Integrand size = 224, antiderivative size = 21 \[ \int \frac {-20 x+364 x^2-288 x^4+72 x^6-6 x^8+\left (-20-20 x-576 x^3+288 x^5-36 x^7\right ) \log (x)+\left (-288 x^2+432 x^4-90 x^6\right ) \log ^2(x)+\left (288 x^3-120 x^5\right ) \log ^3(x)+\left (72 x^2-90 x^4\right ) \log ^4(x)-36 x^3 \log ^5(x)-6 x^2 \log ^6(x)}{-192 x+144 x^3-36 x^5+3 x^7+\left (288 x^2-144 x^4+18 x^6\right ) \log (x)+\left (144 x-216 x^3+45 x^5\right ) \log ^2(x)+\left (-144 x^2+60 x^4\right ) \log ^3(x)+\left (-36 x+45 x^3\right ) \log ^4(x)+18 x^2 \log ^5(x)+3 x \log ^6(x)} \, dx=2-x^2+\frac {5}{3 \left (-4+(x+\log (x))^2\right )^2} \] Output:
2-x^2+5/3/((x+ln(x))^2-4)^2
Time = 0.05 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.52 \[ \int \frac {-20 x+364 x^2-288 x^4+72 x^6-6 x^8+\left (-20-20 x-576 x^3+288 x^5-36 x^7\right ) \log (x)+\left (-288 x^2+432 x^4-90 x^6\right ) \log ^2(x)+\left (288 x^3-120 x^5\right ) \log ^3(x)+\left (72 x^2-90 x^4\right ) \log ^4(x)-36 x^3 \log ^5(x)-6 x^2 \log ^6(x)}{-192 x+144 x^3-36 x^5+3 x^7+\left (288 x^2-144 x^4+18 x^6\right ) \log (x)+\left (144 x-216 x^3+45 x^5\right ) \log ^2(x)+\left (-144 x^2+60 x^4\right ) \log ^3(x)+\left (-36 x+45 x^3\right ) \log ^4(x)+18 x^2 \log ^5(x)+3 x \log ^6(x)} \, dx=-\frac {2}{3} \left (\frac {3 x^2}{2}-\frac {5}{2 \left (-4+x^2+2 x \log (x)+\log ^2(x)\right )^2}\right ) \] Input:
Integrate[(-20*x + 364*x^2 - 288*x^4 + 72*x^6 - 6*x^8 + (-20 - 20*x - 576* x^3 + 288*x^5 - 36*x^7)*Log[x] + (-288*x^2 + 432*x^4 - 90*x^6)*Log[x]^2 + (288*x^3 - 120*x^5)*Log[x]^3 + (72*x^2 - 90*x^4)*Log[x]^4 - 36*x^3*Log[x]^ 5 - 6*x^2*Log[x]^6)/(-192*x + 144*x^3 - 36*x^5 + 3*x^7 + (288*x^2 - 144*x^ 4 + 18*x^6)*Log[x] + (144*x - 216*x^3 + 45*x^5)*Log[x]^2 + (-144*x^2 + 60* x^4)*Log[x]^3 + (-36*x + 45*x^3)*Log[x]^4 + 18*x^2*Log[x]^5 + 3*x*Log[x]^6 ),x]
Output:
(-2*((3*x^2)/2 - 5/(2*(-4 + x^2 + 2*x*Log[x] + Log[x]^2)^2)))/3
Leaf count is larger than twice the leaf count of optimal. \(64\) vs. \(2(21)=42\).
Time = 2.71 (sec) , antiderivative size = 64, normalized size of antiderivative = 3.05, number of steps used = 5, number of rules used = 5, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.022, Rules used = {7292, 27, 27, 7293, 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.
