Integrand size = 98, antiderivative size = 23 \[ \int \frac {e^{5/4} (-360+72 x) \log ^3(x)+e^{5/4} (-90+36 x) \log ^4(x)+(180-72 x) \log ^5(x)}{-e^{25/4}+10 e^5 \log (x)-40 e^{15/4} \log ^2(x)+80 e^{5/2} \log ^3(x)-80 e^{5/4} \log ^4(x)+32 \log ^5(x)} \, dx=\frac {18 (5-x) x}{\left (2-\frac {e^{5/4}}{\log (x)}\right )^4} \] Output:
18*x/(2-exp(5/4)/ln(x))^4*(5-x)
Time = 0.25 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.96 \[ \int \frac {e^{5/4} (-360+72 x) \log ^3(x)+e^{5/4} (-90+36 x) \log ^4(x)+(180-72 x) \log ^5(x)}{-e^{25/4}+10 e^5 \log (x)-40 e^{15/4} \log ^2(x)+80 e^{5/2} \log ^3(x)-80 e^{5/4} \log ^4(x)+32 \log ^5(x)} \, dx=-\frac {18 (-5+x) x \log ^4(x)}{\left (e^{5/4}-2 \log (x)\right )^4} \] Input:
Integrate[(E^(5/4)*(-360 + 72*x)*Log[x]^3 + E^(5/4)*(-90 + 36*x)*Log[x]^4 + (180 - 72*x)*Log[x]^5)/(-E^(25/4) + 10*E^5*Log[x] - 40*E^(15/4)*Log[x]^2 + 80*E^(5/2)*Log[x]^3 - 80*E^(5/4)*Log[x]^4 + 32*Log[x]^5),x]
Output:
(-18*(-5 + x)*x*Log[x]^4)/(E^(5/4) - 2*Log[x])^4
Result contains higher order function than in optimal. Order 4 vs. order 3 in optimal.
Time = 2.38 (sec) , antiderivative size = 911, normalized size of antiderivative = 39.61, number of steps used = 4, number of rules used = 4, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.041, Rules used = {7239, 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.
| \(\displaystyle \int \frac {(180-72 x) \log ^5(x)+e^{5/4} (36 x-90) \log ^4(x)+e^{5/4} (72 x-360) \log ^3(x)}{32 \log ^5(x)-80 e^{5/4} \log ^4(x)+80 e^{5/2} \log ^3(x)-40 e^{15/4} \log ^2(x)+10 e^5 \log (x)-e^{25/4}} \, dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {18 \log ^3(x) \left (-4 e^{5/4} (x-5)-\left ((10-4 x) \log ^2(x)\right )-e^{5/4} (2 x-5) \log (x)\right )}{\left (e^{5/4}-2 \log (x)\right )^5}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle 18 \int \frac {\log ^3(x) \left (-2 (5-2 x) \log ^2(x)+e^{5/4} (5-2 x) \log (x)+4 e^{5/4} (5-x)\right )}{\left (e^{5/4}-2 \log (x)\right )^5}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 18 \int \left (\frac {1}{16} (5-2 x)+\frac {e^{5/4} (2 x-5)}{4 \left (e^{5/4}-2 \log (x)\right )}+\frac {2 e^{5/4} \left (2-3 e^{5/4}\right ) x-5 e^{5/4} \left (4-3 e^{5/4}\right )}{8 \left (e^{5/4}-2 \log (x)\right )^2}+\frac {e^{5/2} \left (5 \left (6-e^{5/4}\right )-2 \left (3-e^{5/4}\right ) x\right )}{4 \left (e^{5/4}-2 \log (x)\right )^3}+\frac {2 e^{15/4} \left (12-e^{5/4}\right ) x-5 e^{15/4} \left (24-e^{5/4}\right )}{16 \left (e^{5/4}-2 \log (x)\right )^4}-\frac {e^5 (x-5)}{2 \left (e^{5/4}-2 \log (x)\right )^5}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle 18 \left (-\frac {1}{64} (5-2 x)^2-\frac {5 e^{\frac {15}{4}+\frac {e^{5/4}}{2}} \left (24-e^{5/4}\right ) \operatorname {ExpIntegralEi}\left (\frac {1}{2} \left (2 \log (x)-e^{5/4}\right )\right )}{1536}-\frac {5}{64} e^{\frac {1}{2} \left (5+e^{5/4}\right )} \left (6-e^{5/4}\right ) \operatorname {ExpIntegralEi}\left (\frac {1}{2} \left (2 \log (x)-e^{5/4}\right )\right )-\frac {5}{32} e^{\frac {5}{4}+\frac {e^{5/4}}{2}} \left (4-3 e^{5/4}\right ) \operatorname {ExpIntegralEi}\left (\frac {1}{2} \left (2 \log (x)-e^{5/4}\right )\right )-\frac {5 e^{5+\frac {e^{5/4}}{2}} \operatorname {ExpIntegralEi}\left (\frac {1}{2} \left (2 \log (x)-e^{5/4}\right )\right )}{1536}+\frac {5}{8} e^{\frac {5}{4}+\frac {e^{5/4}}{2}} \operatorname {ExpIntegralEi}\left (\frac {1}{2} \left (2 \log (x)-e^{5/4}\right )\right )+\frac {1}{96} e^{\frac {15}{4}+e^{5/4}} \left (12-e^{5/4}\right ) \operatorname {ExpIntegralEi}\left (2 \log (x)-e^{5/4}\right )+\frac {1}{8} e^{\frac {5}{2}+e^{5/4}} \left (3-e^{5/4}\right ) \operatorname {ExpIntegralEi}\left (2 \log (x)-e^{5/4}\right )+\frac {1}{8} e^{\frac {5}{4}+e^{5/4}} \left (2-3 e^{5/4}\right ) \operatorname {ExpIntegralEi}\left (2 \log (x)-e^{5/4}\right )+\frac {1}{96} e^{5+e^{5/4}} \operatorname {ExpIntegralEi}\left (2 \log (x)-e^{5/4}\right )-\frac {1}{4} e^{\frac {5}{4}+e^{5/4}} \operatorname {ExpIntegralEi}\left (2 \log (x)-e^{5/4}\right )-\frac {e^5 (5-x) x}{96 \left (e^{5/4}-2 \log (x)\right )}+\frac {5 e^{15/4} \left (24-e^{5/4}\right ) x}{256 \left (e^{5/4}-2 \log (x)\right )}+\frac {5 e^{5/2} \left (6-e^{5/4}\right ) x}{32 \left (e^{5/4}-2 \log (x)\right )}+\frac {35 e^5 x}{768 \left (e^{5/4}-2 \log (x)\right )}-\frac {e^{5/4} x \left (5 \left (4-3 e^{5/4}\right )-2 \left (2-3 e^{5/4}\right ) x\right )}{16 \left (e^{5/4}-2 \log (x)\right )}-\frac {e^{5/2} x \left (5 \left (6-e^{5/4}\right )-2 \left (3-e^{5/4}\right ) x\right )}{16 \left (e^{5/4}-2 \log (x)\right )}-\frac {e^{15/4} x \left (5 \left (24-e^{5/4}\right )-2 \left (12-e^{5/4}\right ) x\right )}{192 \left (e^{5/4}-2 \log (x)\right )}+\frac {e^5 (5-x) x}{96 \left (e^{5/4}-2 \log (x)\right )^2}-\frac {5 e^{15/4} \left (24-e^{5/4}\right ) x}{384 \left (e^{5/4}-2 \log (x)\right )^2}-\frac {5 e^5 x}{128 \left (e^{5/4}-2 \log (x)\right )^2}+\frac {e^{5/2} x \left (5 \left (6-e^{5/4}\right )-2 \left (3-e^{5/4}\right ) x\right )}{16 \left (e^{5/4}-2 \log (x)\right )^2}+\frac {e^{15/4} x \left (5 \left (24-e^{5/4}\right )-2 \left (12-e^{5/4}\right ) x\right )}{192 \left (e^{5/4}-2 \log (x)\right )^2}-\frac {e^5 (5-x) x}{48 \left (e^{5/4}-2 \log (x)\right )^3}+\frac {5 e^5 x}{96 \left (e^{5/4}-2 \log (x)\right )^3}-\frac {e^{15/4} x \left (5 \left (24-e^{5/4}\right )-2 \left (12-e^{5/4}\right ) x\right )}{96 \left (e^{5/4}-2 \log (x)\right )^3}+\frac {e^5 (5-x) x}{16 \left (e^{5/4}-2 \log (x)\right )^4}\right )\) |
Input:
Int[(E^(5/4)*(-360 + 72*x)*Log[x]^3 + E^(5/4)*(-90 + 36*x)*Log[x]^4 + (180 - 72*x)*Log[x]^5)/(-E^(25/4) + 10*E^5*Log[x] - 40*E^(15/4)*Log[x]^2 + 80* E^(5/2)*Log[x]^3 - 80*E^(5/4)*Log[x]^4 + 32*Log[x]^5),x]
Output:
18*(-1/64*(5 - 2*x)^2 + (5*E^(5/4 + E^(5/4)/2)*ExpIntegralEi[(-E^(5/4) + 2 *Log[x])/2])/8 - (5*E^(5 + E^(5/4)/2)*ExpIntegralEi[(-E^(5/4) + 2*Log[x])/ 2])/1536 - (5*E^(5/4 + E^(5/4)/2)*(4 - 3*E^(5/4))*ExpIntegralEi[(-E^(5/4) + 2*Log[x])/2])/32 - (5*E^((5 + E^(5/4))/2)*(6 - E^(5/4))*ExpIntegralEi[(- E^(5/4) + 2*Log[x])/2])/64 - (5*E^(15/4 + E^(5/4)/2)*(24 - E^(5/4))*ExpInt egralEi[(-E^(5/4) + 2*Log[x])/2])/1536 - (E^(5/4 + E^(5/4))*ExpIntegralEi[ -E^(5/4) + 2*Log[x]])/4 + (E^(5 + E^(5/4))*ExpIntegralEi[-E^(5/4) + 2*Log[ x]])/96 + (E^(5/4 + E^(5/4))*(2 - 3*E^(5/4))*ExpIntegralEi[-E^(5/4) + 2*Lo g[x]])/8 + (E^(5/2 + E^(5/4))*(3 - E^(5/4))*ExpIntegralEi[-E^(5/4) + 2*Log [x]])/8 + (E^(15/4 + E^(5/4))*(12 - E^(5/4))*ExpIntegralEi[-E^(5/4) + 2*Lo g[x]])/96 + (E^5*(5 - x)*x)/(16*(E^(5/4) - 2*Log[x])^4) + (5*E^5*x)/(96*(E ^(5/4) - 2*Log[x])^3) - (E^5*(5 - x)*x)/(48*(E^(5/4) - 2*Log[x])^3) - (E^( 15/4)*x*(5*(24 - E^(5/4)) - 2*(12 - E^(5/4))*x))/(96*(E^(5/4) - 2*Log[x])^ 3) - (5*E^5*x)/(128*(E^(5/4) - 2*Log[x])^2) - (5*E^(15/4)*(24 - E^(5/4))*x )/(384*(E^(5/4) - 2*Log[x])^2) + (E^5*(5 - x)*x)/(96*(E^(5/4) - 2*Log[x])^ 2) + (E^(5/2)*x*(5*(6 - E^(5/4)) - 2*(3 - E^(5/4))*x))/(16*(E^(5/4) - 2*Lo g[x])^2) + (E^(15/4)*x*(5*(24 - E^(5/4)) - 2*(12 - E^(5/4))*x))/(192*(E^(5 /4) - 2*Log[x])^2) + (35*E^5*x)/(768*(E^(5/4) - 2*Log[x])) + (5*E^(5/2)*(6 - E^(5/4))*x)/(32*(E^(5/4) - 2*Log[x])) + (5*E^(15/4)*(24 - E^(5/4))*x)/( 256*(E^(5/4) - 2*Log[x])) - (E^5*(5 - x)*x)/(96*(E^(5/4) - 2*Log[x])) -...
