Integrand size = 152, antiderivative size = 19 \[ \int \frac {1500+800 x-480 x^2-384 x^3-64 x^4+\left (3000+3600 x+1440 x^2+192 x^3\right ) \log ^2(3)+\left (900+120 x-336 x^2-96 x^3+\left (1800+1440 x+288 x^2\right ) \log ^2(3)\right ) \log \left (-2+x-3 \log ^2(3)\right )+\left (180-48 x-48 x^2+(360+144 x) \log ^2(3)\right ) \log ^2\left (-2+x-3 \log ^2(3)\right )+\left (12-8 x+24 \log ^2(3)\right ) \log ^3\left (-2+x-3 \log ^2(3)\right )}{2-x+3 \log ^2(3)} \, dx=-1+\left (5+2 x+\log \left (-2+x-3 \log ^2(3)\right )\right )^4 \]
Time = 0.03 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.89 \[ \int \frac {1500+800 x-480 x^2-384 x^3-64 x^4+\left (3000+3600 x+1440 x^2+192 x^3\right ) \log ^2(3)+\left (900+120 x-336 x^2-96 x^3+\left (1800+1440 x+288 x^2\right ) \log ^2(3)\right ) \log \left (-2+x-3 \log ^2(3)\right )+\left (180-48 x-48 x^2+(360+144 x) \log ^2(3)\right ) \log ^2\left (-2+x-3 \log ^2(3)\right )+\left (12-8 x+24 \log ^2(3)\right ) \log ^3\left (-2+x-3 \log ^2(3)\right )}{2-x+3 \log ^2(3)} \, dx=\left (5+2 x+\log \left (-2+x-3 \log ^2(3)\right )\right )^4 \]
Integrate[(1500 + 800*x - 480*x^2 - 384*x^3 - 64*x^4 + (3000 + 3600*x + 14 40*x^2 + 192*x^3)*Log[3]^2 + (900 + 120*x - 336*x^2 - 96*x^3 + (1800 + 144 0*x + 288*x^2)*Log[3]^2)*Log[-2 + x - 3*Log[3]^2] + (180 - 48*x - 48*x^2 + (360 + 144*x)*Log[3]^2)*Log[-2 + x - 3*Log[3]^2]^2 + (12 - 8*x + 24*Log[3 ]^2)*Log[-2 + x - 3*Log[3]^2]^3)/(2 - x + 3*Log[3]^2),x]
Time = 0.48 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.89, number of steps used = 4, number of rules used = 4, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.026, Rules used = {7239, 27, 25, 7237}
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.
| \(\displaystyle \int \frac {-64 x^4-384 x^3-480 x^2+\left (-48 x^2-48 x+(144 x+360) \log ^2(3)+180\right ) \log ^2\left (x-2-3 \log ^2(3)\right )+\left (-96 x^3-336 x^2+\left (288 x^2+1440 x+1800\right ) \log ^2(3)+120 x+900\right ) \log \left (x-2-3 \log ^2(3)\right )+\left (192 x^3+1440 x^2+3600 x+3000\right ) \log ^2(3)+800 x+\left (-8 x+12+24 \log ^2(3)\right ) \log ^3\left (x-2-3 \log ^2(3)\right )+1500}{-x+2+3 \log ^2(3)} \, dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {4 \left (-2 x+3+6 \log ^2(3)\right ) \left (2 x+\log \left (x-2-3 \log ^2(3)\right )+5\right )^3}{-x+2+3 \log ^2(3)}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle 4 \int -\frac {\left (2 x-3 \left (1+2 \log ^2(3)\right )\right ) \left (2 x+\log \left (x-3 \log ^2(3)-2\right )+5\right )^3}{-x+3 \log ^2(3)+2}dx\) |
| \(\Big \downarrow \) 25 |
| \(\displaystyle -4 \int \frac {\left (2 x-3 \left (1+2 \log ^2(3)\right )\right ) \left (2 x+\log \left (x-3 \log ^2(3)-2\right )+5\right )^3}{-x+3 \log ^2(3)+2}dx\) |
| \(\Big \downarrow \) 7237 |
| \(\displaystyle \left (2 x+\log \left (x-2-3 \log ^2(3)\right )+5\right )^4\) |
Int[(1500 + 800*x - 480*x^2 - 384*x^3 - 64*x^4 + (3000 + 3600*x + 1440*x^2 + 192*x^3)*Log[3]^2 + (900 + 120*x - 336*x^2 - 96*x^3 + (1800 + 1440*x + 288*x^2)*Log[3]^2)*Log[-2 + x - 3*Log[3]^2] + (180 - 48*x - 48*x^2 + (360 + 144*x)*Log[3]^2)*Log[-2 + x - 3*Log[3]^2]^2 + (12 - 8*x + 24*Log[3]^2)*L og[-2 + x - 3*Log[3]^2]^3)/(2 - x + 3*Log[3]^2),x]
3.23.4.3.1 Defintions of rubi rules used
Int[(a_)*(Fx_), x_Symbol] :> Simp[a Int[Fx, x], x] /; FreeQ[a, x] && !Ma tchQ[Fx, (b_)*(Gx_) /; FreeQ[b, x]]
Int[(u_)*(y_)^(m_.), x_Symbol] :> With[{q = DerivativeDivides[y, u, x]}, Si mp[q*(y^(m + 1)/(m + 1)), x] /; !FalseQ[q]] /; FreeQ[m, x] && NeQ[m, -1]
Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; Simpl erIntegrandQ[v, u, x]]
Leaf count of result is larger than twice the leaf count of optimal. \(80\) vs. \(2(19)=38\).
