Integrand size = 490, antiderivative size = 30 \[ \int \frac {-72 x+144 x^2-108 x^3+10 x^4+15 x^5+\left (-48 x^2-72 x^3\right ) \log (x)+\left (-12 x^2+12 x^3-36 x^4\right ) \log ^2(x)+\left (-8 x^3-12 x^4\right ) \log ^3(x)+\left (-2 x^4-3 x^5\right ) \log ^4(x)+\left (72 x+108 x^2-30 x^3-45 x^4+\left (96 x+144 x^2\right ) \log (x)+\left (12 x+12 x^2+72 x^3\right ) \log ^2(x)+\left (24 x^2+36 x^3\right ) \log ^3(x)+\left (6 x^3+9 x^4\right ) \log ^4(x)\right ) \log (2+3 x)+\left (30 x^2+45 x^3+(-48-72 x) \log (x)+\left (-24 x-36 x^2\right ) \log ^2(x)+\left (-24 x-36 x^2\right ) \log ^3(x)+\left (-6 x^2-9 x^3\right ) \log ^4(x)\right ) \log ^2(2+3 x)+\left (-10 x-15 x^2+(8+12 x) \log ^3(x)+\left (2 x+3 x^2\right ) \log ^4(x)\right ) \log ^3(2+3 x)}{-72 x^2-108 x^3+10 x^4+15 x^5+\left (-24 x^3-36 x^4\right ) \log ^2(x)+\left (-2 x^4-3 x^5\right ) \log ^4(x)+\left (72 x+108 x^2-30 x^3-45 x^4+\left (48 x^2+72 x^3\right ) \log ^2(x)+\left (6 x^3+9 x^4\right ) \log ^4(x)\right ) \log (2+3 x)+\left (30 x^2+45 x^3+\left (-24 x-36 x^2\right ) \log ^2(x)+\left (-6 x^2-9 x^3\right ) \log ^4(x)\right ) \log ^2(2+3 x)+\left (-10 x-15 x^2+\left (2 x+3 x^2\right ) \log ^4(x)\right ) \log ^3(2+3 x)} \, dx=x+\log \left (5-\left (-\log ^2(x)+\frac {6}{-x+\log (2+3 x)}\right )^2\right ) \] Output:
x+ln(5-(2/(1/3*ln(2+3*x)-1/3*x)-ln(x)^2)^2)
Leaf count is larger than twice the leaf count of optimal. \(95\) vs. \(2(30)=60\).
Time = 0.31 (sec) , antiderivative size = 95, normalized size of antiderivative = 3.17 \[ \int \frac {-72 x+144 x^2-108 x^3+10 x^4+15 x^5+\left (-48 x^2-72 x^3\right ) \log (x)+\left (-12 x^2+12 x^3-36 x^4\right ) \log ^2(x)+\left (-8 x^3-12 x^4\right ) \log ^3(x)+\left (-2 x^4-3 x^5\right ) \log ^4(x)+\left (72 x+108 x^2-30 x^3-45 x^4+\left (96 x+144 x^2\right ) \log (x)+\left (12 x+12 x^2+72 x^3\right ) \log ^2(x)+\left (24 x^2+36 x^3\right ) \log ^3(x)+\left (6 x^3+9 x^4\right ) \log ^4(x)\right ) \log (2+3 x)+\left (30 x^2+45 x^3+(-48-72 x) \log (x)+\left (-24 x-36 x^2\right ) \log ^2(x)+\left (-24 x-36 x^2\right ) \log ^3(x)+\left (-6 x^2-9 x^3\right ) \log ^4(x)\right ) \log ^2(2+3 x)+\left (-10 x-15 x^2+(8+12 x) \log ^3(x)+\left (2 x+3 x^2\right ) \log ^4(x)\right ) \log ^3(2+3 x)}{-72 x^2-108 x^3+10 x^4+15 x^5+\left (-24 x^3-36 x^4\right ) \log ^2(x)+\left (-2 x^4-3 x^5\right ) \log ^4(x)+\left (72 x+108 x^2-30 x^3-45 x^4+\left (48 x^2+72 x^3\right ) \log ^2(x)+\left (6 x^3+9 x^4\right ) \log ^4(x)\right ) \log (2+3 x)+\left (30 x^2+45 x^3+\left (-24 x-36 x^2\right ) \log ^2(x)+\left (-6 x^2-9 x^3\right ) \log ^4(x)\right ) \log ^2(2+3 x)+\left (-10 x-15 x^2+\left (2 x+3 x^2\right ) \log ^4(x)\right ) \log ^3(2+3 x)} \, dx=x-2 \log (x-\log (2+3 x))+\log \left (36-5 x^2+12 x \log ^2(x)+x^2 \log ^4(x)+10 x \log (2+3 x)-12 \log ^2(x) \log (2+3 x)-2 x \log ^4(x) \log (2+3 x)-5 \log ^2(2+3 x)+\log ^4(x) \log ^2(2+3 x)\right ) \] Input:
Integrate[(-72*x + 144*x^2 - 108*x^3 + 10*x^4 + 15*x^5 + (-48*x^2 - 72*x^3 )*Log[x] + (-12*x^2 + 12*x^3 - 36*x^4)*Log[x]^2 + (-8*x^3 - 12*x^4)*Log[x] ^3 + (-2*x^4 - 3*x^5)*Log[x]^4 + (72*x + 108*x^2 - 30*x^3 - 45*x^4 + (96*x + 144*x^2)*Log[x] + (12*x + 12*x^2 + 72*x^3)*Log[x]^2 + (24*x^2 + 36*x^3) *Log[x]^3 + (6*x^3 + 9*x^4)*Log[x]^4)*Log[2 + 3*x] + (30*x^2 + 45*x^3 + (- 48 - 72*x)*Log[x] + (-24*x - 36*x^2)*Log[x]^2 + (-24*x - 36*x^2)*Log[x]^3 + (-6*x^2 - 9*x^3)*Log[x]^4)*Log[2 + 3*x]^2 + (-10*x - 15*x^2 + (8 + 12*x) *Log[x]^3 + (2*x + 3*x^2)*Log[x]^4)*Log[2 + 3*x]^3)/(-72*x^2 - 108*x^3 + 1 0*x^4 + 15*x^5 + (-24*x^3 - 36*x^4)*Log[x]^2 + (-2*x^4 - 3*x^5)*Log[x]^4 + (72*x + 108*x^2 - 30*x^3 - 45*x^4 + (48*x^2 + 72*x^3)*Log[x]^2 + (6*x^3 + 9*x^4)*Log[x]^4)*Log[2 + 3*x] + (30*x^2 + 45*x^3 + (-24*x - 36*x^2)*Log[x ]^2 + (-6*x^2 - 9*x^3)*Log[x]^4)*Log[2 + 3*x]^2 + (-10*x - 15*x^2 + (2*x + 3*x^2)*Log[x]^4)*Log[2 + 3*x]^3),x]
Output:
x - 2*Log[x - Log[2 + 3*x]] + Log[36 - 5*x^2 + 12*x*Log[x]^2 + x^2*Log[x]^ 4 + 10*x*Log[2 + 3*x] - 12*Log[x]^2*Log[2 + 3*x] - 2*x*Log[x]^4*Log[2 + 3* x] - 5*Log[2 + 3*x]^2 + Log[x]^4*Log[2 + 3*x]^2]
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.