| \(\displaystyle \int \frac {-6 x^8+72 x^6-288 x^4-36 x^3 \log ^5(x)+364 x^2-6 x^2 \log ^6(x)+\left (288 x^3-120 x^5\right ) \log ^3(x)+\left (72 x^2-90 x^4\right ) \log ^4(x)+\left (-36 x^7+288 x^5-576 x^3-20 x-20\right ) \log (x)+\left (-90 x^6+432 x^4-288 x^2\right ) \log ^2(x)-20 x}{3 x^7-36 x^5+144 x^3+\left (45 x^3-36 x\right ) \log ^4(x)+18 x^2 \log ^5(x)+\left (45 x^5-216 x^3+144 x\right ) \log ^2(x)+\left (60 x^4-144 x^2\right ) \log ^3(x)+\left (18 x^6-144 x^4+288 x^2\right ) \log (x)-192 x+3 x \log ^6(x)} \, dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \frac {6 x^8-72 x^6+288 x^4+36 x^3 \log ^5(x)-364 x^2+6 x^2 \log ^6(x)-\left (288 x^3-120 x^5\right ) \log ^3(x)-\left (72 x^2-90 x^4\right ) \log ^4(x)-\left (-36 x^7+288 x^5-576 x^3-20 x-20\right ) \log (x)-\left (-90 x^6+432 x^4-288 x^2\right ) \log ^2(x)+20 x}{3 x \left (-x^2-\log ^2(x)-2 x \log (x)+4\right )^3}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {1}{3} \int \frac {2 \left (3 x^8-36 x^6+144 x^4+18 \log ^5(x) x^3+3 \log ^6(x) x^2-182 x^2+10 x-9 \left (4 x^2-5 x^4\right ) \log ^4(x)-12 \left (12 x^3-5 x^5\right ) \log ^3(x)+9 \left (5 x^6-24 x^4+16 x^2\right ) \log ^2(x)+2 \left (9 x^7-72 x^5+144 x^3+5 x+5\right ) \log (x)\right )}{x \left (-x^2-2 \log (x) x-\log ^2(x)+4\right )^3}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {2}{3} \int \frac {3 x^8-36 x^6+144 x^4+18 \log ^5(x) x^3+3 \log ^6(x) x^2-182 x^2+10 x-9 \left (4 x^2-5 x^4\right ) \log ^4(x)-12 \left (12 x^3-5 x^5\right ) \log ^3(x)+9 \left (5 x^6-24 x^4+16 x^2\right ) \log ^2(x)+2 \left (9 x^7-72 x^5+144 x^3+5 x+5\right ) \log (x)}{x \left (-x^2-2 \log (x) x-\log ^2(x)+4\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {2}{3} \int \left (-3 x+\frac {5 (x+1)}{64 (x+\log (x)-2)^2 x}-\frac {5 (x+1)}{64 (x+\log (x)+2)^2 x}-\frac {5 (x+1)}{16 (x+\log (x)-2)^3 x}-\frac {5 (x+1)}{16 (x+\log (x)+2)^3 x}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle \frac {2}{3} \left (-\frac {3 x^2}{2}+\frac {5}{64 (-x-\log (x)+2)}+\frac {5}{64 (x+\log (x)+2)}+\frac {5}{32 (-x-\log (x)+2)^2}+\frac {5}{32 (x+\log (x)+2)^2}\right )\) |
Input:
Int[(-20*x + 364*x^2 - 288*x^4 + 72*x^6 - 6*x^8 + (-20 - 20*x - 576*x^3 + 288*x^5 - 36*x^7)*Log[x] + (-288*x^2 + 432*x^4 - 90*x^6)*Log[x]^2 + (288*x ^3 - 120*x^5)*Log[x]^3 + (72*x^2 - 90*x^4)*Log[x]^4 - 36*x^3*Log[x]^5 - 6* x^2*Log[x]^6)/(-192*x + 144*x^3 - 36*x^5 + 3*x^7 + (288*x^2 - 144*x^4 + 18 *x^6)*Log[x] + (144*x - 216*x^3 + 45*x^5)*Log[x]^2 + (-144*x^2 + 60*x^4)*L og[x]^3 + (-36*x + 45*x^3)*Log[x]^4 + 18*x^2*Log[x]^5 + 3*x*Log[x]^6),x]
Output:
(2*((-3*x^2)/2 + 5/(32*(2 - x - Log[x])^2) + 5/(64*(2 - x - Log[x])) + 5/( 32*(2 + x + Log[x])^2) + 5/(64*(2 + x + Log[x]))))/3
Int[(a_)*(Fx_), x_Symbol] :> Simp[a Int[Fx, x], x] /; FreeQ[a, x] && !Ma tchQ[Fx, (b_)*(Gx_) /; FreeQ[b, x]]
Time = 89.32 (sec) , antiderivative size = 25, normalized size of antiderivative = 1.19
| method | result | size |
| default | \(-x^{2}+\frac {5}{3 \left (\ln \left (x \right )^{2}+2 x \ln \left (x \right )+x^{2}-4\right )^{2}}\) | \(25\) |