Time = 0.35 (sec) , antiderivative size = 81, normalized size of antiderivative = 4.26
| method | result | size |
| risch | \(\ln \left (-3 \ln \left (3\right )^{2}+x -2\right )^{4}+\left (8 x +20\right ) \ln \left (-3 \ln \left (3\right )^{2}+x -2\right )^{3}+\left (24 x^{2}+120 x +150\right ) \ln \left (-3 \ln \left (3\right )^{2}+x -2\right )^{2}+4 \left (5+2 x \right )^{3} \ln \left (-3 \ln \left (3\right )^{2}+x -2\right )+\left (5+2 x \right )^{4}\) | \(81\) |
| norman | \(\ln \left (-3 \ln \left (3\right )^{2}+x -2\right )^{4}+500 \ln \left (-3 \ln \left (3\right )^{2}+x -2\right )+1000 x +600 x^{2}+160 x^{3}+16 x^{4}+150 \ln \left (-3 \ln \left (3\right )^{2}+x -2\right )^{2}+20 \ln \left (-3 \ln \left (3\right )^{2}+x -2\right )^{3}+600 \ln \left (-3 \ln \left (3\right )^{2}+x -2\right ) x +240 \ln \left (-3 \ln \left (3\right )^{2}+x -2\right ) x^{2}+32 \ln \left (-3 \ln \left (3\right )^{2}+x -2\right ) x^{3}+120 \ln \left (-3 \ln \left (3\right )^{2}+x -2\right )^{2} x +24 \ln \left (-3 \ln \left (3\right )^{2}+x -2\right )^{2} x^{2}+8 \ln \left (-3 \ln \left (3\right )^{2}+x -2\right )^{3} x\) | \(162\) |
| parallelrisch | \(-5400 \ln \left (3\right )^{4}+16 x^{4}+32 \ln \left (-3 \ln \left (3\right )^{2}+x -2\right ) x^{3}+24 \ln \left (-3 \ln \left (3\right )^{2}+x -2\right )^{2} x^{2}+8 \ln \left (-3 \ln \left (3\right )^{2}+x -2\right )^{3} x +\ln \left (-3 \ln \left (3\right )^{2}+x -2\right )^{4}+160 x^{3}+240 \ln \left (-3 \ln \left (3\right )^{2}+x -2\right ) x^{2}+120 \ln \left (-3 \ln \left (3\right )^{2}+x -2\right )^{2} x +20 \ln \left (-3 \ln \left (3\right )^{2}+x -2\right )^{3}-1200 \ln \left (3\right )^{2}+600 x^{2}+600 \ln \left (-3 \ln \left (3\right )^{2}+x -2\right ) x +150 \ln \left (-3 \ln \left (3\right )^{2}+x -2\right )^{2}+1000 x +500 \ln \left (-3 \ln \left (3\right )^{2}+x -2\right )+1600\) | \(175\) |
| parts | \(1048 x +1584 \ln \left (3\right )^{6}-216 x \ln \left (3\right )^{2}+7164 \ln \left (3\right )^{4}+8664 \ln \left (3\right )^{2}+16 x^{4}+160 x^{3}+588 x^{2}-4608 \ln \left (-3 \ln \left (3\right )^{2}+x -2\right ) \ln \left (3\right )^{2}+12 \left (-3 \ln \left (3\right )^{2}+x -2\right )^{2}+\ln \left (-3 \ln \left (3\right )^{2}+x -2\right )^{4}+24 \ln \left (3\right )^{2} \ln \left (-3 \ln \left (3\right )^{2}+x -2\right )^{3}-6912 \ln \left (3\right )^{4} \ln \left (-3 \ln \left (3\right )^{2}+x -2\right )+648 \ln \left (3\right )^{2} \ln \left (-3 \ln \left (3\right )^{2}+x -2\right )^{2}+8 \ln \left (-3 \ln \left (3\right )^{2}+x -2\right )^{3} \left (-3 \ln \left (3\right )^{2}+x -2\right )+24 \ln \left (-3 \ln \left (3\right )^{2}+x -2\right )^{2} \left (-3 \ln \left (3\right )^{2}+x -2\right )^{2}+32 \ln \left (-3 \ln \left (3\right )^{2}+x -2\right ) \left (-3 \ln \left (3\right )^{2}+x -2\right )^{3}+432 \ln \left (-3 \ln \left (3\right )^{2}+x -2\right ) \left (-3 \ln \left (3\right )^{2}+x -2\right )^{2}+216 \ln \left (3\right )^{4} \ln \left (-3 \ln \left (3\right )^{2}+x -2\right )^{2}+1944 \ln \left (-3 \ln \left (3\right )^{2}+x -2\right ) \left (-3 \ln \left (3\right )^{2}+x -2\right )+216 \ln \left (-3 \ln \left (3\right )^{2}+x -2\right )^{2} \left (-3 \ln \left (3\right )^{2}+x -2\right )+144 \ln \left (3\right )^{2} \left (\ln \left (-3 \ln \left (3\right )^{2}+x -2\right )^{2} \left (-3 \ln \left (3\right )^{2}+x -2\right )-2 \ln \left (-3 \ln \left (3\right )^{2}+x -2\right ) \left (-3 \ln \left (3\right )^{2}+x -2\right )-6 \ln \left (3\right )^{2}+2 x -4\right )+288 \ln \left (-3 \ln \left (3\right )^{2}+x -2\right ) \ln \left (3\right )^{2} x^{2}+1728 \ln \left (-3 \ln \left (3\right )^{2}+x -2\right ) \ln \left (3\right )^{2} x +4 \left (216 \ln \left (3\right )^{6}+972 \ln \left (3\right )^{4}+1458 \ln \left (3\right )^{2}+729\right ) \ln \left (-3 \ln \left (3\right )^{2}+x -2\right )+\frac {9184}{3}+36 \ln \left (-3 \ln \left (3\right )^{2}+x -2\right )^{3}+486 \ln \left (-3 \ln \left (3\right )^{2}+x -2\right )^{2}-864 \ln \left (3\right )^{4} \ln \left (-3 \ln \left (3\right )^{2}+x -2\right ) x\) | \(468\) |
| derivativedivides | \(-11664+5832 x +2916 \ln \left (-3 \ln \left (3\right )^{2}+x -2\right )-17496 \ln \left (3\right )^{2}+5832 \ln \left (-3 \ln \left (3\right )^{2}+x -2\right ) \ln \left (3\right )^{2}+1944 \left (-3 \ln \left (3\right )^{2}+x -2\right )^{2}+\ln \left (-3 \ln \left (3\right )^{2}+x -2\right )^{4}+16 \left (-3 \ln \left (3\right )^{2}+x -2\right )^{4}+288 \left (-3 \ln \left (3\right )^{2}+x -2\right )^{3}+24 \ln \left (3\right )^{2} \ln \left (-3 \ln \left (3\right )^{2}+x -2\right )^{3}+3888 \ln \left (3\right )^{4} \ln \left (-3 \ln \left (3\right )^{2}+x -2\right )+8640 \ln \left (3\right )^{4} \left (-3 \ln \left (3\right )^{2}+x -2\right )+192 \ln \left (3\right )^{2} \left (-3 \ln \left (3\right )^{2}+x -2\right )^{3}+648 \ln \left (3\right )^{2} \ln \left (-3 \ln \left (3\right )^{2}+x -2\right )^{2}+2736 \ln \left (3\right )^{2} \left (-3 \ln \left (3\right )^{2}+x -2\right )^{2}+8 \ln \left (-3 \ln \left (3\right )^{2}+x -2\right )^{3} \left (-3 \ln \left (3\right )^{2}+x -2\right )+24 \ln \left (-3 \ln \left (3\right )^{2}+x -2\right )^{2} \left (-3 \ln \left (3\right )^{2}+x -2\right )^{2}+32 \ln \left (-3 \ln \left (3\right )^{2}+x -2\right ) \left (-3 \ln \left (3\right )^{2}+x -2\right )^{3}+14256 \ln \left (3\right )^{2} \left (-3 \ln \left (3\right )^{2}+x -2\right )+432 \ln \left (-3 \ln \left (3\right )^{2}+x -2\right ) \left (-3 \ln \left (3\right )^{2}+x -2\right )^{2}+576 \ln \left (3\right )^{2} \left (\frac {\ln \left (-3 \ln \left (3\right )^{2}+x -2\right ) \left (-3 \ln \left (3\right )^{2}+x -2\right )^{2}}{2}-\frac {\left (-3 \ln \left (3\right )^{2}+x -2\right )^{2}}{4}\right )+216 \ln \left (3\right )^{4} \ln \left (-3 \ln \left (3\right )^{2}+x -2\right )^{2}+864 \ln \left (3\right )^{6} \ln \left (-3 \ln \left (3\right )^{2}+x -2\right )+1944 \ln \left (-3 \ln \left (3\right )^{2}+x -2\right ) \left (-3 \ln \left (3\right )^{2}+x -2\right )+2880 \ln \left (3\right )^{2} \left (\ln \left (-3 \ln \left (3\right )^{2}+x -2\right ) \left (-3 \ln \left (3\right )^{2}+x -2\right )+3 \ln \left (3\right )^{2}-x +2\right )+864 \ln \left (3\right )^{4} \left (\ln \left (-3 \ln \left (3\right )^{2}+x -2\right ) \left (-3 \ln \left (3\right )^{2}+x -2\right )+3 \ln \left (3\right )^{2}-x +2\right )+216 \ln \left (-3 \ln \left (3\right )^{2}+x -2\right )^{2} \left (-3 \ln \left (3\right )^{2}+x -2\right )+144 \ln \left (3\right )^{2} \left (\ln \left (-3 \ln \left (3\right )^{2}+x -2\right )^{2} \left (-3 \ln \left (3\right )^{2}+x -2\right )-2 \ln \left (-3 \ln \left (3\right )^{2}+x -2\right ) \left (-3 \ln \left (3\right )^{2}+x -2\right )-6 \ln \left (3\right )^{2}+2 x -4\right )+1728 \ln \left (3\right )^{6} \left (-3 \ln \left (3\right )^{2}+x -2\right )+864 \ln \left (3\right )^{4} \left (-3 \ln \left (3\right )^{2}+x -2\right )^{2}+36 \ln \left (-3 \ln \left (3\right )^{2}+x -2\right )^{3}+486 \ln \left (-3 \ln \left (3\right )^{2}+x -2\right )^{2}\) | \(616\) |
| default | \(-11664+5832 x +2916 \ln \left (-3 \ln \left (3\right )^{2}+x -2\right )-17496 \ln \left (3\right )^{2}+5832 \ln \left (-3 \ln \left (3\right )^{2}+x -2\right ) \ln \left (3\right )^{2}+1944 \left (-3 \ln \left (3\right )^{2}+x -2\right )^{2}+\ln \left (-3 \ln \left (3\right )^{2}+x -2\right )^{4}+16 \left (-3 \ln \left (3\right )^{2}+x -2\right )^{4}+288 \left (-3 \ln \left (3\right )^{2}+x -2\right )^{3}+24 \ln \left (3\right )^{2} \ln \left (-3 \ln \left (3\right )^{2}+x -2\right )^{3}+3888 \ln \left (3\right )^{4} \ln \left (-3 \ln \left (3\right )^{2}+x -2\right )+8640 \ln \left (3\right )^{4} \left (-3 \ln \left (3\right )^{2}+x -2\right )+192 \ln \left (3\right )^{2} \left (-3 \ln \left (3\right )^{2}+x -2\right )^{3}+648 \ln \left (3\right )^{2} \ln \left (-3 \ln \left (3\right )^{2}+x -2\right )^{2}+2736 \ln \left (3\right )^{2} \left (-3 \ln \left (3\right )^{2}+x -2\right )^{2}+8 \ln \left (-3 \ln \left (3\right )^{2}+x -2\right )^{3} \left (-3 \ln \left (3\right )^{2}+x -2\right )+24 \ln \left (-3 \ln \left (3\right )^{2}+x -2\right )^{2} \left (-3 \ln \left (3\right )^{2}+x -2\right )^{2}+32 \ln \left (-3 \ln \left (3\right )^{2}+x -2\right ) \left (-3 \ln \left (3\right )^{2}+x -2\right )^{3}+14256 \ln \left (3\right )^{2} \left (-3 \ln \left (3\right )^{2}+x -2\right )+432 \ln \left (-3 \ln \left (3\right )^{2}+x -2\right ) \left (-3 \ln \left (3\right )^{2}+x -2\right )^{2}+576 \ln \left (3\right )^{2} \left (\frac {\ln \left (-3 \ln \left (3\right )^{2}+x -2\right ) \left (-3 \ln \left (3\right )^{2}+x -2\right )^{2}}{2}-\frac {\left (-3 \ln \left (3\right )^{2}+x -2\right )^{2}}{4}\right )+216 \ln \left (3\right )^{4} \ln \left (-3 \ln \left (3\right )^{2}+x -2\right )^{2}+864 \ln \left (3\right )^{6} \ln \left (-3 \ln \left (3\right )^{2}+x -2\right )+1944 \ln \left (-3 \ln \left (3\right )^{2}+x -2\right ) \left (-3 \ln \left (3\right )^{2}+x -2\right )+2880 \ln \left (3\right )^{2} \left (\ln \left (-3 \ln \left (3\right )^{2}+x -2\right ) \left (-3 \ln \left (3\right )^{2}+x -2\right )+3 \ln \left (3\right )^{2}-x +2\right )+864 \ln \left (3\right )^{4} \left (\ln \left (-3 \ln \left (3\right )^{2}+x -2\right ) \left (-3 \ln \left (3\right )^{2}+x -2\right )+3 \ln \left (3\right )^{2}-x +2\right )+216 \ln \left (-3 \ln \left (3\right )^{2}+x -2\right )^{2} \left (-3 \ln \left (3\right )^{2}+x -2\right )+144 \ln \left (3\right )^{2} \left (\ln \left (-3 \ln \left (3\right )^{2}+x -2\right )^{2} \left (-3 \ln \left (3\right )^{2}+x -2\right )-2 \ln \left (-3 \ln \left (3\right )^{2}+x -2\right ) \left (-3 \ln \left (3\right )^{2}+x -2\right )-6 \ln \left (3\right )^{2}+2 x -4\right )+1728 \ln \left (3\right )^{6} \left (-3 \ln \left (3\right )^{2}+x -2\right )+864 \ln \left (3\right )^{4} \left (-3 \ln \left (3\right )^{2}+x -2\right )^{2}+36 \ln \left (-3 \ln \left (3\right )^{2}+x -2\right )^{3}+486 \ln \left (-3 \ln \left (3\right )^{2}+x -2\right )^{2}\) | \(616\) |
int(((24*ln(3)^2-8*x+12)*ln(-3*ln(3)^2+x-2)^3+((144*x+360)*ln(3)^2-48*x^2- 48*x+180)*ln(-3*ln(3)^2+x-2)^2+((288*x^2+1440*x+1800)*ln(3)^2-96*x^3-336*x ^2+120*x+900)*ln(-3*ln(3)^2+x-2)+(192*x^3+1440*x^2+3600*x+3000)*ln(3)^2-64 *x^4-384*x^3-480*x^2+800*x+1500)/(3*ln(3)^2+2-x),x,method=_RETURNVERBOSE)
ln(-3*ln(3)^2+x-2)^4+(8*x+20)*ln(-3*ln(3)^2+x-2)^3+(24*x^2+120*x+150)*ln(- 3*ln(3)^2+x-2)^2+4*(5+2*x)^3*ln(-3*ln(3)^2+x-2)+(5+2*x)^4
Leaf count of result is larger than twice the leaf count of optimal. 101 vs. \(2 (19) = 38\).
