Integrand size = 100, antiderivative size = 32 \[ \int \frac {-32 x^4+64 x^5-48 x^6+16 x^7-2 x^8+\left (64 x^3-160 x^4+144 x^5-56 x^6+8 x^7\right ) \log \left (5 e^{-3+x}\right )+e^{e^x+x} \left (-25-25 e^x\right ) \log ^3\left (5 e^{-3+x}\right )}{25 \log ^3\left (5 e^{-3+x}\right )} \, dx=-e^{e^x+x}+\frac {(-2+x)^4 x^4}{25 \log ^2\left (5 e^{-3+x}\right )} \] Output:
1/25*(-2+x)^4/ln(5*exp(-3+x))^2*x^4-exp(exp(x)+x)
Leaf count is larger than twice the leaf count of optimal. \(198\) vs. \(2(32)=64\).
Time = 0.37 (sec) , antiderivative size = 198, normalized size of antiderivative = 6.19 \[ \int \frac {-32 x^4+64 x^5-48 x^6+16 x^7-2 x^8+\left (64 x^3-160 x^4+144 x^5-56 x^6+8 x^7\right ) \log \left (5 e^{-3+x}\right )+e^{e^x+x} \left (-25-25 e^x\right ) \log ^3\left (5 e^{-3+x}\right )}{25 \log ^3\left (5 e^{-3+x}\right )} \, dx=\frac {(-2+x)^4 x^4-\left (25 e^{e^x+x}+(-2+x)^3 x^2 (-6+7 x)\right ) \log ^2\left (5 e^{-3+x}\right )+6 (-2+x)^2 x \left (4-12 x+7 x^2\right ) \log ^3\left (5 e^{-3+x}\right )-3 \left (16-128 x+240 x^2-160 x^3+35 x^4\right ) \log ^4\left (5 e^{-3+x}\right )+4 \left (-32+120 x-120 x^2+35 x^3\right ) \log ^5\left (5 e^{-3+x}\right )-15 \left (8-16 x+7 x^2\right ) \log ^6\left (5 e^{-3+x}\right )+6 (-8+7 x) \log ^7\left (5 e^{-3+x}\right )-7 \log ^8\left (5 e^{-3+x}\right )}{25 \log ^2\left (5 e^{-3+x}\right )} \] Input:
Integrate[(-32*x^4 + 64*x^5 - 48*x^6 + 16*x^7 - 2*x^8 + (64*x^3 - 160*x^4 + 144*x^5 - 56*x^6 + 8*x^7)*Log[5*E^(-3 + x)] + E^(E^x + x)*(-25 - 25*E^x) *Log[5*E^(-3 + x)]^3)/(25*Log[5*E^(-3 + x)]^3),x]
Output:
((-2 + x)^4*x^4 - (25*E^(E^x + x) + (-2 + x)^3*x^2*(-6 + 7*x))*Log[5*E^(-3 + x)]^2 + 6*(-2 + x)^2*x*(4 - 12*x + 7*x^2)*Log[5*E^(-3 + x)]^3 - 3*(16 - 128*x + 240*x^2 - 160*x^3 + 35*x^4)*Log[5*E^(-3 + x)]^4 + 4*(-32 + 120*x - 120*x^2 + 35*x^3)*Log[5*E^(-3 + x)]^5 - 15*(8 - 16*x + 7*x^2)*Log[5*E^(- 3 + x)]^6 + 6*(-8 + 7*x)*Log[5*E^(-3 + x)]^7 - 7*Log[5*E^(-3 + x)]^8)/(25* Log[5*E^(-3 + x)]^2)
Leaf count is larger than twice the leaf count of optimal. \(88\) vs. \(2(32)=64\).
Time = 1.84 (sec) , antiderivative size = 88, normalized size of antiderivative = 2.75, number of steps used = 4, number of rules used = 4, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.040, Rules used = {27, 25, 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.