| \(\displaystyle \int \frac {15 x^5+10 x^4-108 x^3+144 x^2+\left (-15 x^2+\left (3 x^2+2 x\right ) \log ^4(x)-10 x+(12 x+8) \log ^3(x)\right ) \log ^3(3 x+2)+\left (-3 x^5-2 x^4\right ) \log ^4(x)+\left (-12 x^4-8 x^3\right ) \log ^3(x)+\left (45 x^3+30 x^2+\left (-36 x^2-24 x\right ) \log ^3(x)+\left (-36 x^2-24 x\right ) \log ^2(x)+\left (-9 x^3-6 x^2\right ) \log ^4(x)+(-72 x-48) \log (x)\right ) \log ^2(3 x+2)+\left (-72 x^3-48 x^2\right ) \log (x)+\left (-36 x^4+12 x^3-12 x^2\right ) \log ^2(x)+\left (-45 x^4-30 x^3+108 x^2+\left (144 x^2+96 x\right ) \log (x)+\left (9 x^4+6 x^3\right ) \log ^4(x)+\left (36 x^3+24 x^2\right ) \log ^3(x)+\left (72 x^3+12 x^2+12 x\right ) \log ^2(x)+72 x\right ) \log (3 x+2)-72 x}{15 x^5+10 x^4-108 x^3-72 x^2+\left (-15 x^2+\left (3 x^2+2 x\right ) \log ^4(x)-10 x\right ) \log ^3(3 x+2)+\left (-3 x^5-2 x^4\right ) \log ^4(x)+\left (-36 x^4-24 x^3\right ) \log ^2(x)+\left (45 x^3+30 x^2+\left (-36 x^2-24 x\right ) \log ^2(x)+\left (-9 x^3-6 x^2\right ) \log ^4(x)\right ) \log ^2(3 x+2)+\left (-45 x^4-30 x^3+108 x^2+\left (9 x^4+6 x^3\right ) \log ^4(x)+\left (72 x^3+48 x^2\right ) \log ^2(x)+72 x\right ) \log (3 x+2)} \, dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {12 x \left (x \left (3 x^2-x+1\right )-\left (6 x^2+x+1\right ) \log (3 x+2)+(3 x+2) \log ^2(3 x+2)\right ) \log ^2(x)+x \left (-15 x^4-10 x^3+108 x^2+3 \left (15 x^3+10 x^2-36 x-24\right ) \log (3 x+2)-144 x+5 (3 x+2) \log ^3(3 x+2)-15 (3 x+2) x \log ^2(3 x+2)+72\right )+x (3 x+2) (x-\log (3 x+2))^3 \log ^4(x)+4 (3 x+2) (x-\log (3 x+2))^3 \log ^3(x)+24 (3 x+2) (x-\log (3 x+2))^2 \log (x)}{x (3 x+2) (x-\log (3 x+2)) \left (-5 x^2+(x-\log (3 x+2))^2 \log ^4(x)+12 (x-\log (3 x+2)) \log ^2(x)-5 \log ^2(3 x+2)+10 x \log (3 x+2)+36\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {2 \left (75 x^3+3 x^3 \log ^8(x)-30 x^3 \log ^4(x)-25 x^2-x^2 \log ^8(x)-3 x^2 \log (3 x+2) \log ^8(x)+18 x^2 \log ^6(x)-36 x^2 \log ^5(x)+10 x^2 \log ^4(x)+30 x^2 \log (3 x+2) \log ^4(x)-90 x^2 \log ^2(x)-180 x^2 \log (x)-75 x^2 \log (3 x+2)+x \log (3 x+2) \log ^8(x)-6 x \log ^6(x)-24 x \log ^5(x)+36 x \log (3 x+2) \log ^5(x)+24 \log (3 x+2) \log ^5(x)-10 x \log (3 x+2) \log ^4(x)-216 x \log ^3(x)-144 \log ^3(x)+30 x \log ^2(x)-120 x \log (x)+180 x \log (3 x+2) \log (x)+120 \log (3 x+2) \log (x)+25 x \log (3 x+2)\right )}{x (3 x+2) \left (\log ^4(x)-5\right ) \left (-5 x^2+x^2 \log ^4(x)-2 x \log (3 x+2) \log ^4(x)+12 x \log ^2(x)-12 \log (3 x+2) \log ^2(x)-5 \log ^2(3 x+2)+\log ^2(3 x+2) \log ^4(x)+10 x \log (3 x+2)+36\right )}+\frac {-5 x+x \log ^4(x)+4 \log ^3(x)}{x \left (\log ^4(x)-5\right )}-\frac {2 (3 x-1)}{(3 x+2) (x-\log (3 x+2))}\right )dx\) |
| \(\Big \downarrow \) 7299 |