Time = 0.25 (sec) , antiderivative size = 101, normalized size of antiderivative = 5.32 \[ \int \frac {1500+800 x-480 x^2-384 x^3-64 x^4+\left (3000+3600 x+1440 x^2+192 x^3\right ) \log ^2(3)+\left (900+120 x-336 x^2-96 x^3+\left (1800+1440 x+288 x^2\right ) \log ^2(3)\right ) \log \left (-2+x-3 \log ^2(3)\right )+\left (180-48 x-48 x^2+(360+144 x) \log ^2(3)\right ) \log ^2\left (-2+x-3 \log ^2(3)\right )+\left (12-8 x+24 \log ^2(3)\right ) \log ^3\left (-2+x-3 \log ^2(3)\right )}{2-x+3 \log ^2(3)} \, dx=16 \, x^{4} + 4 \, {\left (2 \, x + 5\right )} \log \left (-3 \, \log \left (3\right )^{2} + x - 2\right )^{3} + \log \left (-3 \, \log \left (3\right )^{2} + x - 2\right )^{4} + 160 \, x^{3} + 6 \, {\left (4 \, x^{2} + 20 \, x + 25\right )} \log \left (-3 \, \log \left (3\right )^{2} + x - 2\right )^{2} + 600 \, x^{2} + 4 \, {\left (8 \, x^{3} + 60 \, x^{2} + 150 \, x + 125\right )} \log \left (-3 \, \log \left (3\right )^{2} + x - 2\right ) + 1000 \, x \]
integrate(((24*log(3)^2-8*x+12)*log(-3*log(3)^2+x-2)^3+((144*x+360)*log(3) ^2-48*x^2-48*x+180)*log(-3*log(3)^2+x-2)^2+((288*x^2+1440*x+1800)*log(3)^2 -96*x^3-336*x^2+120*x+900)*log(-3*log(3)^2+x-2)+(192*x^3+1440*x^2+3600*x+3 000)*log(3)^2-64*x^4-384*x^3-480*x^2+800*x+1500)/(3*log(3)^2+2-x),x, algor ithm=\
16*x^4 + 4*(2*x + 5)*log(-3*log(3)^2 + x - 2)^3 + log(-3*log(3)^2 + x - 2) ^4 + 160*x^3 + 6*(4*x^2 + 20*x + 25)*log(-3*log(3)^2 + x - 2)^2 + 600*x^2 + 4*(8*x^3 + 60*x^2 + 150*x + 125)*log(-3*log(3)^2 + x - 2) + 1000*x
Leaf count of result is larger than twice the leaf count of optimal. 112 vs. \(2 (19) = 38\).
Time = 0.22 (sec) , antiderivative size = 112, normalized size of antiderivative = 5.89 \[ \int \frac {1500+800 x-480 x^2-384 x^3-64 x^4+\left (3000+3600 x+1440 x^2+192 x^3\right ) \log ^2(3)+\left (900+120 x-336 x^2-96 x^3+\left (1800+1440 x+288 x^2\right ) \log ^2(3)\right ) \log \left (-2+x-3 \log ^2(3)\right )+\left (180-48 x-48 x^2+(360+144 x) \log ^2(3)\right ) \log ^2\left (-2+x-3 \log ^2(3)\right )+\left (12-8 x+24 \log ^2(3)\right ) \log ^3\left (-2+x-3 \log ^2(3)\right )}{2-x+3 \log ^2(3)} \, dx=16 x^{4} + 160 x^{3} + 600 x^{2} + 1000 x + \left (8 x + 20\right ) \log {\left (x - 3 \log {\left (3 \right )}^{2} - 2 \right )}^{3} + \left (24 x^{2} + 120 x + 150\right ) \log {\left (x - 3 \log {\left (3 \right )}^{2} - 2 \right )}^{2} + \left (32 x^{3} + 240 x^{2} + 600 x\right ) \log {\left (x - 3 \log {\left (3 \right )}^{2} - 2 \right )} + \log {\left (x - 3 \log {\left (3 \right )}^{2} - 2 \right )}^{4} + 500 \log {\left (x - 3 \log {\left (3 \right )}^{2} - 2 \right )} \]
integrate(((24*ln(3)**2-8*x+12)*ln(-3*ln(3)**2+x-2)**3+((144*x+360)*ln(3)* *2-48*x**2-48*x+180)*ln(-3*ln(3)**2+x-2)**2+((288*x**2+1440*x+1800)*ln(3)* *2-96*x**3-336*x**2+120*x+900)*ln(-3*ln(3)**2+x-2)+(192*x**3+1440*x**2+360 0*x+3000)*ln(3)**2-64*x**4-384*x**3-480*x**2+800*x+1500)/(3*ln(3)**2+2-x), x)
16*x**4 + 160*x**3 + 600*x**2 + 1000*x + (8*x + 20)*log(x - 3*log(3)**2 - 2)**3 + (24*x**2 + 120*x + 150)*log(x - 3*log(3)**2 - 2)**2 + (32*x**3 + 2 40*x**2 + 600*x)*log(x - 3*log(3)**2 - 2) + log(x - 3*log(3)**2 - 2)**4 + 500*log(x - 3*log(3)**2 - 2)
Leaf count of result is larger than twice the leaf count of optimal. 1368 vs. \(2 (19) = 38\).