Int[(a_)*(Fx_), x_Symbol] :> Simp[a Int[Fx, x], x] /; FreeQ[a, x] && !Ma tchQ[Fx, (b_)*(Gx_) /; FreeQ[b, x]]
Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; Simpl erIntegrandQ[v, u, x]]
Time = 1.42 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.22
| method | result | size |
| norman | \(\frac {90 x \ln \left (x \right )^{4}-18 x^{2} \ln \left (x \right )^{4}}{\left ({\mathrm e}^{\frac {5}{4}}-2 \ln \left (x \right )\right )^{4}}\) | \(28\) |
| risch | \(-\frac {9 x \left (16 x \ln \left (x \right )^{4}-80 \ln \left (x \right )^{4}\right )}{8 \left (2 \ln \left (x \right )-{\mathrm e}^{\frac {5}{4}}\right )^{4}}\) | \(29\) |
| parallelrisch | \(-\frac {288 x^{2} \ln \left (x \right )^{4}-1440 x \ln \left (x \right )^{4}}{16 \left (16 \ln \left (x \right )^{4}-32 \,{\mathrm e}^{\frac {5}{4}} \ln \left (x \right )^{3}+24 \,{\mathrm e}^{\frac {5}{2}} \ln \left (x \right )^{2}-8 \,{\mathrm e}^{\frac {15}{4}} \ln \left (x \right )+{\mathrm e}^{5}\right )}\) | \(59\) |
| default | \(\text {Expression too large to display}\) | \(1258\) |
Input:
int(((-72*x+180)*ln(x)^5+(36*x-90)*exp(5/4)*ln(x)^4+(72*x-360)*exp(5/4)*ln (x)^3)/(32*ln(x)^5-80*exp(5/4)*ln(x)^4+80*exp(5/4)^2*ln(x)^3-40*exp(5/4)^3 *ln(x)^2+10*exp(5/4)^4*ln(x)-exp(5/4)^5),x,method=_RETURNVERBOSE)
Output:
(90*x*ln(x)^4-18*x^2*ln(x)^4)/(exp(5/4)-2*ln(x))^4
Leaf count of result is larger than twice the leaf count of optimal. 48 vs. \(2 (17) = 34\).
Time = 0.07 (sec) , antiderivative size = 48, normalized size of antiderivative = 2.09 \[ \int \frac {e^{5/4} (-360+72 x) \log ^3(x)+e^{5/4} (-90+36 x) \log ^4(x)+(180-72 x) \log ^5(x)}{-e^{25/4}+10 e^5 \log (x)-40 e^{15/4} \log ^2(x)+80 e^{5/2} \log ^3(x)-80 e^{5/4} \log ^4(x)+32 \log ^5(x)} \, dx=\frac {18 \, {\left (x^{2} - 5 \, x\right )} \log \left (x\right )^{4}}{32 \, e^{\frac {5}{4}} \log \left (x\right )^{3} - 16 \, \log \left (x\right )^{4} - 24 \, e^{\frac {5}{2}} \log \left (x\right )^{2} + 8 \, e^{\frac {15}{4}} \log \left (x\right ) - e^{5}} \] Input:
integrate(((-72*x+180)*log(x)^5+(36*x-90)*exp(5/4)*log(x)^4+(72*x-360)*exp (5/4)*log(x)^3)/(32*log(x)^5-80*exp(5/4)*log(x)^4+80*exp(5/4)^2*log(x)^3-4 0*exp(5/4)^3*log(x)^2+10*exp(5/4)^4*log(x)-exp(5/4)^5),x, algorithm="frica s")
Output:
18*(x^2 - 5*x)*log(x)^4/(32*e^(5/4)*log(x)^3 - 16*log(x)^4 - 24*e^(5/2)*lo g(x)^2 + 8*e^(15/4)*log(x) - e^5)
Exception generated. \[ \int \frac {e^{5/4} (-360+72 x) \log ^3(x)+e^{5/4} (-90+36 x) \log ^4(x)+(180-72 x) \log ^5(x)}{-e^{25/4}+10 e^5 \log (x)-40 e^{15/4} \log ^2(x)+80 e^{5/2} \log ^3(x)-80 e^{5/4} \log ^4(x)+32 \log ^5(x)} \, dx=\text {Exception raised: AttributeError} \] Input:
integrate(((-72*x+180)*ln(x)**5+(36*x-90)*exp(5/4)*ln(x)**4+(72*x-360)*exp (5/4)*ln(x)**3)/(32*ln(x)**5-80*exp(5/4)*ln(x)**4+80*exp(5/4)**2*ln(x)**3- 40*exp(5/4)**3*ln(x)**2+10*exp(5/4)**4*ln(x)-exp(5/4)**5),x)
Output:
Exception raised: AttributeError >> 'NoneType' object has no attribute 'ex pr'
Exception generated. \[ \int \frac {e^{5/4} (-360+72 x) \log ^3(x)+e^{5/4} (-90+36 x) \log ^4(x)+(180-72 x) \log ^5(x)}{-e^{25/4}+10 e^5 \log (x)-40 e^{15/4} \log ^2(x)+80 e^{5/2} \log ^3(x)-80 e^{5/4} \log ^4(x)+32 \log ^5(x)} \, dx=\text {Exception raised: RuntimeError} \] Input:
integrate(((-72*x+180)*log(x)^5+(36*x-90)*exp(5/4)*log(x)^4+(72*x-360)*exp (5/4)*log(x)^3)/(32*log(x)^5-80*exp(5/4)*log(x)^4+80*exp(5/4)^2*log(x)^3-4 0*exp(5/4)^3*log(x)^2+10*exp(5/4)^4*log(x)-exp(5/4)^5),x, algorithm="maxim a")
Output:
Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is un defined.
Leaf count of result is larger than twice the leaf count of optimal. 87 vs. \(2 (17) = 34\).
Time = 0.15 (sec) , antiderivative size = 87, normalized size of antiderivative = 3.78 \[ \int \frac {e^{5/4} (-360+72 x) \log ^3(x)+e^{5/4} (-90+36 x) \log ^4(x)+(180-72 x) \log ^5(x)}{-e^{25/4}+10 e^5 \log (x)-40 e^{15/4} \log ^2(x)+80 e^{5/2} \log ^3(x)-80 e^{5/4} \log ^4(x)+32 \log ^5(x)} \, dx=\frac {18 \, x^{2} \log \left (x\right )^{4}}{32 \, e^{\frac {5}{4}} \log \left (x\right )^{3} - 16 \, \log \left (x\right )^{4} - 24 \, e^{\frac {5}{2}} \log \left (x\right )^{2} + 8 \, e^{\frac {15}{4}} \log \left (x\right ) - e^{5}} - \frac {90 \, x \log \left (x\right )^{4}}{32 \, e^{\frac {5}{4}} \log \left (x\right )^{3} - 16 \, \log \left (x\right )^{4} - 24 \, e^{\frac {5}{2}} \log \left (x\right )^{2} + 8 \, e^{\frac {15}{4}} \log \left (x\right ) - e^{5}} \] Input:
integrate(((-72*x+180)*log(x)^5+(36*x-90)*exp(5/4)*log(x)^4+(72*x-360)*exp (5/4)*log(x)^3)/(32*log(x)^5-80*exp(5/4)*log(x)^4+80*exp(5/4)^2*log(x)^3-4 0*exp(5/4)^3*log(x)^2+10*exp(5/4)^4*log(x)-exp(5/4)^5),x, algorithm="giac" )