| \(\displaystyle \int \left (\frac {2 \left (75 x^3+3 x^3 \log ^8(x)-30 x^3 \log ^4(x)-25 x^2-x^2 \log ^8(x)-3 x^2 \log (3 x+2) \log ^8(x)+18 x^2 \log ^6(x)-36 x^2 \log ^5(x)+10 x^2 \log ^4(x)+30 x^2 \log (3 x+2) \log ^4(x)-90 x^2 \log ^2(x)-180 x^2 \log (x)-75 x^2 \log (3 x+2)+x \log (3 x+2) \log ^8(x)-6 x \log ^6(x)-24 x \log ^5(x)+36 x \log (3 x+2) \log ^5(x)+24 \log (3 x+2) \log ^5(x)-10 x \log (3 x+2) \log ^4(x)-216 x \log ^3(x)-144 \log ^3(x)+30 x \log ^2(x)-120 x \log (x)+180 x \log (3 x+2) \log (x)+120 \log (3 x+2) \log (x)+25 x \log (3 x+2)\right )}{x (3 x+2) \left (\log ^4(x)-5\right ) \left (-5 x^2+x^2 \log ^4(x)-2 x \log (3 x+2) \log ^4(x)+12 x \log ^2(x)-12 \log (3 x+2) \log ^2(x)-5 \log ^2(3 x+2)+\log ^2(3 x+2) \log ^4(x)+10 x \log (3 x+2)+36\right )}+\frac {-5 x+x \log ^4(x)+4 \log ^3(x)}{x \left (\log ^4(x)-5\right )}-\frac {2 (3 x-1)}{(3 x+2) (x-\log (3 x+2))}\right )dx\) |
Input:
Int[(-72*x + 144*x^2 - 108*x^3 + 10*x^4 + 15*x^5 + (-48*x^2 - 72*x^3)*Log[ x] + (-12*x^2 + 12*x^3 - 36*x^4)*Log[x]^2 + (-8*x^3 - 12*x^4)*Log[x]^3 + ( -2*x^4 - 3*x^5)*Log[x]^4 + (72*x + 108*x^2 - 30*x^3 - 45*x^4 + (96*x + 144 *x^2)*Log[x] + (12*x + 12*x^2 + 72*x^3)*Log[x]^2 + (24*x^2 + 36*x^3)*Log[x ]^3 + (6*x^3 + 9*x^4)*Log[x]^4)*Log[2 + 3*x] + (30*x^2 + 45*x^3 + (-48 - 7 2*x)*Log[x] + (-24*x - 36*x^2)*Log[x]^2 + (-24*x - 36*x^2)*Log[x]^3 + (-6* x^2 - 9*x^3)*Log[x]^4)*Log[2 + 3*x]^2 + (-10*x - 15*x^2 + (8 + 12*x)*Log[x ]^3 + (2*x + 3*x^2)*Log[x]^4)*Log[2 + 3*x]^3)/(-72*x^2 - 108*x^3 + 10*x^4 + 15*x^5 + (-24*x^3 - 36*x^4)*Log[x]^2 + (-2*x^4 - 3*x^5)*Log[x]^4 + (72*x + 108*x^2 - 30*x^3 - 45*x^4 + (48*x^2 + 72*x^3)*Log[x]^2 + (6*x^3 + 9*x^4 )*Log[x]^4)*Log[2 + 3*x] + (30*x^2 + 45*x^3 + (-24*x - 36*x^2)*Log[x]^2 + (-6*x^2 - 9*x^3)*Log[x]^4)*Log[2 + 3*x]^2 + (-10*x - 15*x^2 + (2*x + 3*x^2 )*Log[x]^4)*Log[2 + 3*x]^3),x]
Output:
$Aborted
Leaf count of result is larger than twice the leaf count of optimal. \(95\) vs. \(2(32)=64\).
Time = 0.28 (sec) , antiderivative size = 96, normalized size of antiderivative = 3.20
\[\ln \left (\ln \left (x \right )^{4}-5\right )+x -2 \ln \left (-x +\ln \left (2+3 x \right )\right )+\ln \left (\ln \left (2+3 x \right )^{2}-\frac {2 \left (x \ln \left (x \right )^{4}+6 \ln \left (x \right )^{2}-5 x \right ) \ln \left (2+3 x \right )}{\ln \left (x \right )^{4}-5}+\frac {x^{2} \ln \left (x \right )^{4}+12 x \ln \left (x \right )^{2}-5 x^{2}+36}{\ln \left (x \right )^{4}-5}\right )\]
Input:
int((((3*x^2+2*x)*ln(x)^4+(12*x+8)*ln(x)^3-15*x^2-10*x)*ln(2+3*x)^3+((-9*x ^3-6*x^2)*ln(x)^4+(-36*x^2-24*x)*ln(x)^3+(-36*x^2-24*x)*ln(x)^2+(-72*x-48) *ln(x)+45*x^3+30*x^2)*ln(2+3*x)^2+((9*x^4+6*x^3)*ln(x)^4+(36*x^3+24*x^2)*l n(x)^3+(72*x^3+12*x^2+12*x)*ln(x)^2+(144*x^2+96*x)*ln(x)-45*x^4-30*x^3+108 *x^2+72*x)*ln(2+3*x)+(-3*x^5-2*x^4)*ln(x)^4+(-12*x^4-8*x^3)*ln(x)^3+(-36*x ^4+12*x^3-12*x^2)*ln(x)^2+(-72*x^3-48*x^2)*ln(x)+15*x^5+10*x^4-108*x^3+144 *x^2-72*x)/(((3*x^2+2*x)*ln(x)^4-15*x^2-10*x)*ln(2+3*x)^3+((-9*x^3-6*x^2)* ln(x)^4+(-36*x^2-24*x)*ln(x)^2+45*x^3+30*x^2)*ln(2+3*x)^2+((9*x^4+6*x^3)*l n(x)^4+(72*x^3+48*x^2)*ln(x)^2-45*x^4-30*x^3+108*x^2+72*x)*ln(2+3*x)+(-3*x ^5-2*x^4)*ln(x)^4+(-36*x^4-24*x^3)*ln(x)^2+15*x^5+10*x^4-108*x^3-72*x^2),x )
Output:
ln(ln(x)^4-5)+x-2*ln(-x+ln(2+3*x))+ln(ln(2+3*x)^2-2*(x*ln(x)^4+6*ln(x)^2-5 *x)/(ln(x)^4-5)*ln(2+3*x)+(x^2*ln(x)^4+12*x*ln(x)^2-5*x^2+36)/(ln(x)^4-5))
Leaf count of result is larger than twice the leaf count of optimal. 93 vs. \(2 (28) = 56\).