| risch | \(-x^{2}+\frac {5}{3 \left (\ln \left (x \right )^{2}+2 x \ln \left (x \right )+x^{2}-4\right )^{2}}\) | \(25\) |
| parallelrisch | \(\frac {5-3 x^{6}-48 x^{2}+24 x^{4}-12 x^{3} \ln \left (x \right )^{3}+24 x^{2} \ln \left (x \right )^{2}-3 x^{2} \ln \left (x \right )^{4}+48 x^{3} \ln \left (x \right )-12 x^{5} \ln \left (x \right )-18 x^{4} \ln \left (x \right )^{2}}{3 x^{4}+12 x^{3} \ln \left (x \right )+18 x^{2} \ln \left (x \right )^{2}+12 x \ln \left (x \right )^{3}+3 \ln \left (x \right )^{4}-24 x^{2}-48 x \ln \left (x \right )-24 \ln \left (x \right )^{2}+48}\) | \(120\) |
Input:
int((-6*x^2*ln(x)^6-36*x^3*ln(x)^5+(-90*x^4+72*x^2)*ln(x)^4+(-120*x^5+288* x^3)*ln(x)^3+(-90*x^6+432*x^4-288*x^2)*ln(x)^2+(-36*x^7+288*x^5-576*x^3-20 *x-20)*ln(x)-6*x^8+72*x^6-288*x^4+364*x^2-20*x)/(3*x*ln(x)^6+18*x^2*ln(x)^ 5+(45*x^3-36*x)*ln(x)^4+(60*x^4-144*x^2)*ln(x)^3+(45*x^5-216*x^3+144*x)*ln (x)^2+(18*x^6-144*x^4+288*x^2)*ln(x)+3*x^7-36*x^5+144*x^3-192*x),x,method= _RETURNVERBOSE)
Output:
-x^2+5/3/(ln(x)^2+2*x*ln(x)+x^2-4)^2
Leaf count of result is larger than twice the leaf count of optimal. 114 vs. \(2 (19) = 38\).
Time = 0.07 (sec) , antiderivative size = 114, normalized size of antiderivative = 5.43 \[ \int \frac {-20 x+364 x^2-288 x^4+72 x^6-6 x^8+\left (-20-20 x-576 x^3+288 x^5-36 x^7\right ) \log (x)+\left (-288 x^2+432 x^4-90 x^6\right ) \log ^2(x)+\left (288 x^3-120 x^5\right ) \log ^3(x)+\left (72 x^2-90 x^4\right ) \log ^4(x)-36 x^3 \log ^5(x)-6 x^2 \log ^6(x)}{-192 x+144 x^3-36 x^5+3 x^7+\left (288 x^2-144 x^4+18 x^6\right ) \log (x)+\left (144 x-216 x^3+45 x^5\right ) \log ^2(x)+\left (-144 x^2+60 x^4\right ) \log ^3(x)+\left (-36 x+45 x^3\right ) \log ^4(x)+18 x^2 \log ^5(x)+3 x \log ^6(x)} \, dx=-\frac {3 \, x^{6} + 12 \, x^{3} \log \left (x\right )^{3} + 3 \, x^{2} \log \left (x\right )^{4} - 24 \, x^{4} + 6 \, {\left (3 \, x^{4} - 4 \, x^{2}\right )} \log \left (x\right )^{2} + 48 \, x^{2} + 12 \, {\left (x^{5} - 4 \, x^{3}\right )} \log \left (x\right ) - 5}{3 \, {\left (x^{4} + 4 \, x \log \left (x\right )^{3} + \log \left (x\right )^{4} + 2 \, {\left (3 \, x^{2} - 4\right )} \log \left (x\right )^{2} - 8 \, x^{2} + 4 \, {\left (x^{3} - 4 \, x\right )} \log \left (x\right ) + 16\right )}} \] Input:
integrate((-6*x^2*log(x)^6-36*x^3*log(x)^5+(-90*x^4+72*x^2)*log(x)^4+(-120 *x^5+288*x^3)*log(x)^3+(-90*x^6+432*x^4-288*x^2)*log(x)^2+(-36*x^7+288*x^5 -576*x^3-20*x-20)*log(x)-6*x^8+72*x^6-288*x^4+364*x^2-20*x)/(3*x*log(x)^6+ 18*x^2*log(x)^5+(45*x^3-36*x)*log(x)^4+(60*x^4-144*x^2)*log(x)^3+(45*x^5-2 16*x^3+144*x)*log(x)^2+(18*x^6-144*x^4+288*x^2)*log(x)+3*x^7-36*x^5+144*x^ 3-192*x),x, algorithm="fricas")
Output:
-1/3*(3*x^6 + 12*x^3*log(x)^3 + 3*x^2*log(x)^4 - 24*x^4 + 6*(3*x^4 - 4*x^2 )*log(x)^2 + 48*x^2 + 12*(x^5 - 4*x^3)*log(x) - 5)/(x^4 + 4*x*log(x)^3 + l og(x)^4 + 2*(3*x^2 - 4)*log(x)^2 - 8*x^2 + 4*(x^3 - 4*x)*log(x) + 16)
Leaf count of result is larger than twice the leaf count of optimal. 54 vs. \(2 (17) = 34\).
