\frac {3}{5}}}{22}\right ) x^4+650 \left (1-\frac {4 \sqrt {\frac {3}{5}}}{13}\right ) x^2+30 \left (1-\frac {4}{\sqrt {15}}\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -\frac {1}{8} \int \frac {245 \sqrt {11} x^4+770 x^3-14 \sqrt {55} \left (\sqrt {3}+\sqrt {5}\right ) x^2-14 \sqrt {15} x+2 \sqrt {11} \left (4-\sqrt {15}\right )}{13475 x^6-35 \left (110+29 \sqrt {15}\right ) x^4-10 \left (-65+4 \sqrt {15}\right ) x^2+30 \left (1-\frac {4}{\sqrt {15}}\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -\frac {1}{8} \int \left (\frac {245 \sqrt {11} x^4}{13475 x^6-3850 \left (1+\frac {29 \sqrt {\frac {3}{5}}}{22}\right ) x^4+650 \left (1-\frac {4 \sqrt {\frac {3}{5}}}{13}\right ) x^2+30 \left (1-\frac {4}{\sqrt {15}}\right )}+\frac {770 x^3}{13475 x^6-3850 \left (1+\frac {29 \sqrt {\frac {3}{5}}}{22}\right ) x^4+650 \left (1-\frac {4 \sqrt {\frac {3}{5}}}{13}\right ) x^2+30 \left (1-\frac {4}{\sqrt {15}}\right )}+\frac {14 \sqrt {55} \left (-\sqrt {3}-\sqrt {5}\right ) x^2}{13475 x^6-3850 \left (1+\frac {29 \sqrt {\frac {3}{5}}}{22}\right ) x^4+650 \left (1-\frac {4 \sqrt {\frac {3}{5}}}{13}\right ) x^2+30 \left (1-\frac {4}{\sqrt {15}}\right )}+\frac {14 \sqrt {15} x}{-13475 x^6+3850 \left (1+\frac {29 \sqrt {\frac {3}{5}}}{22}\right ) x^4-650 \left (1-\frac {4 \sqrt {\frac {3}{5}}}{13}\right ) x^2-30 \left (1-\frac {4}{\sqrt {15}}\right )}+\frac {2 \sqrt {11} \left (4-\sqrt {15}\right )}{13475 x^6-3850 \left (1+\frac {29 \sqrt {\frac {3}{5}}}{22}\right ) x^4+650 \left (1-\frac {4 \sqrt {\frac {3}{5}}}{13}\right ) x^2+30 \left (1-\frac {4}{\sqrt {15}}\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -\frac {1}{8} \int \frac {245 \sqrt {11} x^4+770 x^3-14 \sqrt {55} \left (\sqrt {3}+\sqrt {5}\right ) x^2-14 \sqrt {15} x+2 \sqrt {11} \left (4-\sqrt {15}\right )}{13475 x^6-35 \left (110+29 \sqrt {15}\right ) x^4-10 \left (-65+4 \sqrt {15}\right ) x^2+30 \left (1-\frac {4}{\sqrt {15}}\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -\frac {1}{8} \int \left (\frac {245 \sqrt {11} x^4}{13475 x^6-3850 \left (1+\frac {29 \sqrt {\frac {3}{5}}}{22}\right ) x^4+650 \left (1-\frac {4 \sqrt {\frac {3}{5}}}{13}\right ) x^2+30 \left (1-\frac {4}{\sqrt {15}}\right )}+\frac {770 x^3}{13475 x^6-3850 \left (1+\frac {29 \sqrt {\frac {3}{5}}}{22}\right ) x^4+650 \left (1-\frac {4 \sqrt {\frac {3}{5}}}{13}\right ) x^2+30 \left (1-\frac {4}{\sqrt {15}}\right )}+\frac {14 \sqrt {55} \left (-\sqrt {3}-\sqrt {5}\right ) x^2}{13475 x^6-3850 \left (1+\frac {29 \sqrt {\frac {3}{5}}}{22}\right ) x^4+650 \left (1-\frac {4 \sqrt {\frac {3}{5}}}{13}\right ) x^2+30 \left (1-\frac {4}{\sqrt {15}}\right )}+\frac {14 \sqrt {15} x}{-13475 x^6+3850 \left (1+\frac {29 \sqrt {\frac {3}{5}}}{22}\right ) x^4-650 \left (1-\frac {4 \sqrt {\frac {3}{5}}}{13}\right ) x^2-30 \left (1-\frac {4}{\sqrt {15}}\right )}+\frac {2 \sqrt {11} \left (4-\sqrt {15}\right )}{13475 x^6-3850 \left (1+\frac {29 \sqrt {\frac {3}{5}}}{22}\right ) x^4+650 \left (1-\frac {4 \sqrt {\frac {3}{5}}}{13}\right ) x^2+30 \left (1-\frac {4}{\sqrt {15}}\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -\frac {1}{8} \int \frac {245 \sqrt {11} x^4+770 x^3-14 \sqrt {55} \left (\sqrt {3}+\sqrt {5}\right ) x^2-14 \sqrt {15} x+2 \sqrt {11} \left (4-\sqrt {15}\right )}{13475 x^6-35 \left (110+29 \sqrt {15}\right ) x^4-10 \left (-65+4 \sqrt {15}\right ) x^2+30 \left (1-\frac {4}{\sqrt {15}}\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -\frac {1}{8} \int \left (\frac {245 \sqrt {11} x^4}{13475 x^6-3850 \left (1+\frac {29 \sqrt {\frac {3}{5}}}{22}\right ) x^4+650 \left (1-\frac {4 \sqrt {\frac {3}{5}}}{13}\right ) x^2+30 \left (1-\frac {4}{\sqrt {15}}\right )}+\frac {770 x^3}{13475 x^6-3850 \left (1+\frac {29 \sqrt {\frac {3}{5}}}{22}\right ) x^4+650 \left (1-\frac {4 \sqrt {\frac {3}{5}}}{13}\right ) x^2+30 \left (1-\frac {4}{\sqrt {15}}\right )}+\frac {14 \sqrt {55} \left (-\sqrt {3}-\sqrt {5}\right ) x^2}{13475 x^6-3850 \left (1+\frac {29 \sqrt {\frac {3}{5}}}{22}\right ) x^4+650 \left (1-\frac {4 \sqrt {\frac {3}{5}}}{13}\right ) x^2+30 \left (1-\frac {4}{\sqrt {15}}\right )}+\frac {14 \sqrt {15} x}{-13475 x^6+3850 \left (1+\frac {29 \sqrt {\frac {3}{5}}}{22}\right ) x^4-650 \left (1-\frac {4 \sqrt {\frac {3}{5}}}{13}\right ) x^2-30 \left (1-\frac {4}{\sqrt {15}}\right )}+\frac {2 \sqrt {11} \left (4-\sqrt {15}\right )}{13475 x^6-3850 \left (1+\frac {29 \sqrt {\frac {3}{5}}}{22}\right ) x^4+650 \left (1-\frac {4 \sqrt {\frac {3}{5}}}{13}\right ) x^2+30 \left (1-\frac {4}{\sqrt {15}}\right )}\right )dx\) |
Input:
Int[(8*Sqrt[11] - 2*Sqrt[165] - 14*Sqrt[15]*x + (-70*Sqrt[11] - 14*Sqrt[16 5])*x^2 + 770*x^3 + 245*Sqrt[11]*x^4)/(8*(-30 + 8*Sqrt[15]) + 8*(-650 + 40 *Sqrt[15])*x^2 + 8*(3850 + 1015*Sqrt[15])*x^4 - 107800*x^6),x]
Output:
$Aborted