\(\displaystyle \int \frac {-2 x^8+16 x^7-48 x^6+64 x^5-32 x^4+\left (8 x^7-56 x^6+144 x^5-160 x^4+64 x^3\right ) \log \left (5 e^{x-3}\right )+e^{x+e^x} \left (-25 e^x-25\right ) \log ^3\left (5 e^{x-3}\right )}{25 \log ^3\left (5 e^{x-3}\right )} \, dx\) |
\(\Big \downarrow \) 27 |
\(\displaystyle \frac {1}{25} \int -\frac {2 x^8-16 x^7+48 x^6-64 x^5+32 x^4+25 e^{x+e^x} \left (1+e^x\right ) \log ^3\left (5 e^{x-3}\right )-8 \left (x^7-7 x^6+18 x^5-20 x^4+8 x^3\right ) \log \left (5 e^{x-3}\right )}{\log ^3\left (5 e^{x-3}\right )}dx\) |
\(\Big \downarrow \) 25 |
\(\displaystyle -\frac {1}{25} \int \frac {2 x^8-16 x^7+48 x^6-64 x^5+32 x^4+25 e^{x+e^x} \left (1+e^x\right ) \log ^3\left (5 e^{x-3}\right )-8 \left (x^7-7 x^6+18 x^5-20 x^4+8 x^3\right ) \log \left (5 e^{x-3}\right )}{\log ^3\left (5 e^{x-3}\right )}dx\) |
\(\Big \downarrow \) 7293 |
\(\displaystyle -\frac {1}{25} \int \left (\frac {2 (x-2)^3 \left (x^2-4 \log \left (5 e^{x-3}\right ) x-2 x+4 \log \left (5 e^{x-3}\right )\right ) x^3}{\log ^3\left (5 e^{x-3}\right )}+25 e^{x+e^x}+25 e^{2 x+e^x}\right )dx\) |
\(\Big \downarrow \) 2009 |
\(\displaystyle \frac {1}{25} \left (\frac {x^8}{\log ^2\left (5 e^{x-3}\right )}-\frac {8 x^7}{\log ^2\left (5 e^{x-3}\right )}+\frac {24 x^6}{\log ^2\left (5 e^{x-3}\right )}-\frac {32 x^5}{\log ^2\left (5 e^{x-3}\right )}+\frac {16 x^4}{\log ^2\left (5 e^{x-3}\right )}-25 e^{x+e^x}\right )\) |
Input:
Int[(-32*x^4 + 64*x^5 - 48*x^6 + 16*x^7 - 2*x^8 + (64*x^3 - 160*x^4 + 144* x^5 - 56*x^6 + 8*x^7)*Log[5*E^(-3 + x)] + E^(E^x + x)*(-25 - 25*E^x)*Log[5 *E^(-3 + x)]^3)/(25*Log[5*E^(-3 + x)]^3),x]
Output:
(-25*E^(E^x + x) + (16*x^4)/Log[5*E^(-3 + x)]^2 - (32*x^5)/Log[5*E^(-3 + x )]^2 + (24*x^6)/Log[5*E^(-3 + x)]^2 - (8*x^7)/Log[5*E^(-3 + x)]^2 + x^8/Lo g[5*E^(-3 + x)]^2)/25
Int[(a_)*(Fx_), x_Symbol] :> Simp[a Int[Fx, x], x] /; FreeQ[a, x] && !Ma tchQ[Fx, (b_)*(Gx_) /; FreeQ[b, x]]
Result contains complex when optimal does not.
Time = 0.98 (sec) , antiderivative size = 51, normalized size of antiderivative = 1.59
method | result | size |
risch | \(-{\mathrm e}^{{\mathrm e}^{x}+x}-\frac {4 \left (x^{8}-8 x^{7}+24 x^{6}-32 x^{5}+16 x^{4}\right )}{25 {\left (-2 i \ln \left (5\right )-2 i \ln \left ({\mathrm e}^{x}\right )+6 i\right )}^{2}}\) | \(51\) |
parallelrisch | \(\frac {-3360 x^{7}+420 x^{8}+6720 x^{4}+10080 x^{6}-13440 x^{5}-10500 \ln \left (5 \,{\mathrm e}^{-3+x}\right )^{2} {\mathrm e}^{{\mathrm e}^{x}+x}}{10500 \ln \left (5 \,{\mathrm e}^{-3+x}\right )^{2}}\) | \(54\) |
default | \(\text {Expression too large to display}\) | \(889\) |
parts | \(\text {Expression too large to display}\) | \(889\) |
Input:
int(1/25*((-25*exp(x)-25)*exp(exp(x)+x)*ln(5*exp(-3+x))^3+(8*x^7-56*x^6+14 4*x^5-160*x^4+64*x^3)*ln(5*exp(-3+x))-2*x^8+16*x^7-48*x^6+64*x^5-32*x^4)/l n(5*exp(-3+x))^3,x,method=_RETURNVERBOSE)
Output:
-exp(exp(x)+x)-4/25*(x^8-8*x^7+24*x^6-32*x^5+16*x^4)/(-2*I*ln(5)-2*I*ln(ex p(x))+6*I)^2
Leaf count of result is larger than twice the leaf count of optimal. 193 vs. \(2 (27) = 54\).