Time = 0.30 (sec) , antiderivative size = 1368, normalized size of antiderivative = 72.00 \[ \int \frac {1500+800 x-480 x^2-384 x^3-64 x^4+\left (3000+3600 x+1440 x^2+192 x^3\right ) \log ^2(3)+\left (900+120 x-336 x^2-96 x^3+\left (1800+1440 x+288 x^2\right ) \log ^2(3)\right ) \log \left (-2+x-3 \log ^2(3)\right )+\left (180-48 x-48 x^2+(360+144 x) \log ^2(3)\right ) \log ^2\left (-2+x-3 \log ^2(3)\right )+\left (12-8 x+24 \log ^2(3)\right ) \log ^3\left (-2+x-3 \log ^2(3)\right )}{2-x+3 \log ^2(3)} \, dx=\text {Too large to display} \]
integrate(((24*log(3)^2-8*x+12)*log(-3*log(3)^2+x-2)^3+((144*x+360)*log(3) ^2-48*x^2-48*x+180)*log(-3*log(3)^2+x-2)^2+((288*x^2+1440*x+1800)*log(3)^2 -96*x^3-336*x^2+120*x+900)*log(-3*log(3)^2+x-2)+(192*x^3+1440*x^2+3600*x+3 000)*log(3)^2-64*x^4-384*x^3-480*x^2+800*x+1500)/(3*log(3)^2+2-x),x, algor ithm=\
-6*log(3)^2*log(-3*log(3)^2 + x - 2)^4 - 120*log(3)^2*log(-3*log(3)^2 + x - 2)^3 + 2*(3*log(3)^2 + 2)*log(-3*log(3)^2 + x - 2)^4 + 64/3*(3*log(3)^2 + 2)*x^3 + 16*x^4 - 144*(2*(3*log(3)^2 + 2)*x + x^2 + 2*(9*log(3)^4 + 12*l og(3)^2 + 4)*log(-3*log(3)^2 + x - 2))*log(3)^2*log(-3*log(3)^2 + x - 2) - 1440*((3*log(3)^2 + 2)*log(-3*log(3)^2 + x - 2) + x)*log(3)^2*log(-3*log( 3)^2 + x - 2) - 1800*log(3)^2*log(3*log(3)^2 - x + 2)*log(-3*log(3)^2 + x - 2) + 16*(9*log(3)^4 + 12*log(3)^2 + 4)*log(-3*log(3)^2 + x - 2)^3 + 16*( 3*log(3)^2 + 2)*log(-3*log(3)^2 + x - 2)^3 - 3*log(-3*log(3)^2 + x - 2)^4 + 12*(3*log(3)^2 - x + 2)^2*(2*log(-3*log(3)^2 + x - 2)^2 - 2*log(-3*log(3 )^2 + x - 2) + 1) + 32*(9*log(3)^4 + 12*log(3)^2 + 4)*x^2 + 152*(3*log(3)^ 2 + 2)*x^2 + 352/3*x^3 - 48*((3*log(3)^2 + 2)*log(-3*log(3)^2 + x - 2)^3 - 3*(3*log(3)^2 - x + 2)*(log(-3*log(3)^2 + x - 2)^2 - 2*log(-3*log(3)^2 + x - 2) + 2))*log(3)^2 - 32*(3*(3*log(3)^2 + 2)*x^2 + 2*x^3 + 6*(9*log(3)^4 + 12*log(3)^2 + 4)*x + 6*(27*log(3)^6 + 54*log(3)^4 + 36*log(3)^2 + 8)*lo g(-3*log(3)^2 + x - 2))*log(3)^2 + 72*(2*(9*log(3)^4 + 12*log(3)^2 + 4)*lo g(-3*log(3)^2 + x - 2)^2 + 6*(3*log(3)^2 + 2)*x + x^2 + 6*(9*log(3)^4 + 12 *log(3)^2 + 4)*log(-3*log(3)^2 + x - 2))*log(3)^2 + 720*((3*log(3)^2 + 2)* log(-3*log(3)^2 + x - 2)^2 + 2*(3*log(3)^2 + 2)*log(-3*log(3)^2 + x - 2) + 2*x)*log(3)^2 - 720*(2*(3*log(3)^2 + 2)*x + x^2 + 2*(9*log(3)^4 + 12*log( 3)^2 + 4)*log(-3*log(3)^2 + x - 2))*log(3)^2 - 3600*((3*log(3)^2 + 2)*l...
Leaf count of result is larger than twice the leaf count of optimal. 112 vs. \(2 (19) = 38\).