Output:
18*x^2*log(x)^4/(32*e^(5/4)*log(x)^3 - 16*log(x)^4 - 24*e^(5/2)*log(x)^2 + 8*e^(15/4)*log(x) - e^5) - 90*x*log(x)^4/(32*e^(5/4)*log(x)^3 - 16*log(x) ^4 - 24*e^(5/2)*log(x)^2 + 8*e^(15/4)*log(x) - e^5)
Time = 0.88 (sec) , antiderivative size = 738, normalized size of antiderivative = 32.09 \[ \int \frac {e^{5/4} (-360+72 x) \log ^3(x)+e^{5/4} (-90+36 x) \log ^4(x)+(180-72 x) \log ^5(x)}{-e^{25/4}+10 e^5 \log (x)-40 e^{15/4} \log ^2(x)+80 e^{5/2} \log ^3(x)-80 e^{5/4} \log ^4(x)+32 \log ^5(x)} \, dx=\text {Too large to display} \] Input:
int(-(exp(5/4)*log(x)^4*(36*x - 90) - log(x)^5*(72*x - 180) + exp(5/4)*log (x)^3*(72*x - 360))/(exp(25/4) - 80*exp(5/2)*log(x)^3 + 80*exp(5/4)*log(x) ^4 + 40*exp(15/4)*log(x)^2 - 32*log(x)^5 - 10*exp(5)*log(x)),x)
Output:
((3*x*(100*exp(5) - 400*exp(15/4) - 5*exp(25/4) - 80*x*exp(5) + 160*x*exp( 15/4) + 8*x*exp(25/4)))/2048 + (3*x*log(x)*(25*exp(5) + 1200*exp(5/2) + 96 0*exp(5/4) - 400*exp(15/4) - 40*x*exp(5) - 480*x*exp(5/2) - 192*x*exp(5/4) + 320*x*exp(15/4)))/1024 - (3*x*log(x)^4*(5*exp(5/4) - 8*x*exp(5/4)))/32 + (3*x*log(x)^3*(25*exp(5/2) - 140*exp(5/4) - 40*x*exp(5/2) + 112*x*exp(5/ 4)))/128 + (3*x*log(x)^2*(300*exp(5/2) - 240*exp(5/4) - 25*exp(15/4) - 240 *x*exp(5/2) + 96*x*exp(5/4) + 40*x*exp(15/4)))/256)/(exp(5/2)/4 + log(x)^2 - exp(5/4)*log(x)) + x*((45*exp(5/4))/4 - (135*exp(5/2))/32 - (15*exp(5)) /1024 + (15*exp(15/4))/32 + 45/8) - ((3*x*(150*exp(5) + 2400*exp(5/2) + 19 20*exp(5/4) - 1200*exp(15/4) - 5*exp(25/4) - 240*x*exp(5) - 960*x*exp(5/2) - 384*x*exp(5/4) + 960*x*exp(15/4) + 16*x*exp(25/4)))/2048 + (3*x*log(x)* (25*exp(5) + 3600*exp(5/2) - 960*exp(5/4) - 600*exp(15/4) - 80*x*exp(5) - 2880*x*exp(5/2) + 384*x*exp(5/4) + 960*x*exp(15/4)))/1024 - (3*x*log(x)^4* (5*exp(5/4) - 16*x*exp(5/4)))/32 + (3*x*log(x)^3*(25*exp(5/2) - 220*exp(5/ 4) - 80*x*exp(5/2) + 352*x*exp(5/4)))/128 + (3*x*log(x)^2*(450*exp(5/2) - 1080*exp(5/4) - 25*exp(15/4) - 720*x*exp(5/2) + 864*x*exp(5/4) + 80*x*exp( 15/4)))/256)/(exp(5/4)/2 - log(x)) - log(x)^2*((45*x*exp(5/4)*(exp(5/4) - 16))/128 - (9*x^2*exp(5/4)*(exp(5/4) - 8))/8) - ((3*x*(50*exp(5) - 5*exp(2 5/4) - 20*x*exp(5) + 4*x*exp(25/4)))/1024 + (15*x*log(x)*(5*exp(5) - 40*ex p(15/4) - 4*x*exp(5) + 16*x*exp(15/4)))/512 - (3*x*log(x)^4*(5*exp(5/4)...
