Integrand size = 87, antiderivative size = 71 \[ \int \frac {15 x-2 \sqrt {3} x+12 \sqrt {3} x^3+3 \sqrt {3} x^5}{-4-20 x^2+60 \sqrt {3} x^2-100 x^4+10 \sqrt {3} x^4+12 x^6+60 \sqrt {3} x^6-36 x^8} \, dx=-\frac {1}{8} \sqrt [4]{3} \arctan \left (\sqrt {-\frac {1}{2}+\frac {1}{\sqrt {3}}}-\frac {1}{2} 3^{3/4} x^2\right )-\frac {1}{8} \sqrt [4]{3} \text {arctanh}\left (\sqrt {\frac {1}{2}+\frac {1}{\sqrt {3}}}-\frac {x^2}{\sqrt [4]{3}}\right ) \] Output:
1/8*3^(1/4)*arctan(-1/6*(-18+12*3^(1/2))^(1/2)+1/2*3^(3/4)*x^2)+1/8*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 = 178, normalized size of antiderivative = 2.51 \[ \int \frac {15 x-2 \sqrt {3} x+12 \sqrt {3} x^3+3 \sqrt {3} x^5}{-4-20 x^2+60 \sqrt {3} x^2-100 x^4+10 \sqrt {3} x^4+12 x^6+60 \sqrt {3} x^6-36 x^8} \, dx=\frac {1}{8} \text {RootSum}\left [2+10 \text {$\#$1}^2-30 \sqrt {3} \text {$\#$1}^2+50 \text {$\#$1}^4-5 \sqrt {3} \text {$\#$1}^4-6 \text {$\#$1}^6-30 \sqrt {3} \text {$\#$1}^6+18 \text {$\#$1}^8\&,\frac {15 \log (x-\text {$\#$1})-2 \sqrt {3} \log (x-\text {$\#$1})+12 \sqrt {3} \log (x-\text {$\#$1}) \text {$\#$1}^2+3 \sqrt {3} \log (x-\text {$\#$1}) \text {$\#$1}^4}{-5+15 \sqrt {3}-50 \text {$\#$1}^2+5 \sqrt {3} \text {$\#$1}^2+9 \text {$\#$1}^4+45 \sqrt {3} \text {$\#$1}^4-36 \text {$\#$1}^6}\&\right ] \] Input:
Integrate[(15*x - 2*Sqrt[3]*x + 12*Sqrt[3]*x^3 + 3*Sqrt[3]*x^5)/(-4 - 20*x ^2 + 60*Sqrt[3]*x^2 - 100*x^4 + 10*Sqrt[3]*x^4 + 12*x^6 + 60*Sqrt[3]*x^6 - 36*x^8),x]
Output:
RootSum[2 + 10*#1^2 - 30*Sqrt[3]*#1^2 + 50*#1^4 - 5*Sqrt[3]*#1^4 - 6*#1^6 - 30*Sqrt[3]*#1^6 + 18*#1^8 & , (15*Log[x - #1] - 2*Sqrt[3]*Log[x - #1] + 12*Sqrt[3]*Log[x - #1]*#1^2 + 3*Sqrt[3]*Log[x - #1]*#1^4)/(-5 + 15*Sqrt[3] - 50*#1^2 + 5*Sqrt[3]*#1^2 + 9*#1^4 + 45*Sqrt[3]*#1^4 - 36*#1^6) & ]/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.