Time = 0.12 (sec) , antiderivative size = 93, normalized size of antiderivative = 3.10 \[ \int \frac {-72 x+144 x^2-108 x^3+10 x^4+15 x^5+\left (-48 x^2-72 x^3\right ) \log (x)+\left (-12 x^2+12 x^3-36 x^4\right ) \log ^2(x)+\left (-8 x^3-12 x^4\right ) \log ^3(x)+\left (-2 x^4-3 x^5\right ) \log ^4(x)+\left (72 x+108 x^2-30 x^3-45 x^4+\left (96 x+144 x^2\right ) \log (x)+\left (12 x+12 x^2+72 x^3\right ) \log ^2(x)+\left (24 x^2+36 x^3\right ) \log ^3(x)+\left (6 x^3+9 x^4\right ) \log ^4(x)\right ) \log (2+3 x)+\left (30 x^2+45 x^3+(-48-72 x) \log (x)+\left (-24 x-36 x^2\right ) \log ^2(x)+\left (-24 x-36 x^2\right ) \log ^3(x)+\left (-6 x^2-9 x^3\right ) \log ^4(x)\right ) \log ^2(2+3 x)+\left (-10 x-15 x^2+(8+12 x) \log ^3(x)+\left (2 x+3 x^2\right ) \log ^4(x)\right ) \log ^3(2+3 x)}{-72 x^2-108 x^3+10 x^4+15 x^5+\left (-24 x^3-36 x^4\right ) \log ^2(x)+\left (-2 x^4-3 x^5\right ) \log ^4(x)+\left (72 x+108 x^2-30 x^3-45 x^4+\left (48 x^2+72 x^3\right ) \log ^2(x)+\left (6 x^3+9 x^4\right ) \log ^4(x)\right ) \log (2+3 x)+\left (30 x^2+45 x^3+\left (-24 x-36 x^2\right ) \log ^2(x)+\left (-6 x^2-9 x^3\right ) \log ^4(x)\right ) \log ^2(2+3 x)+\left (-10 x-15 x^2+\left (2 x+3 x^2\right ) \log ^4(x)\right ) \log ^3(2+3 x)} \, dx=x + \log \left (\log \left (x\right )^{4} - 5\right ) - 2 \, \log \left (-x + \log \left (3 \, x + 2\right )\right ) + \log \left (\frac {x^{2} \log \left (x\right )^{4} + {\left (\log \left (x\right )^{4} - 5\right )} \log \left (3 \, x + 2\right )^{2} + 12 \, x \log \left (x\right )^{2} - 5 \, x^{2} - 2 \, {\left (x \log \left (x\right )^{4} + 6 \, \log \left (x\right )^{2} - 5 \, x\right )} \log \left (3 \, x + 2\right ) + 36}{\log \left (x\right )^{4} - 5}\right ) \] Input:
integrate((((3*x^2+2*x)*log(x)^4+(12*x+8)*log(x)^3-15*x^2-10*x)*log(2+3*x) ^3+((-9*x^3-6*x^2)*log(x)^4+(-36*x^2-24*x)*log(x)^3+(-36*x^2-24*x)*log(x)^ 2+(-72*x-48)*log(x)+45*x^3+30*x^2)*log(2+3*x)^2+((9*x^4+6*x^3)*log(x)^4+(3 6*x^3+24*x^2)*log(x)^3+(72*x^3+12*x^2+12*x)*log(x)^2+(144*x^2+96*x)*log(x) -45*x^4-30*x^3+108*x^2+72*x)*log(2+3*x)+(-3*x^5-2*x^4)*log(x)^4+(-12*x^4-8 *x^3)*log(x)^3+(-36*x^4+12*x^3-12*x^2)*log(x)^2+(-72*x^3-48*x^2)*log(x)+15 *x^5+10*x^4-108*x^3+144*x^2-72*x)/(((3*x^2+2*x)*log(x)^4-15*x^2-10*x)*log( 2+3*x)^3+((-9*x^3-6*x^2)*log(x)^4+(-36*x^2-24*x)*log(x)^2+45*x^3+30*x^2)*l og(2+3*x)^2+((9*x^4+6*x^3)*log(x)^4+(72*x^3+48*x^2)*log(x)^2-45*x^4-30*x^3 +108*x^2+72*x)*log(2+3*x)+(-3*x^5-2*x^4)*log(x)^4+(-36*x^4-24*x^3)*log(x)^ 2+15*x^5+10*x^4-108*x^3-72*x^2),x, algorithm="fricas")
Output:
x + log(log(x)^4 - 5) - 2*log(-x + log(3*x + 2)) + log((x^2*log(x)^4 + (lo g(x)^4 - 5)*log(3*x + 2)^2 + 12*x*log(x)^2 - 5*x^2 - 2*(x*log(x)^4 + 6*log (x)^2 - 5*x)*log(3*x + 2) + 36)/(log(x)^4 - 5))
Exception generated. \[ \int \frac {-72 x+144 x^2-108 x^3+10 x^4+15 x^5+\left (-48 x^2-72 x^3\right ) \log (x)+\left (-12 x^2+12 x^3-36 x^4\right ) \log ^2(x)+\left (-8 x^3-12 x^4\right ) \log ^3(x)+\left (-2 x^4-3 x^5\right ) \log ^4(x)+\left (72 x+108 x^2-30 x^3-45 x^4+\left (96 x+144 x^2\right ) \log (x)+\left (12 x+12 x^2+72 x^3\right ) \log ^2(x)+\left (24 x^2+36 x^3\right ) \log ^3(x)+\left (6 x^3+9 x^4\right ) \log ^4(x)\right ) \log (2+3 x)+\left (30 x^2+45 x^3+(-48-72 x) \log (x)+\left (-24 x-36 x^2\right ) \log ^2(x)+\left (-24 x-36 x^2\right ) \log ^3(x)+\left (-6 x^2-9 x^3\right ) \log ^4(x)\right ) \log ^2(2+3 x)+\left (-10 x-15 x^2+(8+12 x) \log ^3(x)+\left (2 x+3 x^2\right ) \log ^4(x)\right ) \log ^3(2+3 x)}{-72 x^2-108 x^3+10 x^4+15 x^5+\left (-24 x^3-36 x^4\right ) \log ^2(x)+\left (-2 x^4-3 x^5\right ) \log ^4(x)+\left (72 x+108 x^2-30 x^3-45 x^4+\left (48 x^2+72 x^3\right ) \log ^2(x)+\left (6 x^3+9 x^4\right ) \log ^4(x)\right ) \log (2+3 x)+\left (30 x^2+45 x^3+\left (-24 x-36 x^2\right ) \log ^2(x)+\left (-6 x^2-9 x^3\right ) \log ^4(x)\right ) \log ^2(2+3 x)+\left (-10 x-15 x^2+\left (2 x+3 x^2\right ) \log ^4(x)\right ) \log ^3(2+3 x)} \, dx=\text {Exception raised: PolynomialError} \] Input:
integrate((((3*x**2+2*x)*ln(x)**4+(12*x+8)*ln(x)**3-15*x**2-10*x)*ln(2+3*x )**3+((-9*x**3-6*x**2)*ln(x)**4+(-36*x**2-24*x)*ln(x)**3+(-36*x**2-24*x)*l n(x)**2+(-72*x-48)*ln(x)+45*x**3+30*x**2)*ln(2+3*x)**2+((9*x**4+6*x**3)*ln (x)**4+(36*x**3+24*x**2)*ln(x)**3+(72*x**3+12*x**2+12*x)*ln(x)**2+(144*x** 2+96*x)*ln(x)-45*x**4-30*x**3+108*x**2+72*x)*ln(2+3*x)+(-3*x**5-2*x**4)*ln (x)**4+(-12*x**4-8*x**3)*ln(x)**3+(-36*x**4+12*x**3-12*x**2)*ln(x)**2+(-72 *x**3-48*x**2)*ln(x)+15*x**5+10*x**4-108*x**3+144*x**2-72*x)/(((3*x**2+2*x )*ln(x)**4-15*x**2-10*x)*ln(2+3*x)**3+((-9*x**3-6*x**2)*ln(x)**4+(-36*x**2 -24*x)*ln(x)**2+45*x**3+30*x**2)*ln(2+3*x)**2+((9*x**4+6*x**3)*ln(x)**4+(7 2*x**3+48*x**2)*ln(x)**2-45*x**4-30*x**3+108*x**2+72*x)*ln(2+3*x)+(-3*x**5 -2*x**4)*ln(x)**4+(-36*x**4-24*x**3)*ln(x)**2+15*x**5+10*x**4-108*x**3-72* x**2),x)
Output:
Exception raised: PolynomialError >> 1/(9*_t0**16*x**4 + 12*_t0**16*x**3 + 4*_t0**16*x**2 - 180*_t0**12*x**4 - 240*_t0**12*x**3 - 80*_t0**12*x**2 + 1350*_t0**8*x**4 + 1800*_t0**8*x**3 + 600*_t0**8*x**2 - 4500*_t0**4*x**4 - 6000*_t0**4*x*
Leaf count of result is larger than twice the leaf count of optimal. 93 vs. \(2 (28) = 56\).