Time = 0.56 (sec) , antiderivative size = 52, normalized size of antiderivative = 0.69
| method | result | size |
| default | \(\frac {\sqrt {11}\, \sqrt {55}\, 15^{\frac {3}{4}} \operatorname {arctanh}\left (\frac {x \sqrt {55}\, 15^{\frac {3}{4}}}{15}\right )}{6600}+\frac {\sqrt {5}\, 15^{\frac {3}{4}} \operatorname {arctanh}\left (\frac {\left (490 x^{2}-14 \sqrt {15}-70\right ) \sqrt {5}\, 15^{\frac {3}{4}}}{2100}\right )}{1200}\) | \(52\) |
Input:
int((8*11^(1/2)-2*165^(1/2)-14*15^(1/2)*x+(-70*11^(1/2)-14*165^(1/2))*x^2+ 770*x^3+245*11^(1/2)*x^4)/(-240+64*15^(1/2)+8*(-650+40*15^(1/2))*x^2+8*(38 50+1015*15^(1/2))*x^4-107800*x^6),x,method=_RETURNVERBOSE)
Output:
1/6600*11^(1/2)*55^(1/2)*15^(3/4)*arctanh(1/15*x*55^(1/2)*15^(3/4))+1/1200 *5^(1/2)*15^(3/4)*arctanh(1/2100*(490*x^2-14*15^(1/2)-70)*5^(1/2)*15^(3/4) )
Timed out. \[ \int \frac {8 \sqrt {11}-2 \sqrt {165}-14 \sqrt {15} x+\left (-70 \sqrt {11}-14 \sqrt {165}\right ) x^2+770 x^3+245 \sqrt {11} x^4}{8 \left (-30+8 \sqrt {15}\right )+8 \left (-650+40 \sqrt {15}\right ) x^2+8 \left (3850+1015 \sqrt {15}\right ) x^4-107800 x^6} \, dx=\text {Timed out} \] Input:
integrate((8*11^(1/2)-2*165^(1/2)-14*15^(1/2)*x+(-70*11^(1/2)-14*165^(1/2) )*x^2+770*x^3+245*11^(1/2)*x^4)/(-240+64*15^(1/2)+8*(-650+40*15^(1/2))*x^2 +8*(3850+1015*15^(1/2))*x^4-107800*x^6),x, algorithm="fricas")
Output:
Timed out
Exception generated. \[ \int \frac {8 \sqrt {11}-2 \sqrt {165}-14 \sqrt {15} x+\left (-70 \sqrt {11}-14 \sqrt {165}\right ) x^2+770 x^3+245 \sqrt {11} x^4}{8 \left (-30+8 \sqrt {15}\right )+8 \left (-650+40 \sqrt {15}\right ) x^2+8 \left (3850+1015 \sqrt {15}\right ) x^4-107800 x^6} \, dx=\text {Exception raised: PolynomialError} \] Input:
integrate((8*11**(1/2)-2*165**(1/2)-14*15**(1/2)*x+(-70*11**(1/2)-14*165** (1/2))*x**2+770*x**3+245*11**(1/2)*x**4)/(-240+64*15**(1/2)+8*(-650+40*15* *(1/2))*x**2+8*(3850+1015*15**(1/2))*x**4-107800*x**6),x)
Output:
Exception raised: PolynomialError >> 1/(8026406129722253778490365429016317 86571585667051597111057095382995817099486707204483301622083173133484870882 512219322449920000000000000000000000000000000000*_t**48 + 2072409151354094 443219300735040