Time = 0.08 (sec) , antiderivative size = 193, normalized size of antiderivative = 6.03 \[ \int \frac {-32 x^4+64 x^5-48 x^6+16 x^7-2 x^8+\left (64 x^3-160 x^4+144 x^5-56 x^6+8 x^7\right ) \log \left (5 e^{-3+x}\right )+e^{e^x+x} \left (-25-25 e^x\right ) \log ^3\left (5 e^{-3+x}\right )}{25 \log ^3\left (5 e^{-3+x}\right )} \, dx=\frac {x^{8} - 2 \, {\left (7 \, x - 60\right )} \log \left (5\right )^{7} - 7 \, \log \left (5\right )^{8} - 8 \, x^{7} - {\left (7 \, x^{2} - 198 \, x + 876\right )} \log \left (5\right )^{6} + 24 \, x^{6} + 2 \, {\left (39 \, x^{2} - 579 \, x + 1772\right )} \log \left (5\right )^{5} - 32 \, x^{5} - {\left (345 \, x^{2} - 3614 \, x + 8658\right )} \log \left (5\right )^{4} + 16 \, x^{4} + 2 \, {\left (386 \, x^{2} - 3237 \, x + 6516\right )} \log \left (5\right )^{3} - 3 \, {\left (307 \, x^{2} - 2214 \, x + 3924\right )} \log \left (5\right )^{2} - 135 \, x^{2} - 25 \, {\left (x^{2} + 2 \, {\left (x - 3\right )} \log \left (5\right ) + \log \left (5\right )^{2} - 6 \, x + 9\right )} e^{\left (x + e^{x}\right )} + 18 \, {\left (31 \, x^{2} - 201 \, x + 324\right )} \log \left (5\right ) + 810 \, x - 1215}{25 \, {\left (x^{2} + 2 \, {\left (x - 3\right )} \log \left (5\right ) + \log \left (5\right )^{2} - 6 \, x + 9\right )}} \] Input:
integrate(1/25*((-25*exp(x)-25)*exp(exp(x)+x)*log(5*exp(-3+x))^3+(8*x^7-56 *x^6+144*x^5-160*x^4+64*x^3)*log(5*exp(-3+x))-2*x^8+16*x^7-48*x^6+64*x^5-3 2*x^4)/log(5*exp(-3+x))^3,x, algorithm="fricas")
Output:
1/25*(x^8 - 2*(7*x - 60)*log(5)^7 - 7*log(5)^8 - 8*x^7 - (7*x^2 - 198*x + 876)*log(5)^6 + 24*x^6 + 2*(39*x^2 - 579*x + 1772)*log(5)^5 - 32*x^5 - (34 5*x^2 - 3614*x + 8658)*log(5)^4 + 16*x^4 + 2*(386*x^2 - 3237*x + 6516)*log (5)^3 - 3*(307*x^2 - 2214*x + 3924)*log(5)^2 - 135*x^2 - 25*(x^2 + 2*(x - 3)*log(5) + log(5)^2 - 6*x + 9)*e^(x + e^x) + 18*(31*x^2 - 201*x + 324)*lo g(5) + 810*x - 1215)/(x^2 + 2*(x - 3)*log(5) + log(5)^2 - 6*x + 9)
Leaf count of result is larger than twice the leaf count of optimal. 291 vs. \(2 (26) = 52\).