Time = 0.13 (sec) , antiderivative size = 54, normalized size of antiderivative = 2.57 \[ \int \frac {-20 x+364 x^2-288 x^4+72 x^6-6 x^8+\left (-20-20 x-576 x^3+288 x^5-36 x^7\right ) \log (x)+\left (-288 x^2+432 x^4-90 x^6\right ) \log ^2(x)+\left (288 x^3-120 x^5\right ) \log ^3(x)+\left (72 x^2-90 x^4\right ) \log ^4(x)-36 x^3 \log ^5(x)-6 x^2 \log ^6(x)}{-192 x+144 x^3-36 x^5+3 x^7+\left (288 x^2-144 x^4+18 x^6\right ) \log (x)+\left (144 x-216 x^3+45 x^5\right ) \log ^2(x)+\left (-144 x^2+60 x^4\right ) \log ^3(x)+\left (-36 x+45 x^3\right ) \log ^4(x)+18 x^2 \log ^5(x)+3 x \log ^6(x)} \, dx=- x^{2} + \frac {5}{3 x^{4} - 24 x^{2} + 12 x \log {\left (x \right )}^{3} + \left (18 x^{2} - 24\right ) \log {\left (x \right )}^{2} + \left (12 x^{3} - 48 x\right ) \log {\left (x \right )} + 3 \log {\left (x \right )}^{4} + 48} \] Input:
integrate((-6*x**2*ln(x)**6-36*x**3*ln(x)**5+(-90*x**4+72*x**2)*ln(x)**4+( -120*x**5+288*x**3)*ln(x)**3+(-90*x**6+432*x**4-288*x**2)*ln(x)**2+(-36*x* *7+288*x**5-576*x**3-20*x-20)*ln(x)-6*x**8+72*x**6-288*x**4+364*x**2-20*x) /(3*x*ln(x)**6+18*x**2*ln(x)**5+(45*x**3-36*x)*ln(x)**4+(60*x**4-144*x**2) *ln(x)**3+(45*x**5-216*x**3+144*x)*ln(x)**2+(18*x**6-144*x**4+288*x**2)*ln (x)+3*x**7-36*x**5+144*x**3-192*x),x)
Output:
-x**2 + 5/(3*x**4 - 24*x**2 + 12*x*log(x)**3 + (18*x**2 - 24)*log(x)**2 + (12*x**3 - 48*x)*log(x) + 3*log(x)**4 + 48)
Leaf count of result is larger than twice the leaf count of optimal. 114 vs. \(2 (19) = 38\).