\[ \int \frac {8 \sqrt {11}-2 \sqrt {165}-14 \sqrt {15} x+\left (-70 \sqrt {11}-14 \sqrt {165}\right ) x^2+770 x^3+245 \sqrt {11} x^4}{8 \left (-30+8 \sqrt {15}\right )+8 \left (-650+40 \sqrt {15}\right ) x^2+8 \left (3850+1015 \sqrt {15}\right ) x^4-107800 x^6} \, dx=\int { -\frac {245 \, \sqrt {11} x^{4} + 770 \, x^{3} - 14 \, x^{2} {\left (\sqrt {165} + 5 \, \sqrt {11}\right )} - 14 \, \sqrt {15} x - 2 \, \sqrt {165} + 8 \, \sqrt {11}}{8 \, {\left (13475 \, x^{6} - 35 \, x^{4} {\left (29 \, \sqrt {15} + 110\right )} - 10 \, x^{2} {\left (4 \, \sqrt {15} - 65\right )} - 8 \, \sqrt {15} + 30\right )}} \,d x } \] Input:
integrate((8*11^(1/2)-2*165^(1/2)-14*15^(1/2)*x+(-70*11^(1/2)-14*165^(1/2) )*x^2+770*x^3+245*11^(1/2)*x^4)/(-240+64*15^(1/2)+8*(-650+40*15^(1/2))*x^2 +8*(3850+1015*15^(1/2))*x^4-107800*x^6),x, algorithm="maxima")
Output:
-1/8*integrate((245*sqrt(11)*x^4 + 770*x^3 - 14*x^2*(sqrt(165) + 5*sqrt(11 )) - 14*sqrt(15)*x - 2*sqrt(165) + 8*sqrt(11))/(13475*x^6 - 35*x^4*(29*sqr t(15) + 110) - 10*x^2*(4*sqrt(15) - 65) - 8*sqrt(15) + 30), x)
Timed out. \[ \int \frac {8 \sqrt {11}-2 \sqrt {165}-14 \sqrt {15} x+\left (-70 \sqrt {11}-14 \sqrt {165}\right ) x^2+770 x^3+245 \sqrt {11} x^4}{8 \left (-30+8 \sqrt {15}\right )+8 \left (-650+40 \sqrt {15}\right ) x^2+8 \left (3850+1015 \sqrt {15}\right ) x^4-107800 x^6} \, dx=\text {Timed out} \] Input:
integrate((8*11^(1/2)-2*165^(1/2)-14*15^(1/2)*x+(-70*11^(1/2)-14*165^(1/2) )*x^2+770*x^3+245*11^(1/2)*x^4)/(-240+64*15^(1/2)+8*(-650+40*15^(1/2))*x^2 +8*(3850+1015*15^(1/2))*x^4-107800*x^6),x, algorithm="giac")
Output:
Timed out
Time = 53.74 (sec) , antiderivative size = 850, normalized size of antiderivative = 11.33 \[ \int \frac {8 \sqrt {11}-2 \sqrt {165}-14 \sqrt {15} x+\left (-70 \sqrt {11}-14 \sqrt {165}\right ) x^2+770 x^3+245 \sqrt {11} x^4}{8 \left (-30+8 \sqrt {15}\right )+8 \left (-650+40 \sqrt {15}\right ) x^2+8 \left (3850+1015 \sqrt {15}\right ) x^4-107800 x^6} \, dx=\text {Too large to display} \] Input:
int(-(x^2*(70*11^(1/2) + 14*165^(1/2)) + 14*15^(1/2)*x - 8*11^(1/2) + 2*16 5^(1/2) - 245*11^(1/2)*x^4 - 770*x^3)/(8*x^2*(40*15^(1/2) - 650) + 8*x^4*( 1015*15^(1/2) + 3850) + 64*15^(1/2) - 107800*x^6 - 240),x)
Output:
symsum(log((1087204857*x)/1258204224121275200000000 - (76374500551*root(31 15770387240868380672000000000*15^(1/2)*z^6 - 12057085996284861480960000000 000*z^6 + 941959843459754803200000000*15^(1/2)*z^4 - 365129342254789263360 0000000*z^4 + 71314324659138528000000*15^(1/2)*z^2 - 275964797888600040000 000*z^2 + 1597018506299768750*15^(1/2) - 6190479571105775000, z, k)*x)/110 092869610611580000000 - (63923093*15^(1/2)*x)/57191101096421600000000 - (4 718059*11^(1/2))/4549292132669900000000 + (692479*165^(1/2))/2599595504382 800000000 - (4154874*11^(1/2)*root(3115770387240868380672000000000*15^(1/2 )*z^6 - 12057085996284861480960000000000*z^6 + 941959843459754803200000000 *15^(1/2)*z^4 - 3651293422547892633600000000*z^4 + 71314324659138528000000 *15^(1/2)*z^2 - 275964797888600040000000*z^2 + 1597018506299768750*15^(1/2 ) - 6190479571105775000, z, k)^2)/101546699389953125 - (57975508992*11^(1/ 2)*root(3115770387240868380672000000000*15^(1/2)*z^6 - 1205708599628486148 0960000000000*z^6 + 941959843459754803200000000*15^(1/2)*z^4 - 36512934225 47892633600000000*z^4 + 71314324659138528000000*15^(1/2)*z^2 - 27596479788 8600040000000*z^2 + 1597018506299768750*15^(1/2) - 6190479571105775000, z, k)^4)/142165379145934375 + (37744472*165^(1/2)*root(311577038724086838067 2000000000*15^(1/2)*z^6 - 12057085996284861480960000000000*z^6 + 941959843 459754803200000000*15^(1/2)*z^4 - 3651293422547892633600000000*z^4 + 71314 324659138528000000*15^(1/2)*z^2 - 275964797888600040000000*z^2 + 159701...
\[ \int \frac {8 \sqrt {11}-2 \sqrt {165}-14 \sqrt {15} x+\left (-70 \sqrt {11}-14 \sqrt {165}\right ) x^2+770 x^3+245 \sqrt {11} x^4}{8 \left (-30+8 \sqrt {15}\right )+8 \left (-650+40 \sqrt {15}\right ) x^2+8 \left (3850+1015 \sqrt {15}\right ) x^4-107800 x^6} \, dx=\frac {\sqrt {3}\, 15^{\frac {1}{4}} \mathrm {log}\left (5^{\frac {1}{4}} \sqrt {11}\, x +3^{\frac {1}{4}}\right )}{240}-\frac {\sqrt {3}\, 15^{\frac {1}{4}} \mathrm {log}\left (5^{\frac {1}{4}} \sqrt {11}\, x -3^{\frac {1}{4}}\right )}{240}+\frac {3807265 \sqrt {15}\, \left (\int \frac {x^{5}}{36315125 x^{12}-20751500 x^{10}+3377325 x^{8}-1082900 x^{6}-15220 x^{4}+5880 x^{2}-12}d x \right )}{821}+\frac {3948159 \sqrt {15}\, \left (\int \frac {x^{3}}{36315125 x^{12}-20751500 x^{10}+3377325 x^{8}-1082900 x^{6}-15220 x^{4}+5880 x^{2}-12}d x \right )}{1642}+\frac {311141 \sqrt {15}\, \left (\int \frac {x}{36315125 x^{12}-20751500 x^{10}+3377325 x^{8}-1082900 x^{6}-15220 x^{4}+5880 x^{2}-12}d x \right )}{11494}+\frac {9361 \sqrt {15}\, \mathrm {log}\left (5^{\frac {1}{4}} \sqrt {11}\, x +3^{\frac {1}{4}}\right )}{1379280}+\frac {9361 \sqrt {15}\, \mathrm {log}\left (5^{\frac {1}{4}} \sqrt {11}\, x -3^{\frac {1}{4}}\right )}{1379280}-\frac {121 \sqrt {15}\, \mathrm {log}\left (60025 x^{8}-34300 x^{6}+5880 x^{4}-1960 x^{2}+4\right )}{65680}+\frac {803 \sqrt {15}\, \mathrm {log}\left (11 \sqrt {5}\, x^{2}+\sqrt {3}\right )}{1379280}+\frac {170769655 \left (\int \frac {x^{5}}{36315125 x^{12}-20751500 x^{10}+3377325 x^{8}-1082900 x^{6}-15220 x^{4}+5880 x^{2}-12}d x \right )}{3284}+\frac {4626185 \left (\int \frac {x^{3}}{36315125 x^{12}-20751500 x^{10}+3377325 x^{8}-1082900 x^{6}-15220 x^{4}+5880 x^{2}-12}d x \right )}{1642}+\frac {816850 \left (\int \frac {x}{36315125 x^{12}-20751500 x^{10}+3377325 x^{8}-1082900 x^{6}-15220 x^{4}+5880 x^{2}-12}d x \right )}{5747}+\frac {1089 \,\mathrm {log}\left (5^{\frac {1}{4}} \sqrt {11}\, x +3^{\frac {1}{4}}\right )}{22988}+\frac {1089 \,\mathrm {log}\left (5^{\frac {1}{4}} \sqrt {11}\, x -3^{\frac {1}{4}}\right )}{22988}-\frac {121 \,\mathrm {log}\left (60025 x^{8}-34300 x^{6}+5880 x^{4}-1960 x^{2}+4\right )}{13136}-\frac {121 \,\mathrm {log}\left (11 \sqrt {5}\, x^{2}+\sqrt {3}\right )}{11494} \] Input:
int((8*11^(1/2)-2*165^(1/2)-14*15^(1/2)*x+(-70*11^(1/2)-14*165^(1/2))*x^2+ 770*x^3+245*11^(1/2)*x^4)/(-240+64*15^(1/2)+8*(-650+40*15^(1/2))*x^2+8*(38 50+1015*15^(1/2))*x^4-107800*x^6),x)
Output:
(5747*sqrt(3)*15**(1/4)*log(5**(1/4)*sqrt(11)*x + 3**(1/4)) - 5747*sqrt(3) *15**(1/4)*log(5**(1/4)*sqrt(11)*x - 3**(1/4)) + 6396205200*sqrt(15)*int(x **5/(36315125*x**12 - 20751500*x**10 + 3377325*x**8 - 1082900*x**6 - 15220 *x**4 + 5880*x**2 - 12),x) + 3316453560*sqrt(15)*int(x**3/(36315125*x**12 - 20751500*x**10 + 3377325*x**8 - 1082900*x**6 - 15220*x**4 + 5880*x**2 - 12),x) + 37336920*sqrt(15)*int(x/(36315125*x**12 - 20751500*x**10 + 337732 5*x**8 - 1082900*x**6 - 15220*x**4 + 5880*x**2 - 12),x) + 9361*sqrt(15)*lo g(5**(1/4)*sqrt(11)*x + 3**(1/4)) + 9361*sqrt(15)*log(5**(1/4)*sqrt(11)*x - 3**(1/4)) - 2541*sqrt(15)*log(60025*x**8 - 34300*x**6 + 5880*x**4 - 1960 *x**2 + 4) + 803*sqrt(15)*log(11*sqrt(5)*x**2 + sqrt(3)) + 71723255100*int (x**5/(36315125*x**12 - 20751500*x**10 + 3377325*x**8 - 1082900*x**6 - 152 20*x**4 + 5880*x**2 - 12),x) + 3885995400*int(x**3/(36315125*x**12 - 20751 500*x**10 + 3377325*x**8 - 1082900*x**6 - 15220*x**4 + 5880*x**2 - 12),x) + 196044000*int(x/(36315125*x**12 - 20751500*x**10 + 3377325*x**8 - 108290 0*x**6 - 15220*x**4 + 5880*x**2 - 12),x) + 65340*log(5**(1/4)*sqrt(11)*x + 3**(1/4)) + 65340*log(5**(1/4)*sqrt(11)*x - 3**(1/4)) - 12705*log(60025*x **8 - 34300*x**6 + 5880*x**4 - 1960*x**2 + 4) - 14520*log(11*sqrt(5)*x**2 + sqrt(3)))/1379280