Time = 0.24 (sec) , antiderivative size = 93, normalized size of antiderivative = 3.10 \[ \int \frac {-72 x+144 x^2-108 x^3+10 x^4+15 x^5+\left (-48 x^2-72 x^3\right ) \log (x)+\left (-12 x^2+12 x^3-36 x^4\right ) \log ^2(x)+\left (-8 x^3-12 x^4\right ) \log ^3(x)+\left (-2 x^4-3 x^5\right ) \log ^4(x)+\left (72 x+108 x^2-30 x^3-45 x^4+\left (96 x+144 x^2\right ) \log (x)+\left (12 x+12 x^2+72 x^3\right ) \log ^2(x)+\left (24 x^2+36 x^3\right ) \log ^3(x)+\left (6 x^3+9 x^4\right ) \log ^4(x)\right ) \log (2+3 x)+\left (30 x^2+45 x^3+(-48-72 x) \log (x)+\left (-24 x-36 x^2\right ) \log ^2(x)+\left (-24 x-36 x^2\right ) \log ^3(x)+\left (-6 x^2-9 x^3\right ) \log ^4(x)\right ) \log ^2(2+3 x)+\left (-10 x-15 x^2+(8+12 x) \log ^3(x)+\left (2 x+3 x^2\right ) \log ^4(x)\right ) \log ^3(2+3 x)}{-72 x^2-108 x^3+10 x^4+15 x^5+\left (-24 x^3-36 x^4\right ) \log ^2(x)+\left (-2 x^4-3 x^5\right ) \log ^4(x)+\left (72 x+108 x^2-30 x^3-45 x^4+\left (48 x^2+72 x^3\right ) \log ^2(x)+\left (6 x^3+9 x^4\right ) \log ^4(x)\right ) \log (2+3 x)+\left (30 x^2+45 x^3+\left (-24 x-36 x^2\right ) \log ^2(x)+\left (-6 x^2-9 x^3\right ) \log ^4(x)\right ) \log ^2(2+3 x)+\left (-10 x-15 x^2+\left (2 x+3 x^2\right ) \log ^4(x)\right ) \log ^3(2+3 x)} \, dx=x + \log \left (\log \left (x\right )^{4} - 5\right ) - 2 \, \log \left (-x + \log \left (3 \, x + 2\right )\right ) + \log \left (\frac {x^{2} \log \left (x\right )^{4} + {\left (\log \left (x\right )^{4} - 5\right )} \log \left (3 \, x + 2\right )^{2} + 12 \, x \log \left (x\right )^{2} - 5 \, x^{2} - 2 \, {\left (x \log \left (x\right )^{4} + 6 \, \log \left (x\right )^{2} - 5 \, x\right )} \log \left (3 \, x + 2\right ) + 36}{\log \left (x\right )^{4} - 5}\right ) \] Input:
integrate((((3*x^2+2*x)*log(x)^4+(12*x+8)*log(x)^3-15*x^2-10*x)*log(2+3*x) ^3+((-9*x^3-6*x^2)*log(x)^4+(-36*x^2-24*x)*log(x)^3+(-36*x^2-24*x)*log(x)^ 2+(-72*x-48)*log(x)+45*x^3+30*x^2)*log(2+3*x)^2+((9*x^4+6*x^3)*log(x)^4+(3 6*x^3+24*x^2)*log(x)^3+(72*x^3+12*x^2+12*x)*log(x)^2+(144*x^2+96*x)*log(x) -45*x^4-30*x^3+108*x^2+72*x)*log(2+3*x)+(-3*x^5-2*x^4)*log(x)^4+(-12*x^4-8 *x^3)*log(x)^3+(-36*x^4+12*x^3-12*x^2)*log(x)^2+(-72*x^3-48*x^2)*log(x)+15 *x^5+10*x^4-108*x^3+144*x^2-72*x)/(((3*x^2+2*x)*log(x)^4-15*x^2-10*x)*log( 2+3*x)^3+((-9*x^3-6*x^2)*log(x)^4+(-36*x^2-24*x)*log(x)^2+45*x^3+30*x^2)*l og(2+3*x)^2+((9*x^4+6*x^3)*log(x)^4+(72*x^3+48*x^2)*log(x)^2-45*x^4-30*x^3 +108*x^2+72*x)*log(2+3*x)+(-3*x^5-2*x^4)*log(x)^4+(-36*x^4-24*x^3)*log(x)^ 2+15*x^5+10*x^4-108*x^3-72*x^2),x, algorithm="maxima")
Output:
x + log(log(x)^4 - 5) - 2*log(-x + log(3*x + 2)) + log((x^2*log(x)^4 + (lo g(x)^4 - 5)*log(3*x + 2)^2 + 12*x*log(x)^2 - 5*x^2 - 2*(x*log(x)^4 + 6*log (x)^2 - 5*x)*log(3*x + 2) + 36)/(log(x)^4 - 5))
Leaf count of result is larger than twice the leaf count of optimal. 95 vs. \(2 (28) = 56\).