\[ \int \frac {e^{5/4} (-360+72 x) \log ^3(x)+e^{5/4} (-90+36 x) \log ^4(x)+(180-72 x) \log ^5(x)}{-e^{25/4}+10 e^5 \log (x)-40 e^{15/4} \log ^2(x)+80 e^{5/2} \log ^3(x)-80 e^{5/4} \log ^4(x)+32 \log ^5(x)} \, dx=\text {too large to display} \] Input:
int(((-72*x+180)*log(x)^5+(36*x-90)*exp(5/4)*log(x)^4+(72*x-360)*exp(5/4)* log(x)^3)/(32*log(x)^5-80*exp(5/4)*log(x)^4+80*exp(5/4)^2*log(x)^3-40*exp( 5/4)^3*log(x)^2+10*exp(5/4)^4*log(x)-exp(5/4)^5),x)
Output:
(9*( - 6400*e**(3/4)*int(log(x)**7/(2560*e**(3/4)*log(x)**7*e**3 + 800*e** (3/4)*log(x)**3*e**8 + 5120*e**(1/4)*log(x)**9*e + 1664*e**(1/4)*log(x)**5 *e**6 + 20*e**(1/4)*log(x)*e**11 - 6400*sqrt(e)*log(x)**8*e**2 - 1760*sqrt (e)*log(x)**4*e**7 - sqrt(e)*e**12 - 1024*log(x)**10 - 640*log(x)**6*e**5 - 180*log(x)**2*e**10),x)*e**3 - 12000*e**(3/4)*int(log(x)**3/(2560*e**(3/ 4)*log(x)**7*e**3 + 800*e**(3/4)*log(x)**3*e**8 + 5120*e**(1/4)*log(x)**9* e + 1664*e**(1/4)*log(x)**5*e**6 + 20*e**(1/4)*log(x)*e**11 - 6400*sqrt(e) *log(x)**8*e**2 - 1760*sqrt(e)*log(x)**4*e**7 - sqrt(e)*e**12 - 1024*log(x )**10 - 640*log(x)**6*e**5 - 180*log(x)**2*e**10),x)*e**8 + 2560*e**(3/4)* int((log(x)**7*x)/(2560*e**(3/4)*log(x)**7*e**3 + 800*e**(3/4)*log(x)**3*e **8 + 5120*e**(1/4)*log(x)**9*e + 1664*e**(1/4)*log(x)**5*e**6 + 20*e**(1/ 4)*log(x)*e**11 - 6400*sqrt(e)*log(x)**8*e**2 - 1760*sqrt(e)*log(x)**4*e** 7 - sqrt(e)*e**12 - 1024*log(x)**10 - 640*log(x)**6*e**5 - 180*log(x)**2*e **10),x)*e**3 + 4800*e**(3/4)*int((log(x)**3*x)/(2560*e**(3/4)*log(x)**7*e **3 + 800*e**(3/4)*log(x)**3*e**8 + 5120*e**(1/4)*log(x)**9*e + 1664*e**(1 /4)*log(x)**5*e**6 + 20*e**(1/4)*log(x)*e**11 - 6400*sqrt(e)*log(x)**8*e** 2 - 1760*sqrt(e)*log(x)**4*e**7 - sqrt(e)*e**12 - 1024*log(x)**10 - 640*lo g(x)**6*e**5 - 180*log(x)**2*e**10),x)*e**8 - 32000*e**(3/4)*int(log(x)**7 /(2560*e**(3/4)*log(x)**7*e**3 + 800*e**(3/4)*log(x)**3*e**8 + 5120*e**(1/ 4)*log(x)**9*e + 1664*e**(1/4)*log(x)**5*e**6 + 20*e**(1/4)*log(x)*e**1...