Time = 0.28 (sec) , antiderivative size = 112, normalized size of antiderivative = 5.89 \[ \int \frac {1500+800 x-480 x^2-384 x^3-64 x^4+\left (3000+3600 x+1440 x^2+192 x^3\right ) \log ^2(3)+\left (900+120 x-336 x^2-96 x^3+\left (1800+1440 x+288 x^2\right ) \log ^2(3)\right ) \log \left (-2+x-3 \log ^2(3)\right )+\left (180-48 x-48 x^2+(360+144 x) \log ^2(3)\right ) \log ^2\left (-2+x-3 \log ^2(3)\right )+\left (12-8 x+24 \log ^2(3)\right ) \log ^3\left (-2+x-3 \log ^2(3)\right )}{2-x+3 \log ^2(3)} \, dx=16 \, x^{4} + 4 \, {\left (2 \, x + 5\right )} \log \left (-3 \, \log \left (3\right )^{2} + x - 2\right )^{3} + \log \left (-3 \, \log \left (3\right )^{2} + x - 2\right )^{4} + 160 \, x^{3} + 6 \, {\left (4 \, x^{2} + 20 \, x + 25\right )} \log \left (-3 \, \log \left (3\right )^{2} + x - 2\right )^{2} + 600 \, x^{2} + 8 \, {\left (4 \, x^{3} + 30 \, x^{2} + 75 \, x\right )} \log \left (-3 \, \log \left (3\right )^{2} + x - 2\right ) + 1000 \, x + 500 \, \log \left (-3 \, \log \left (3\right )^{2} + x - 2\right ) \]
integrate(((24*log(3)^2-8*x+12)*log(-3*log(3)^2+x-2)^3+((144*x+360)*log(3) ^2-48*x^2-48*x+180)*log(-3*log(3)^2+x-2)^2+((288*x^2+1440*x+1800)*log(3)^2 -96*x^3-336*x^2+120*x+900)*log(-3*log(3)^2+x-2)+(192*x^3+1440*x^2+3600*x+3 000)*log(3)^2-64*x^4-384*x^3-480*x^2+800*x+1500)/(3*log(3)^2+2-x),x, algor ithm=\
16*x^4 + 4*(2*x + 5)*log(-3*log(3)^2 + x - 2)^3 + log(-3*log(3)^2 + x - 2) ^4 + 160*x^3 + 6*(4*x^2 + 20*x + 25)*log(-3*log(3)^2 + x - 2)^2 + 600*x^2 + 8*(4*x^3 + 30*x^2 + 75*x)*log(-3*log(3)^2 + x - 2) + 1000*x + 500*log(-3 *log(3)^2 + x - 2)
Time = 10.04 (sec) , antiderivative size = 109, normalized size of antiderivative = 5.74 \[ \int \frac {1500+800 x-480 x^2-384 x^3-64 x^4+\left (3000+3600 x+1440 x^2+192 x^3\right ) \log ^2(3)+\left (900+120 x-336 x^2-96 x^3+\left (1800+1440 x+288 x^2\right ) \log ^2(3)\right ) \log \left (-2+x-3 \log ^2(3)\right )+\left (180-48 x-48 x^2+(360+144 x) \log ^2(3)\right ) \log ^2\left (-2+x-3 \log ^2(3)\right )+\left (12-8 x+24 \log ^2(3)\right ) \log ^3\left (-2+x-3 \log ^2(3)\right )}{2-x+3 \log ^2(3)} \, dx=1000\,x+500\,\ln \left (x-3\,{\ln \left (3\right )}^2-2\right )+{\ln \left (x-3\,{\ln \left (3\right )}^2-2\right )}^3\,\left (8\,x+20\right )+\ln \left (x-3\,{\ln \left (3\right )}^2-2\right )\,\left (32\,x^3+240\,x^2+600\,x\right )+{\ln \left (x-3\,{\ln \left (3\right )}^2-2\right )}^2\,\left (24\,x^2+120\,x+150\right )+{\ln \left (x-3\,{\ln \left (3\right )}^2-2\right )}^4+600\,x^2+160\,x^3+16\,x^4 \]
int((800*x + log(x - 3*log(3)^2 - 2)*(120*x + log(3)^2*(1440*x + 288*x^2 + 1800) - 336*x^2 - 96*x^3 + 900) + log(x - 3*log(3)^2 - 2)^3*(24*log(3)^2 - 8*x + 12) + log(3)^2*(3600*x + 1440*x^2 + 192*x^3 + 3000) - 480*x^2 - 38 4*x^3 - 64*x^4 - log(x - 3*log(3)^2 - 2)^2*(48*x - log(3)^2*(144*x + 360) + 48*x^2 - 180) + 1500)/(3*log(3)^2 - x + 2),x)