Time = 0.76 (sec) , antiderivative size = 95, normalized size of antiderivative = 3.17 \[ \int \frac {-72 x+144 x^2-108 x^3+10 x^4+15 x^5+\left (-48 x^2-72 x^3\right ) \log (x)+\left (-12 x^2+12 x^3-36 x^4\right ) \log ^2(x)+\left (-8 x^3-12 x^4\right ) \log ^3(x)+\left (-2 x^4-3 x^5\right ) \log ^4(x)+\left (72 x+108 x^2-30 x^3-45 x^4+\left (96 x+144 x^2\right ) \log (x)+\left (12 x+12 x^2+72 x^3\right ) \log ^2(x)+\left (24 x^2+36 x^3\right ) \log ^3(x)+\left (6 x^3+9 x^4\right ) \log ^4(x)\right ) \log (2+3 x)+\left (30 x^2+45 x^3+(-48-72 x) \log (x)+\left (-24 x-36 x^2\right ) \log ^2(x)+\left (-24 x-36 x^2\right ) \log ^3(x)+\left (-6 x^2-9 x^3\right ) \log ^4(x)\right ) \log ^2(2+3 x)+\left (-10 x-15 x^2+(8+12 x) \log ^3(x)+\left (2 x+3 x^2\right ) \log ^4(x)\right ) \log ^3(2+3 x)}{-72 x^2-108 x^3+10 x^4+15 x^5+\left (-24 x^3-36 x^4\right ) \log ^2(x)+\left (-2 x^4-3 x^5\right ) \log ^4(x)+\left (72 x+108 x^2-30 x^3-45 x^4+\left (48 x^2+72 x^3\right ) \log ^2(x)+\left (6 x^3+9 x^4\right ) \log ^4(x)\right ) \log (2+3 x)+\left (30 x^2+45 x^3+\left (-24 x-36 x^2\right ) \log ^2(x)+\left (-6 x^2-9 x^3\right ) \log ^4(x)\right ) \log ^2(2+3 x)+\left (-10 x-15 x^2+\left (2 x+3 x^2\right ) \log ^4(x)\right ) \log ^3(2+3 x)} \, dx=x + \log \left (x^{2} \log \left (x\right )^{4} - 2 \, x \log \left (3 \, x + 2\right ) \log \left (x\right )^{4} + \log \left (3 \, x + 2\right )^{2} \log \left (x\right )^{4} + 12 \, x \log \left (x\right )^{2} - 12 \, \log \left (3 \, x + 2\right ) \log \left (x\right )^{2} - 5 \, x^{2} + 10 \, x \log \left (3 \, x + 2\right ) - 5 \, \log \left (3 \, x + 2\right )^{2} + 36\right ) - 2 \, \log \left (x - \log \left (3 \, x + 2\right )\right ) \] Input:
integrate((((3*x^2+2*x)*log(x)^4+(12*x+8)*log(x)^3-15*x^2-10*x)*log(2+3*x) ^3+((-9*x^3-6*x^2)*log(x)^4+(-36*x^2-24*x)*log(x)^3+(-36*x^2-24*x)*log(x)^ 2+(-72*x-48)*log(x)+45*x^3+30*x^2)*log(2+3*x)^2+((9*x^4+6*x^3)*log(x)^4+(3 6*x^3+24*x^2)*log(x)^3+(72*x^3+12*x^2+12*x)*log(x)^2+(144*x^2+96*x)*log(x) -45*x^4-30*x^3+108*x^2+72*x)*log(2+3*x)+(-3*x^5-2*x^4)*log(x)^4+(-12*x^4-8 *x^3)*log(x)^3+(-36*x^4+12*x^3-12*x^2)*log(x)^2+(-72*x^3-48*x^2)*log(x)+15 *x^5+10*x^4-108*x^3+144*x^2-72*x)/(((3*x^2+2*x)*log(x)^4-15*x^2-10*x)*log( 2+3*x)^3+((-9*x^3-6*x^2)*log(x)^4+(-36*x^2-24*x)*log(x)^2+45*x^3+30*x^2)*l og(2+3*x)^2+((9*x^4+6*x^3)*log(x)^4+(72*x^3+48*x^2)*log(x)^2-45*x^4-30*x^3 +108*x^2+72*x)*log(2+3*x)+(-3*x^5-2*x^4)*log(x)^4+(-36*x^4-24*x^3)*log(x)^ 2+15*x^5+10*x^4-108*x^3-72*x^2),x, algorithm="giac")
Output:
x + log(x^2*log(x)^4 - 2*x*log(3*x + 2)*log(x)^4 + log(3*x + 2)^2*log(x)^4 + 12*x*log(x)^2 - 12*log(3*x + 2)*log(x)^2 - 5*x^2 + 10*x*log(3*x + 2) - 5*log(3*x + 2)^2 + 36) - 2*log(x - log(3*x + 2))
Timed out. \[ \int \frac {-72 x+144 x^2-108 x^3+10 x^4+15 x^5+\left (-48 x^2-72 x^3\right ) \log (x)+\left (-12 x^2+12 x^3-36 x^4\right ) \log ^2(x)+\left (-8 x^3-12 x^4\right ) \log ^3(x)+\left (-2 x^4-3 x^5\right ) \log ^4(x)+\left (72 x+108 x^2-30 x^3-45 x^4+\left (96 x+144 x^2\right ) \log (x)+\left (12 x+12 x^2+72 x^3\right ) \log ^2(x)+\left (24 x^2+36 x^3\right ) \log ^3(x)+\left (6 x^3+9 x^4\right ) \log ^4(x)\right ) \log (2+3 x)+\left (30 x^2+45 x^3+(-48-72 x) \log (x)+\left (-24 x-36 x^2\right ) \log ^2(x)+\left (-24 x-36 x^2\right ) \log ^3(x)+\left (-6 x^2-9 x^3\right ) \log ^4(x)\right ) \log ^2(2+3 x)+\left (-10 x-15 x^2+(8+12 x) \log ^3(x)+\left (2 x+3 x^2\right ) \log ^4(x)\right ) \log ^3(2+3 x)}{-72 x^2-108 x^3+10 x^4+15 x^5+\left (-24 x^3-36 x^4\right ) \log ^2(x)+\left (-2 x^4-3 x^5\right ) \log ^4(x)+\left (72 x+108 x^2-30 x^3-45 x^4+\left (48 x^2+72 x^3\right ) \log ^2(x)+\left (6 x^3+9 x^4\right ) \log ^4(x)\right ) \log (2+3 x)+\left (30 x^2+45 x^3+\left (-24 x-36 x^2\right ) \log ^2(x)+\left (-6 x^2-9 x^3\right ) \log ^4(x)\right ) \log ^2(2+3 x)+\left (-10 x-15 x^2+\left (2 x+3 x^2\right ) \log ^4(x)\right ) \log ^3(2+3 x)} \, dx=\int \frac {72\,x+\ln \left (x\right )\,\left (72\,x^3+48\,x^2\right )+{\ln \left (3\,x+2\right )}^2\,\left ({\ln \left (x\right )}^2\,\left (36\,x^2+24\,x\right )+{\ln \left (x\right )}^3\,\left (36\,x^2+24\,x\right )+{\ln \left (x\right )}^4\,\left (9\,x^3+6\,x^2\right )+\ln \left (x\right )\,\left (72\,x+48\right )-30\,x^2-45\,x^3\right )+{\ln \left (x\right )}^4\,\left (3\,x^5+2\,x^4\right )+{\ln \left (x\right )}^3\,\left (12\,x^4+8\,x^3\right )+{\ln \left (x\right )}^2\,\left (36\,x^4-12\,x^3+12\,x^2\right )-\ln \left (3\,x+2\right )\,\left (72\,x+{\ln \left (x\right )}^2\,\left (72\,x^3+12\,x^2+12\,x\right )+{\ln \left (x\right )}^4\,\left (9\,x^4+6\,x^3\right )+{\ln \left (x\right )}^3\,\left (36\,x^3+24\,x^2\right )+\ln \left (x\right )\,\left (144\,x^2+96\,x\right )+108\,x^2-30\,x^3-45\,x^4\right )+{\ln \left (3\,x+2\right )}^3\,\left (10\,x-{\ln \left (x\right )}^4\,\left (3\,x^2+2\,x\right )+15\,x^2-{\ln \left (x\right )}^3\,\left (12\,x+8\right )\right )-144\,x^2+108\,x^3-10\,x^4-15\,x^5}{{\ln \left (x\right )}^4\,\left (3\,x^5+2\,x^4\right )+{\ln \left (x\right )}^2\,\left (36\,x^4+24\,x^3\right )+{\ln \left (3\,x+2\right )}^2\,\left ({\ln \left (x\right )}^2\,\left (36\,x^2+24\,x\right )+{\ln \left (x\right )}^4\,\left (9\,x^3+6\,x^2\right )-30\,x^2-45\,x^3\right )-\ln \left (3\,x+2\right )\,\left (72\,x+{\ln \left (x\right )}^4\,\left (9\,x^4+6\,x^3\right )+{\ln \left (x\right )}^2\,\left (72\,x^3+48\,x^2\right )+108\,x^2-30\,x^3-45\,x^4\right )+72\,x^2+108\,x^3-10\,x^4-15\,x^5+{\ln \left (3\,x+2\right )}^3\,\left (10\,x-{\ln \left (x\right )}^4\,\left (3\,x^2+2\,x\right )+15\,x^2\right )} \,d x \] Input:
int((72*x + log(x)*(48*x^2 + 72*x^3) + log(3*x + 2)^2*(log(x)^2*(24*x + 36 *x^2) + log(x)^3*(24*x + 36*x^2) + log(x)^4*(6*x^2 + 9*x^3) + log(x)*(72*x + 48) - 30*x^2 - 45*x^3) + log(x)^4*(2*x^4 + 3*x^5) + log(x)^3*(8*x^3 + 1 2*x^4) + log(x)^2*(12*x^2 - 12*x^3 + 36*x^4) - log(3*x + 2)*(72*x + log(x) ^2*(12*x + 12*x^2 + 72*x^3) + log(x)^4*(6*x^3 + 9*x^4) + log(x)^3*(24*x^2 + 36*x^3) + log(x)*(96*x + 144*x^2) + 108*x^2 - 30*x^3 - 45*x^4) + log(3*x + 2)^3*(10*x - log(x)^4*(2*x + 3*x^2) + 15*x^2 - log(x)^3*(12*x + 8)) - 1 44*x^2 + 108*x^3 - 10*x^4 - 15*x^5)/(log(x)^4*(2*x^4 + 3*x^5) + log(x)^2*( 24*x^3 + 36*x^4) + log(3*x + 2)^2*(log(x)^2*(24*x + 36*x^2) + log(x)^4*(6* x^2 + 9*x^3) - 30*x^2 - 45*x^3) - log(3*x + 2)*(72*x + log(x)^4*(6*x^3 + 9 *x^4) + log(x)^2*(48*x^2 + 72*x^3) + 108*x^2 - 30*x^3 - 45*x^4) + 72*x^2 + 108*x^3 - 10*x^4 - 15*x^5 + log(3*x + 2)^3*(10*x - log(x)^4*(2*x + 3*x^2) + 15*x^2)),x)
Output:
int((72*x + log(x)*(48*x^2 + 72*x^3) + log(3*x + 2)^2*(log(x)^2*(24*x + 36 *x^2) + log(x)^3*(24*x + 36*x^2) + log(x)^4*(6*x^2 + 9*x^3) + log(x)*(72*x + 48) - 30*x^2 - 45*x^3) + log(x)^4*(2*x^4 + 3*x^5) + log(x)^3*(8*x^3 + 1 2*x^4) + log(x)^2*(12*x^2 - 12*x^3 + 36*x^4) - log(3*x + 2)*(72*x + log(x) ^2*(12*x + 12*x^2 + 72*x^3) + log(x)^4*(6*x^3 + 9*x^4) + log(x)^3*(24*x^2 + 36*x^3) + log(x)*(96*x + 144*x^2) + 108*x^2 - 30*x^3 - 45*x^4) + log(3*x + 2)^3*(10*x - log(x)^4*(2*x + 3*x^2) + 15*x^2 - log(x)^3*(12*x + 8)) - 1 44*x^2 + 108*x^3 - 10*x^4 - 15*x^5)/(log(x)^4*(2*x^4 + 3*x^5) + log(x)^2*( 24*x^3 + 36*x^4) + log(3*x + 2)^2*(log(x)^2*(24*x + 36*x^2) + log(x)^4*(6* x^2 + 9*x^3) - 30*x^2 - 45*x^3) - log(3*x + 2)*(72*x + log(x)^4*(6*x^3 + 9 *x^4) + log(x)^2*(48*x^2 + 72*x^3) + 108*x^2 - 30*x^3 - 45*x^4) + 72*x^2 + 108*x^3 - 10*x^4 - 15*x^5 + log(3*x + 2)^3*(10*x - log(x)^4*(2*x + 3*x^2) + 15*x^2)), x)