Time = 1.31 (sec) , antiderivative size = 291, normalized size of antiderivative = 9.09 \[ \int \frac {-32 x^4+64 x^5-48 x^6+16 x^7-2 x^8+\left (64 x^3-160 x^4+144 x^5-56 x^6+8 x^7\right ) \log \left (5 e^{-3+x}\right )+e^{e^x+x} \left (-25-25 e^x\right ) \log ^3\left (5 e^{-3+x}\right )}{25 \log ^3\left (5 e^{-3+x}\right )} \, dx=\frac {x^{6}}{25} + x^{5} \left (- \frac {2 \log {\left (5 \right )}}{25} - \frac {2}{25}\right ) + x^{4} \left (- \frac {2 \log {\left (5 \right )}}{25} + \frac {3}{25} + \frac {3 \log {\left (5 \right )}^{2}}{25}\right ) + x^{3} \left (- \frac {12 \log {\left (5 \right )}}{25} - \frac {4 \log {\left (5 \right )}^{3}}{25} + \frac {4}{25} + \frac {12 \log {\left (5 \right )}^{2}}{25}\right ) + x^{2} \left (- \frac {28 \log {\left (5 \right )}^{3}}{25} - \frac {44 \log {\left (5 \right )}}{25} + \frac {13}{25} + \frac {\log {\left (5 \right )}^{4}}{5} + \frac {54 \log {\left (5 \right )}^{2}}{25}\right ) + x \left (- \frac {156 \log {\left (5 \right )}^{3}}{25} - \frac {158 \log {\left (5 \right )}}{25} - \frac {6 \log {\left (5 \right )}^{5}}{25} + \frac {42}{25} + 2 \log {\left (5 \right )}^{4} + \frac {228 \log {\left (5 \right )}^{2}}{25}\right ) - e^{x + e^{x}} + \frac {x \left (- 3544 \log {\left (5 \right )}^{3} - 648 \log {\left (5 \right )}^{5} - 1944 \log {\left (5 \right )} - 8 \log {\left (5 \right )}^{7} + 432 + 112 \log {\left (5 \right )}^{6} + 3600 \log {\left (5 \right )}^{2} + 2000 \log {\left (5 \right )}^{4}\right ) - 8658 \log {\left (5 \right )}^{4} - 11772 \log {\left (5 \right )}^{2} - 876 \log {\left (5 \right )}^{6} - 1215 - 7 \log {\left (5 \right )}^{8} + 120 \log {\left (5 \right )}^{7} + 5832 \log {\left (5 \right )} + 3544 \log {\left (5 \right )}^{5} + 13032 \log {\left (5 \right )}^{3}}{25 x^{2} + x \left (-150 + 50 \log {\left (5 \right )}\right ) - 150 \log {\left (5 \right )} + 25 \log {\left (5 \right )}^{2} + 225} \] Input:
integrate(1/25*((-25*exp(x)-25)*exp(exp(x)+x)*ln(5*exp(-3+x))**3+(8*x**7-5 6*x**6+144*x**5-160*x**4+64*x**3)*ln(5*exp(-3+x))-2*x**8+16*x**7-48*x**6+6 4*x**5-32*x**4)/ln(5*exp(-3+x))**3,x)
Output:
x**6/25 + x**5*(-2*log(5)/25 - 2/25) + x**4*(-2*log(5)/25 + 3/25 + 3*log(5 )**2/25) + x**3*(-12*log(5)/25 - 4*log(5)**3/25 + 4/25 + 12*log(5)**2/25) + x**2*(-28*log(5)**3/25 - 44*log(5)/25 + 13/25 + log(5)**4/5 + 54*log(5)* *2/25) + x*(-156*log(5)**3/25 - 158*log(5)/25 - 6*log(5)**5/25 + 42/25 + 2 *log(5)**4 + 228*log(5)**2/25) - exp(x + exp(x)) + (x*(-3544*log(5)**3 - 6 48*log(5)**5 - 1944*log(5) - 8*log(5)**7 + 432 + 112*log(5)**6 + 3600*log( 5)**2 + 2000*log(5)**4) - 8658*log(5)**4 - 11772*log(5)**2 - 876*log(5)**6 - 1215 - 7*log(5)**8 + 120*log(5)**7 + 5832*log(5) + 3544*log(5)**5 + 130 32*log(5)**3)/(25*x**2 + x*(-150 + 50*log(5)) - 150*log(5) + 25*log(5)**2 + 225)
Leaf count of result is larger than twice the leaf count of optimal. 1477 vs. \(2 (27) = 54\).