| \(\displaystyle \int \frac {3 \sqrt {3} x^5+12 \sqrt {3} x^3-2 \sqrt {3} x+15 x}{-36 x^8+60 \sqrt {3} x^6+12 x^6+10 \sqrt {3} x^4-100 x^4+60 \sqrt {3} x^2-20 x^2-4} \, dx\) |
| \(\Big \downarrow \) 6 |
| \(\displaystyle \int \frac {3 \sqrt {3} x^5+12 \sqrt {3} x^3+\left (15-2 \sqrt {3}\right ) x}{-36 x^8+60 \sqrt {3} x^6+12 x^6+10 \sqrt {3} x^4-100 x^4+60 \sqrt {3} x^2-20 x^2-4}dx\) |
| \(\Big \downarrow \) 6 |
| \(\displaystyle \int \frac {3 \sqrt {3} x^5+12 \sqrt {3} x^3+\left (15-2 \sqrt {3}\right ) x}{-36 x^8+60 \sqrt {3} x^6+12 x^6+10 \sqrt {3} x^4-100 x^4+\left (60 \sqrt {3}-20\right ) x^2-4}dx\) |
| \(\Big \downarrow \) 6 |
| \(\displaystyle \int \frac {3 \sqrt {3} x^5+12 \sqrt {3} x^3+\left (15-2 \sqrt {3}\right ) x}{-36 x^8+60 \sqrt {3} x^6+12 x^6+\left (10 \sqrt {3}-100\right ) x^4+\left (60 \sqrt {3}-20\right ) x^2-4}dx\) |
| \(\Big \downarrow \) 6 |
| \(\displaystyle \int \frac {3 \sqrt {3} x^5+12 \sqrt {3} x^3+\left (15-2 \sqrt {3}\right ) x}{-36 x^8+\left (12+60 \sqrt {3}\right ) x^6+\left (10 \sqrt {3}-100\right ) x^4+\left (60 \sqrt {3}-20\right ) x^2-4}dx\) |
| \(\Big \downarrow \) 2028 |
| \(\displaystyle \int \frac {x \left (3 \sqrt {3} x^4+12 \sqrt {3} x^2-2 \sqrt {3}+15\right )}{-36 x^8+\left (12+60 \sqrt {3}\right ) x^6+\left (10 \sqrt {3}-100\right ) x^4+\left (60 \sqrt {3}-20\right ) x^2-4}dx\) |
| \(\Big \downarrow \) 7266 |
| \(\displaystyle \frac {1}{2} \int -\frac {3 \sqrt {3} x^4+12 \sqrt {3} x^2-2 \sqrt {3}+15}{2 \left (18 x^8-6 \left (1+5 \sqrt {3}\right ) x^6+5 \left (10-\sqrt {3}\right ) x^4+10 \left (1-3 \sqrt {3}\right ) x^2+2\right )}dx^2\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle -\frac {1}{4} \int \frac {3 \sqrt {3} x^4+12 \sqrt {3} x^2-2 \sqrt {3}+15}{18 x^8-6 \left (1+5 \sqrt {3}\right ) x^6+5 \left (10-\sqrt {3}\right ) x^4+10 \left (1-3 \sqrt {3}\right ) x^2+2}dx^2\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -\frac {1}{4} \int \left (\frac {3 \sqrt {3} x^4}{18 x^8-6 \left (1+5 \sqrt {3}\right ) x^6+5 \left (10-\sqrt {3}\right ) x^4+10 \left (1-3 \sqrt {3}\right ) x^2+2}+\frac {12 \sqrt {3} x^2}{18 x^8-6 \left (1+5 \sqrt {3}\right ) x^6+5 \left (10-\sqrt {3}\right ) x^4+10 \left (1-3 \sqrt {3}\right ) x^2+2}+\frac {2 \sqrt {3} \left (1-\frac {5 \sqrt {3}}{2}\right )}{-18 x^8+6 \left (1+5 \sqrt {3}\right ) x^6-5 \left (10-\sqrt {3}\right ) x^4-10 \left (1-3 \sqrt {3}\right ) x^2-2}\right )dx^2\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle \frac {1}{4} \left (\left (15-2 \sqrt {3}\right ) \int \frac {1}{-18 x^8+6 \left (1+5 \sqrt {3}\right ) x^6-5 \left (10-\sqrt {3}\right ) x^4-10 \left (1-3 \sqrt {3}\right ) x^2-2}dx^2-12 \sqrt {3} \int \frac {x^2}{18 x^8-6 \left (1+5 \sqrt {3}\right ) x^6+5 \left (10-\sqrt {3}\right ) x^4+10 \left (1-3 \sqrt {3}\right ) x^2+2}dx^2-3 \sqrt {3} \int \frac {x^4}{18 x^8-6 \left (1+5 \sqrt {3}\right ) x^6+5 \left (10-\sqrt {3}\right ) x^4+10 \left (1-3 \sqrt {3}\right ) x^2+2}dx^2\right )\) |
Input:
Int[(15*x - 2*Sqrt[3]*x + 12*Sqrt[3]*x^3 + 3*Sqrt[3]*x^5)/(-4 - 20*x^2 + 6 0*Sqrt[3]*x^2 - 100*x^4 + 10*Sqrt[3]*x^4 + 12*x^6 + 60*Sqrt[3]*x^6 - 36*x^ 8),x]
Output:
$Aborted
Time = 0.39 (sec) , antiderivative size = 48, normalized size of antiderivative = 0.68
| method | result | size |
| default | \(\frac {3^{\frac {1}{4}} \operatorname {arctanh}\left (\frac {\left (4 x^{2}-2 \sqrt {3}-2\right ) 3^{\frac {3}{4}}}{12}\right )}{8}+\frac {3^{\frac {1}{4}} \arctan \left (\frac {\left (18 x^{2}-6 \sqrt {3}+6\right ) 3^{\frac {3}{4}}}{36}\right )}{8}\) | \(48\) |
Input:
int((15*x-2*3^(1/2)*x+12*3^(1/2)*x^3+3*3^(1/2)*x^5)/(-4-20*x^2+60*3^(1/2)* x^2-100*x^4+10*3^(1/2)*x^4+12*x^6+60*3^(1/2)*x^6-36*x^8),x,method=_RETURNV ERBOSE)
Output:
1/8*3^(1/4)*arctanh(1/12*(4*x^2-2*3^(1/2)-2)*3^(3/4))+1/8*3^(1/4)*arctan(1 /36*(18*x^2-6*3^(1/2)+6)*3^(3/4))
Time = 0.09 (sec) , antiderivative size = 104, normalized size of antiderivative = 1.46 \[ \int \frac {15 x-2 \sqrt {3} x+12 \sqrt {3} x^3+3 \sqrt {3} x^5}{-4-20 x^2+60 \sqrt {3} x^2-100 x^4+10 \sqrt {3} x^4+12 x^6+60 \sqrt {3} x^6-36 x^8} \, dx=-\frac {1}{8} \cdot 3^{\frac {1}{4}} \arctan \left (-\frac {1}{12} \cdot 3^{\frac {3}{4}} {\left (5 \, x^{2} - 2 \, \sqrt {3}\right )} - \frac {1}{12} \cdot 3^{\frac {3}{4}} {\left (x^{2} + 2\right )}\right ) + \frac {1}{16} \cdot 3^{\frac {1}{4}} \log \left (36 \, x^{2} - \sqrt {3} {\left (5 \, \sqrt {3} + 3\right )} - 15 \, \sqrt {3} + 36 \cdot 3^{\frac {1}{4}} - 3\right ) - \frac {1}{16} \cdot 3^{\frac {1}{4}} \log \left (36 \, x^{2} - \sqrt {3} {\left (5 \, \sqrt {3} + 3\right )} - 15 \, \sqrt {3} - 36 \cdot 3^{\frac {1}{4}} - 3\right ) \] Input:
integrate((15*x-2*3^(1/2)*x+12*3^(1/2)*x^3+3*3^(1/2)*x^5)/(-4-20*x^2+60*3^ (1/2)*x^2-100*x^4+10*3^(1/2)*x^4+12*x^6+60*x^6*3^(1/2)-36*x^8),x, algorith m="fricas")
Output:
-1/8*3^(1/4)*arctan(-1/12*3^(3/4)*(5*x^2 - 2*sqrt(3)) - 1/12*3^(3/4)*(x^2 + 2)) + 1/16*3^(1/4)*log(36*x^2 - sqrt(3)*(5*sqrt(3) + 3) - 15*sqrt(3) + 3 6*3^(1/4) - 3) - 1/16*3^(1/4)*log(36*x^2 - sqrt(3)*(5*sqrt(3) + 3) - 15*sq rt(3) - 36*3^(1/4) - 3)
Timed out. \[ \int \frac {15 x-2 \sqrt {3} x+12 \sqrt {3} x^3+3 \sqrt {3} x^5}{-4-20 x^2+60 \sqrt {3} x^2-100 x^4+10 \sqrt {3} x^4+12 x^6+60 \sqrt {3} x^6-36 x^8} \, dx=\text {Timed out} \] Input:
integrate((15*x-2*3**(1/2)*x+12*3**(1/2)*x**3+3*3**(1/2)*x**5)/(-4-20*x**2 +60*3**(1/2)*x**2-100*x**4+10*3**(1/2)*x**4+12*x**6+60*x**6*3**(1/2)-36*x* *8),x)
Output:
Timed out
\[ \int \frac {15 x-2 \sqrt {3} x+12 \sqrt {3} x^3+3 \sqrt {3} x^5}{-4-20 x^2+60 \sqrt {3} x^2-100 x^4+10 \sqrt {3} x^4+12 x^6+60 \sqrt {3} x^6-36 x^8} \, dx=\int { -\frac {3 \, \sqrt {3} x^{5} + 12 \, \sqrt {3} x^{3} - 2 \, \sqrt {3} x + 15 \, x}{2 \, {\left (18 \, x^{8} - 30 \, \sqrt {3} x^{6} - 6 \, x^{6} - 5 \, \sqrt {3} x^{4} + 50 \, x^{4} - 30 \, \sqrt {3} x^{2} + 10 \, x^{2} + 2\right )}} \,d x } \] Input:
integrate((15*x-2*3^(1/2)*x+12*3^(1/2)*x^3+3*3^(1/2)*x^5)/(-4-20*x^2+60*3^ (1/2)*x^2-100*x^4+10*3^(1/2)*x^4+12*x^6+60*x^6*3^(1/2)-36*x^8),x, algorith m="maxima")
Output:
-1/2*integrate((3*sqrt(3)*x^5 + 12*sqrt(3)*x^3 - 2*sqrt(3)*x + 15*x)/(18*x ^8 - 30*sqrt(3)*x^6 - 6*x^6 - 5*sqrt(3)*x^4 + 50*x^4 - 30*sqrt(3)*x^2 + 10 *x^2 + 2), x)
Exception generated. \[ \int \frac {15 x-2 \sqrt {3} x+12 \sqrt {3} x^3+3 \sqrt {3} x^5}{-4-20 x^2+60 \sqrt {3} x^2-100 x^4+10 \sqrt {3} x^4+12 x^6+60 \sqrt {3} x^6-36 x^8} \, dx=\text {Exception raised: TypeError} \] Input:
integrate((15*x-2*3^(1/2)*x+12*3^(1/2)*x^3+3*3^(1/2)*x^5)/(-4-20*x^2+60*3^ (1/2)*x^2-100*x^4+10*3^(1/2)*x^4+12*x^6+60*x^6*3^(1/2)-36*x^8),x, algorith m="giac")
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 = 10.97 (sec) , antiderivative size = 761, normalized size of antiderivative = 10.72 \[ \int \frac {15 x-2 \sqrt {3} x+12 \sqrt {3} x^3+3 \sqrt {3} x^5}{-4-20 x^2+60 \sqrt {3} x^2-100 x^4+10 \sqrt {3} x^4+12 x^6+60 \sqrt {3} x^6-36 x^8} \, dx=\text {Too large to display} \] Input:
int((15*x - 2*3^(1/2)*x + 12*3^(1/2)*x^3 + 3*3^(1/2)*x^5)/(60*3^(1/2)*x^2 + 10*3^(1/2)*x^4 + 60*3^(1/2)*x^6 - 20*x^2 - 100*x^4 + 12*x^6 - 36*x^8 - 4 ),x)
Output:
symsum(log(913779360*root(110045429760*3^(1/2)*z^4 - 797206315008*z^4 - 50 37480*3^(1/2) + 36493209, z, k) + 2494825632*3^(1/2)*root(110045429760*3^( 1/2)*z^4 - 797206315008*z^4 - 5037480*3^(1/2) + 36493209, z, k) + 29231280 *3^(1/2) + 15800090880*3^(1/2)*root(110045429760*3^(1/2)*z^4 - 79720631500 8*z^4 - 5037480*3^(1/2) + 36493209, z, k)^2 + 1595164114944*3^(1/2)*root(1 10045429760*3^(1/2)*z^4 - 797206315008*z^4 - 5037480*3^(1/2) + 36493209, z , k)^3 + 6872364728320*3^(1/2)*root(110045429760*3^(1/2)*z^4 - 79720631500 8*z^4 - 5037480*3^(1/2) + 36493209, z, k)^4 + 208043658706944*3^(1/2)*root (110045429760*3^(1/2)*z^4 - 797206315008*z^4 - 5037480*3^(1/2) + 36493209, z, k)^5 + 514188032081920*3^(1/2)*root(110045429760*3^(1/2)*z^4 - 7972063 15008*z^4 - 5037480*3^(1/2) + 36493209, z, k)^6 - 173691869310*root(110045 429760*3^(1/2)*z^4 - 797206315008*z^4 - 5037480*3^(1/2) + 36493209, z, k)* x^2 - 2446451235*3^(1/2)*x^2 + 142704702816*root(110045429760*3^(1/2)*z^4 - 797206315008*z^4 - 5037480*3^(1/2) + 36493209, z, k)^2 + 766721802240*ro ot(110045429760*3^(1/2)*z^4 - 797206315008*z^4 - 5037480*3^(1/2) + 3649320 9, z, k)^3 + 38013718364160*root(110045429760*3^(1/2)*z^4 - 797206315008*z ^4 - 5037480*3^(1/2) + 36493209, z, k)^4 + 180885808742400*root(1100454297 60*3^(1/2)*z^4 - 797206315008*z^4 - 5037480*3^(1/2) + 36493209, z, k)^5 + 1892922901397504*root(110045429760*3^(1/2)*z^4 - 797206315008*z^4 - 503748 0*3^(1/2) + 36493209, z, k)^6 - 1303067223*x^2 - 465671581680*root(1100...
\[ \int \frac {15 x-2 \sqrt {3} x+12 \sqrt {3} x^3+3 \sqrt {3} x^5}{-4-20 x^2+60 \sqrt {3} x^2-100 x^4+10 \sqrt {3} x^4+12 x^6+60 \sqrt {3} x^6-36 x^8} \, dx=-27 \sqrt {3}\, \left (\int \frac {x^{13}}{324 x^{16}-216 x^{14}-864 x^{12}-1140 x^{10}-3023 x^{8}+76 x^{6}-2400 x^{4}+40 x^{2}+4}d x \right )-99 \sqrt {3}\, \left (\int \frac {x^{11}}{324 x^{16}-216 x^{14}-864 x^{12}-1140 x^{10}-3023 x^{8}+76 x^{6}-2400 x^{4}+40 x^{2}+4}d x \right )-21 \sqrt {3}\, \left (\int \frac {x^{9}}{324 x^{16}-216 x^{14}-864 x^{12}-1140 x^{10}-3023 x^{8}+76 x^{6}-2400 x^{4}+40 x^{2}+4}d x \right )-546 \sqrt {3}\, \left (\int \frac {x^{7}}{324 x^{16}-216 x^{14}-864 x^{12}-1140 x^{10}-3023 x^{8}+76 x^{6}-2400 x^{4}+40 x^{2}+4}d x \right )-\frac {101 \sqrt {3}\, \left (\int \frac {x^{5}}{324 x^{16}-216 x^{14}-864 x^{12}-1140 x^{10}-3023 x^{8}+76 x^{6}-2400 x^{4}+40 x^{2}+4}d x \right )}{2}-227 \sqrt {3}\, \left (\int \frac {x^{3}}{324 x^{16}-216 x^{14}-864 x^{12}-1140 x^{10}-3023 x^{8}+76 x^{6}-2400 x^{4}+40 x^{2}+4}d x \right )+2 \sqrt {3}\, \left (\int \frac {x}{324 x^{16}-216 x^{14}-864 x^{12}-1140 x^{10}-3023 x^{8}+76 x^{6}-2400 x^{4}+40 x^{2}+4}d x \right )-135 \left (\int \frac {x^{11}}{324 x^{16}-216 x^{14}-864 x^{12}-1140 x^{10}-3023 x^{8}+76 x^{6}-2400 x^{4}+40 x^{2}+4}d x \right )-\frac {1395 \left (\int \frac {x^{9}}{324 x^{16}-216 x^{14}-864 x^{12}-1140 x^{10}-3023 x^{8}+76 x^{6}-2400 x^{4}+40 x^{2}+4}d x \right )}{2}-90 \left (\int \frac {x^{7}}{324 x^{16}-216 x^{14}-864 x^{12}-1140 x^{10}-3023 x^{8}+76 x^{6}-2400 x^{4}+40 x^{2}+4}d x \right )-900 \left (\int \frac {x^{5}}{324 x^{16}-216 x^{14}-864 x^{12}-1140 x^{10}-3023 x^{8}+76 x^{6}-2400 x^{4}+40 x^{2}+4}d x \right )+15 \left (\int \frac {x^{3}}{324 x^{16}-216 x^{14}-864 x^{12}-1140 x^{10}-3023 x^{8}+76 x^{6}-2400 x^{4}+40 x^{2}+4}d x \right )-15 \left (\int \frac {x}{324 x^{16}-216 x^{14}-864 x^{12}-1140 x^{10}-3023 x^{8}+76 x^{6}-2400 x^{4}+40 x^{2}+4}d x \right ) \] Input:
int((15*x-2*3^(1/2)*x+12*3^(1/2)*x^3+3*3^(1/2)*x^5)/(-4-20*x^2+60*3^(1/2)* x^2-100*x^4+10*3^(1/2)*x^4+12*x^6+60*x^6*3^(1/2)-36*x^8),x)
Output:
( - 54*sqrt(3)*int(x**13/(324*x**16 - 216*x**14 - 864*x**12 - 1140*x**10 - 3023*x**8 + 76*x**6 - 2400*x**4 + 40*x**2 + 4),x) - 198*sqrt(3)*int(x**11 /(324*x**16 - 216*x**14 - 864*x**12 - 1140*x**10 - 3023*x**8 + 76*x**6 - 2 400*x**4 + 40*x**2 + 4),x) - 42*sqrt(3)*int(x**9/(324*x**16 - 216*x**14 - 864*x**12 - 1140*x**10 - 3023*x**8 + 76*x**6 - 2400*x**4 + 40*x**2 + 4),x) - 1092*sqrt(3)*int(x**7/(324*x**16 - 216*x**14 - 864*x**12 - 1140*x**10 - 3023*x**8 + 76*x**6 - 2400*x**4 + 40*x**2 + 4),x) - 101*sqrt(3)*int(x**5/ (324*x**16 - 216*x**14 - 864*x**12 - 1140*x**10 - 3023*x**8 + 76*x**6 - 24 00*x**4 + 40*x**2 + 4),x) - 454*sqrt(3)*int(x**3/(324*x**16 - 216*x**14 - 864*x**12 - 1140*x**10 - 3023*x**8 + 76*x**6 - 2400*x**4 + 40*x**2 + 4),x) + 4*sqrt(3)*int(x/(324*x**16 - 216*x**14 - 864*x**12 - 1140*x**10 - 3023* x**8 + 76*x**6 - 2400*x**4 + 40*x**2 + 4),x) - 270*int(x**11/(324*x**16 - 216*x**14 - 864*x**12 - 1140*x**10 - 3023*x**8 + 76*x**6 - 2400*x**4 + 40* x**2 + 4),x) - 1395*int(x**9/(324*x**16 - 216*x**14 - 864*x**12 - 1140*x** 10 - 3023*x**8 + 76*x**6 - 2400*x**4 + 40*x**2 + 4),x) - 180*int(x**7/(324 *x**16 - 216*x**14 - 864*x**12 - 1140*x**10 - 3023*x**8 + 76*x**6 - 2400*x **4 + 40*x**2 + 4),x) - 1800*int(x**5/(324*x**16 - 216*x**14 - 864*x**12 - 1140*x**10 - 3023*x**8 + 76*x**6 - 2400*x**4 + 40*x**2 + 4),x) + 30*int(x **3/(324*x**16 - 216*x**14 - 864*x**12 - 1140*x**10 - 3023*x**8 + 76*x**6 - 2400*x**4 + 40*x**2 + 4),x) - 30*int(x/(324*x**16 - 216*x**14 - 864*x...