\[ \int \frac {-72 x+144 x^2-108 x^3+10 x^4+15 x^5+\left (-48 x^2-72 x^3\right ) \log (x)+\left (-12 x^2+12 x^3-36 x^4\right ) \log ^2(x)+\left (-8 x^3-12 x^4\right ) \log ^3(x)+\left (-2 x^4-3 x^5\right ) \log ^4(x)+\left (72 x+108 x^2-30 x^3-45 x^4+\left (96 x+144 x^2\right ) \log (x)+\left (12 x+12 x^2+72 x^3\right ) \log ^2(x)+\left (24 x^2+36 x^3\right ) \log ^3(x)+\left (6 x^3+9 x^4\right ) \log ^4(x)\right ) \log (2+3 x)+\left (30 x^2+45 x^3+(-48-72 x) \log (x)+\left (-24 x-36 x^2\right ) \log ^2(x)+\left (-24 x-36 x^2\right ) \log ^3(x)+\left (-6 x^2-9 x^3\right ) \log ^4(x)\right ) \log ^2(2+3 x)+\left (-10 x-15 x^2+(8+12 x) \log ^3(x)+\left (2 x+3 x^2\right ) \log ^4(x)\right ) \log ^3(2+3 x)}{-72 x^2-108 x^3+10 x^4+15 x^5+\left (-24 x^3-36 x^4\right ) \log ^2(x)+\left (-2 x^4-3 x^5\right ) \log ^4(x)+\left (72 x+108 x^2-30 x^3-45 x^4+\left (48 x^2+72 x^3\right ) \log ^2(x)+\left (6 x^3+9 x^4\right ) \log ^4(x)\right ) \log (2+3 x)+\left (30 x^2+45 x^3+\left (-24 x-36 x^2\right ) \log ^2(x)+\left (-6 x^2-9 x^3\right ) \log ^4(x)\right ) \log ^2(2+3 x)+\left (-10 x-15 x^2+\left (2 x+3 x^2\right ) \log ^4(x)\right ) \log ^3(2+3 x)} \, dx=\text {too large to display} \] Input:
int((((3*x^2+2*x)*log(x)^4+(12*x+8)*log(x)^3-15*x^2-10*x)*log(2+3*x)^3+((- 9*x^3-6*x^2)*log(x)^4+(-36*x^2-24*x)*log(x)^3+(-36*x^2-24*x)*log(x)^2+(-72 *x-48)*log(x)+45*x^3+30*x^2)*log(2+3*x)^2+((9*x^4+6*x^3)*log(x)^4+(36*x^3+ 24*x^2)*log(x)^3+(72*x^3+12*x^2+12*x)*log(x)^2+(144*x^2+96*x)*log(x)-45*x^ 4-30*x^3+108*x^2+72*x)*log(2+3*x)+(-3*x^5-2*x^4)*log(x)^4+(-12*x^4-8*x^3)* log(x)^3+(-36*x^4+12*x^3-12*x^2)*log(x)^2+(-72*x^3-48*x^2)*log(x)+15*x^5+1 0*x^4-108*x^3+144*x^2-72*x)/(((3*x^2+2*x)*log(x)^4-15*x^2-10*x)*log(2+3*x) ^3+((-9*x^3-6*x^2)*log(x)^4+(-36*x^2-24*x)*log(x)^2+45*x^3+30*x^2)*log(2+3 *x)^2+((9*x^4+6*x^3)*log(x)^4+(72*x^3+48*x^2)*log(x)^2-45*x^4-30*x^3+108*x ^2+72*x)*log(2+3*x)+(-3*x^5-2*x^4)*log(x)^4+(-36*x^4-24*x^3)*log(x)^2+15*x ^5+10*x^4-108*x^3-72*x^2),x)
Output:
- 10*int(log(3*x + 2)**3/(3*log(3*x + 2)**3*log(x)**4*x + 2*log(3*x + 2)* *3*log(x)**4 - 15*log(3*x + 2)**3*x - 10*log(3*x + 2)**3 - 9*log(3*x + 2)* *2*log(x)**4*x**2 - 6*log(3*x + 2)**2*log(x)**4*x - 36*log(3*x + 2)**2*log (x)**2*x - 24*log(3*x + 2)**2*log(x)**2 + 45*log(3*x + 2)**2*x**2 + 30*log (3*x + 2)**2*x + 9*log(3*x + 2)*log(x)**4*x**3 + 6*log(3*x + 2)*log(x)**4* x**2 + 72*log(3*x + 2)*log(x)**2*x**2 + 48*log(3*x + 2)*log(x)**2*x - 45*l og(3*x + 2)*x**3 - 30*log(3*x + 2)*x**2 + 108*log(3*x + 2)*x + 72*log(3*x + 2) - 3*log(x)**4*x**4 - 2*log(x)**4*x**3 - 36*log(x)**2*x**3 - 24*log(x) **2*x**2 + 15*x**4 + 10*x**3 - 108*x**2 - 72*x),x) + 15*int(x**4/(3*log(3* x + 2)**3*log(x)**4*x + 2*log(3*x + 2)**3*log(x)**4 - 15*log(3*x + 2)**3*x - 10*log(3*x + 2)**3 - 9*log(3*x + 2)**2*log(x)**4*x**2 - 6*log(3*x + 2)* *2*log(x)**4*x - 36*log(3*x + 2)**2*log(x)**2*x - 24*log(3*x + 2)**2*log(x )**2 + 45*log(3*x + 2)**2*x**2 + 30*log(3*x + 2)**2*x + 9*log(3*x + 2)*log (x)**4*x**3 + 6*log(3*x + 2)*log(x)**4*x**2 + 72*log(3*x + 2)*log(x)**2*x* *2 + 48*log(3*x + 2)*log(x)**2*x - 45*log(3*x + 2)*x**3 - 30*log(3*x + 2)* x**2 + 108*log(3*x + 2)*x + 72*log(3*x + 2) - 3*log(x)**4*x**4 - 2*log(x)* *4*x**3 - 36*log(x)**2*x**3 - 24*log(x)**2*x**2 + 15*x**4 + 10*x**3 - 108* x**2 - 72*x),x) + 10*int(x**3/(3*log(3*x + 2)**3*log(x)**4*x + 2*log(3*x + 2)**3*log(x)**4 - 15*log(3*x + 2)**3*x - 10*log(3*x + 2)**3 - 9*log(3*x + 2)**2*log(x)**4*x**2 - 6*log(3*x + 2)**2*log(x)**4*x - 36*log(3*x + 2)...