Time = 0.11 (sec) , antiderivative size = 114, normalized size of antiderivative = 5.43 \[ \int \frac {-20 x+364 x^2-288 x^4+72 x^6-6 x^8+\left (-20-20 x-576 x^3+288 x^5-36 x^7\right ) \log (x)+\left (-288 x^2+432 x^4-90 x^6\right ) \log ^2(x)+\left (288 x^3-120 x^5\right ) \log ^3(x)+\left (72 x^2-90 x^4\right ) \log ^4(x)-36 x^3 \log ^5(x)-6 x^2 \log ^6(x)}{-192 x+144 x^3-36 x^5+3 x^7+\left (288 x^2-144 x^4+18 x^6\right ) \log (x)+\left (144 x-216 x^3+45 x^5\right ) \log ^2(x)+\left (-144 x^2+60 x^4\right ) \log ^3(x)+\left (-36 x+45 x^3\right ) \log ^4(x)+18 x^2 \log ^5(x)+3 x \log ^6(x)} \, dx=-\frac {3 \, x^{6} + 12 \, x^{3} \log \left (x\right )^{3} + 3 \, x^{2} \log \left (x\right )^{4} - 24 \, x^{4} + 6 \, {\left (3 \, x^{4} - 4 \, x^{2}\right )} \log \left (x\right )^{2} + 48 \, x^{2} + 12 \, {\left (x^{5} - 4 \, x^{3}\right )} \log \left (x\right ) - 5}{3 \, {\left (x^{4} + 4 \, x \log \left (x\right )^{3} + \log \left (x\right )^{4} + 2 \, {\left (3 \, x^{2} - 4\right )} \log \left (x\right )^{2} - 8 \, x^{2} + 4 \, {\left (x^{3} - 4 \, x\right )} \log \left (x\right ) + 16\right )}} \] Input:
integrate((-6*x^2*log(x)^6-36*x^3*log(x)^5+(-90*x^4+72*x^2)*log(x)^4+(-120 *x^5+288*x^3)*log(x)^3+(-90*x^6+432*x^4-288*x^2)*log(x)^2+(-36*x^7+288*x^5 -576*x^3-20*x-20)*log(x)-6*x^8+72*x^6-288*x^4+364*x^2-20*x)/(3*x*log(x)^6+ 18*x^2*log(x)^5+(45*x^3-36*x)*log(x)^4+(60*x^4-144*x^2)*log(x)^3+(45*x^5-2 16*x^3+144*x)*log(x)^2+(18*x^6-144*x^4+288*x^2)*log(x)+3*x^7-36*x^5+144*x^ 3-192*x),x, algorithm="maxima")
Output:
-1/3*(3*x^6 + 12*x^3*log(x)^3 + 3*x^2*log(x)^4 - 24*x^4 + 6*(3*x^4 - 4*x^2 )*log(x)^2 + 48*x^2 + 12*(x^5 - 4*x^3)*log(x) - 5)/(x^4 + 4*x*log(x)^3 + l og(x)^4 + 2*(3*x^2 - 4)*log(x)^2 - 8*x^2 + 4*(x^3 - 4*x)*log(x) + 16)
Leaf count of result is larger than twice the leaf count of optimal. 117 vs. \(2 (19) = 38\).
Time = 0.17 (sec) , antiderivative size = 117, normalized size of antiderivative = 5.57 \[ \int \frac {-20 x+364 x^2-288 x^4+72 x^6-6 x^8+\left (-20-20 x-576 x^3+288 x^5-36 x^7\right ) \log (x)+\left (-288 x^2+432 x^4-90 x^6\right ) \log ^2(x)+\left (288 x^3-120 x^5\right ) \log ^3(x)+\left (72 x^2-90 x^4\right ) \log ^4(x)-36 x^3 \log ^5(x)-6 x^2 \log ^6(x)}{-192 x+144 x^3-36 x^5+3 x^7+\left (288 x^2-144 x^4+18 x^6\right ) \log (x)+\left (144 x-216 x^3+45 x^5\right ) \log ^2(x)+\left (-144 x^2+60 x^4\right ) \log ^3(x)+\left (-36 x+45 x^3\right ) \log ^4(x)+18 x^2 \log ^5(x)+3 x \log ^6(x)} \, dx=-x^{2} + \frac {5 \, {\left (x + 1\right )}}{3 \, {\left (x^{5} + 4 \, x^{4} \log \left (x\right ) + 6 \, x^{3} \log \left (x\right )^{2} + 4 \, x^{2} \log \left (x\right )^{3} + x \log \left (x\right )^{4} + x^{4} + 4 \, x^{3} \log \left (x\right ) + 6 \, x^{2} \log \left (x\right )^{2} + 4 \, x \log \left (x\right )^{3} + \log \left (x\right )^{4} - 8 \, x^{3} - 16 \, x^{2} \log \left (x\right ) - 8 \, x \log \left (x\right )^{2} - 8 \, x^{2} - 16 \, x \log \left (x\right ) - 8 \, \log \left (x\right )^{2} + 16 \, x + 16\right )}} \] Input:
integrate((-6*x^2*log(x)^6-36*x^3*log(x)^5+(-90*x^4+72*x^2)*log(x)^4+(-120 *x^5+288*x^3)*log(x)^3+(-90*x^6+432*x^4-288*x^2)*log(x)^2+(-36*x^7+288*x^5 -576*x^3-20*x-20)*log(x)-6*x^8+72*x^6-288*x^4+364*x^2-20*x)/(3*x*log(x)^6+ 18*x^2*log(x)^5+(45*x^3-36*x)*log(x)^4+(60*x^4-144*x^2)*log(x)^3+(45*x^5-2 16*x^3+144*x)*log(x)^2+(18*x^6-144*x^4+288*x^2)*log(x)+3*x^7-36*x^5+144*x^ 3-192*x),x, algorithm="giac")
Output:
-x^2 + 5/3*(x + 1)/(x^5 + 4*x^4*log(x) + 6*x^3*log(x)^2 + 4*x^2*log(x)^3 + x*log(x)^4 + x^4 + 4*x^3*log(x) + 6*x^2*log(x)^2 + 4*x*log(x)^3 + log(x)^ 4 - 8*x^3 - 16*x^2*log(x) - 8*x*log(x)^2 - 8*x^2 - 16*x*log(x) - 8*log(x)^ 2 + 16*x + 16)
Timed out. \[ \int \frac {-20 x+364 x^2-288 x^4+72 x^6-6 x^8+\left (-20-20 x-576 x^3+288 x^5-36 x^7\right ) \log (x)+\left (-288 x^2+432 x^4-90 x^6\right ) \log ^2(x)+\left (288 x^3-120 x^5\right ) \log ^3(x)+\left (72 x^2-90 x^4\right ) \log ^4(x)-36 x^3 \log ^5(x)-6 x^2 \log ^6(x)}{-192 x+144 x^3-36 x^5+3 x^7+\left (288 x^2-144 x^4+18 x^6\right ) \log (x)+\left (144 x-216 x^3+45 x^5\right ) \log ^2(x)+\left (-144 x^2+60 x^4\right ) \log ^3(x)+\left (-36 x+45 x^3\right ) \log ^4(x)+18 x^2 \log ^5(x)+3 x \log ^6(x)} \, dx=\int -\frac {20\,x+\ln \left (x\right )\,\left (36\,x^7-288\,x^5+576\,x^3+20\,x+20\right )-{\ln \left (x\right )}^4\,\left (72\,x^2-90\,x^4\right )-{\ln \left (x\right )}^3\,\left (288\,x^3-120\,x^5\right )+6\,x^2\,{\ln \left (x\right )}^6+36\,x^3\,{\ln \left (x\right )}^5+{\ln \left (x\right )}^2\,\left (90\,x^6-432\,x^4+288\,x^2\right )-364\,x^2+288\,x^4-72\,x^6+6\,x^8}{3\,x\,{\ln \left (x\right )}^6-{\ln \left (x\right )}^4\,\left (36\,x-45\,x^3\right )-192\,x+{\ln \left (x\right )}^2\,\left (45\,x^5-216\,x^3+144\,x\right )+\ln \left (x\right )\,\left (18\,x^6-144\,x^4+288\,x^2\right )-{\ln \left (x\right )}^3\,\left (144\,x^2-60\,x^4\right )+18\,x^2\,{\ln \left (x\right )}^5+144\,x^3-36\,x^5+3\,x^7} \,d x \] Input:
int(-(20*x + log(x)*(20*x + 576*x^3 - 288*x^5 + 36*x^7 + 20) - log(x)^4*(7 2*x^2 - 90*x^4) - log(x)^3*(288*x^3 - 120*x^5) + 6*x^2*log(x)^6 + 36*x^3*l og(x)^5 + log(x)^2*(288*x^2 - 432*x^4 + 90*x^6) - 364*x^2 + 288*x^4 - 72*x ^6 + 6*x^8)/(3*x*log(x)^6 - log(x)^4*(36*x - 45*x^3) - 192*x + log(x)^2*(1 44*x - 216*x^3 + 45*x^5) + log(x)*(288*x^2 - 144*x^4 + 18*x^6) - log(x)^3* (144*x^2 - 60*x^4) + 18*x^2*log(x)^5 + 144*x^3 - 36*x^5 + 3*x^7),x)
Output:
int(-(20*x + log(x)*(20*x + 576*x^3 - 288*x^5 + 36*x^7 + 20) - log(x)^4*(7 2*x^2 - 90*x^4) - log(x)^3*(288*x^3 - 120*x^5) + 6*x^2*log(x)^6 + 36*x^3*l og(x)^5 + log(x)^2*(288*x^2 - 432*x^4 + 90*x^6) - 364*x^2 + 288*x^4 - 72*x ^6 + 6*x^8)/(3*x*log(x)^6 - log(x)^4*(36*x - 45*x^3) - 192*x + log(x)^2*(1 44*x - 216*x^3 + 45*x^5) + log(x)*(288*x^2 - 144*x^4 + 18*x^6) - log(x)^3* (144*x^2 - 60*x^4) + 18*x^2*log(x)^5 + 144*x^3 - 36*x^5 + 3*x^7), x)
Time = 0.22 (sec) , antiderivative size = 122, normalized size of antiderivative = 5.81 \[ \int \frac {-20 x+364 x^2-288 x^4+72 x^6-6 x^8+\left (-20-20 x-576 x^3+288 x^5-36 x^7\right ) \log (x)+\left (-288 x^2+432 x^4-90 x^6\right ) \log ^2(x)+\left (288 x^3-120 x^5\right ) \log ^3(x)+\left (72 x^2-90 x^4\right ) \log ^4(x)-36 x^3 \log ^5(x)-6 x^2 \log ^6(x)}{-192 x+144 x^3-36 x^5+3 x^7+\left (288 x^2-144 x^4+18 x^6\right ) \log (x)+\left (144 x-216 x^3+45 x^5\right ) \log ^2(x)+\left (-144 x^2+60 x^4\right ) \log ^3(x)+\left (-36 x+45 x^3\right ) \log ^4(x)+18 x^2 \log ^5(x)+3 x \log ^6(x)} \, dx=\frac {-3 \mathrm {log}\left (x \right )^{4} x^{2}-12 \mathrm {log}\left (x \right )^{3} x^{3}-18 \mathrm {log}\left (x \right )^{2} x^{4}+24 \mathrm {log}\left (x \right )^{2} x^{2}-12 \,\mathrm {log}\left (x \right ) x^{5}+48 \,\mathrm {log}\left (x \right ) x^{3}-3 x^{6}+24 x^{4}-48 x^{2}+5}{3 \mathrm {log}\left (x \right )^{4}+12 \mathrm {log}\left (x \right )^{3} x +18 \mathrm {log}\left (x \right )^{2} x^{2}-24 \mathrm {log}\left (x \right )^{2}+12 \,\mathrm {log}\left (x \right ) x^{3}-48 \,\mathrm {log}\left (x \right ) x +3 x^{4}-24 x^{2}+48} \] Input:
int((-6*x^2*log(x)^6-36*x^3*log(x)^5+(-90*x^4+72*x^2)*log(x)^4+(-120*x^5+2 88*x^3)*log(x)^3+(-90*x^6+432*x^4-288*x^2)*log(x)^2+(-36*x^7+288*x^5-576*x ^3-20*x-20)*log(x)-6*x^8+72*x^6-288*x^4+364*x^2-20*x)/(3*x*log(x)^6+18*x^2 *log(x)^5+(45*x^3-36*x)*log(x)^4+(60*x^4-144*x^2)*log(x)^3+(45*x^5-216*x^3 +144*x)*log(x)^2+(18*x^6-144*x^4+288*x^2)*log(x)+3*x^7-36*x^5+144*x^3-192* x),x)
Output:
( - 3*log(x)**4*x**2 - 12*log(x)**3*x**3 - 18*log(x)**2*x**4 + 24*log(x)** 2*x**2 - 12*log(x)*x**5 + 48*log(x)*x**3 - 3*x**6 + 24*x**4 - 48*x**2 + 5) /(3*(log(x)**4 + 4*log(x)**3*x + 6*log(x)**2*x**2 - 8*log(x)**2 + 4*log(x) *x**3 - 16*log(x)*x + x**4 - 8*x**2 + 16))