Time = 0.16 (sec) , antiderivative size = 1477, normalized size of antiderivative = 46.16 \[ \int \frac {-32 x^4+64 x^5-48 x^6+16 x^7-2 x^8+\left (64 x^3-160 x^4+144 x^5-56 x^6+8 x^7\right ) \log \left (5 e^{-3+x}\right )+e^{e^x+x} \left (-25-25 e^x\right ) \log ^3\left (5 e^{-3+x}\right )}{25 \log ^3\left (5 e^{-3+x}\right )} \, dx=\text {Too large to display} \] Input:
integrate(1/25*((-25*exp(x)-25)*exp(exp(x)+x)*log(5*exp(-3+x))^3+(8*x^7-56 *x^6+144*x^5-160*x^4+64*x^3)*log(5*exp(-3+x))-2*x^8+16*x^7-48*x^6+64*x^5-3 2*x^4)/log(5*exp(-3+x))^3,x, algorithm="maxima")
Output:
-(e^x - 1)*e^(e^x) - 1/375*(5*x^8 - 8*x^7*(log(5) - 3) + 225*log(5)^8 + 14 *(log(5)^2 - 6*log(5) + 9)*x^6 - 5400*log(5)^7 - 28*(log(5)^3 - 9*log(5)^2 + 27*log(5) - 27)*x^5 + 56700*log(5)^6 + 70*(log(5)^4 - 12*log(5)^3 + 54* log(5)^2 - 108*log(5) + 81)*x^4 - 340200*log(5)^5 - 280*(log(5)^5 - 15*log (5)^4 + 90*log(5)^3 - 270*log(5)^2 + 405*log(5) - 243)*x^3 + 1275750*log(5 )^4 - 1035*(log(5)^6 - 18*log(5)^5 + 135*log(5)^4 - 540*log(5)^3 + 1215*lo g(5)^2 - 1458*log(5) + 729)*x^2 - 3061800*log(5)^3 - 390*(log(5)^7 - 21*lo g(5)^6 + 189*log(5)^5 - 945*log(5)^4 + 2835*log(5)^3 - 5103*log(5)^2 + 510 3*log(5) - 2187)*x + 4592700*log(5)^2 - 3936600*log(5) + 1476225)/(x^2 + 2 *x*(log(5) - 3) + log(5)^2 - 6*log(5) + 9) + 4/125*(4*x^7 - 7*x^6*(log(5) - 3) - 130*log(5)^7 + 14*(log(5)^2 - 6*log(5) + 9)*x^5 + 2730*log(5)^6 - 3 5*(log(5)^3 - 9*log(5)^2 + 27*log(5) - 27)*x^4 - 24570*log(5)^5 + 140*(log (5)^4 - 12*log(5)^3 + 54*log(5)^2 - 108*log(5) + 81)*x^3 + 122850*log(5)^4 + 500*(log(5)^5 - 15*log(5)^4 + 90*log(5)^3 - 270*log(5)^2 + 405*log(5) - 243)*x^2 - 368550*log(5)^3 + 160*(log(5)^6 - 18*log(5)^5 + 135*log(5)^4 - 540*log(5)^3 + 1215*log(5)^2 - 1458*log(5) + 729)*x + 663390*log(5)^2 - 6 63390*log(5) + 284310)/(x^2 + 2*x*(log(5) - 3) + log(5)^2 - 6*log(5) + 9) - 12/25*(x^6 - 2*x^5*(log(5) - 3) + 22*log(5)^6 + 5*(log(5)^2 - 6*log(5) + 9)*x^4 - 396*log(5)^5 - 20*(log(5)^3 - 9*log(5)^2 + 27*log(5) - 27)*x^3 + 2970*log(5)^4 - 68*(log(5)^4 - 12*log(5)^3 + 54*log(5)^2 - 108*log(5) ...
Leaf count of result is larger than twice the leaf count of optimal. 415 vs. \(2 (27) = 54\).
Time = 0.14 (sec) , antiderivative size = 415, normalized size of antiderivative = 12.97 \[ \int \frac {-32 x^4+64 x^5-48 x^6+16 x^7-2 x^8+\left (64 x^3-160 x^4+144 x^5-56 x^6+8 x^7\right ) \log \left (5 e^{-3+x}\right )+e^{e^x+x} \left (-25-25 e^x\right ) \log ^3\left (5 e^{-3+x}\right )}{25 \log ^3\left (5 e^{-3+x}\right )} \, dx =\text {Too large to display} \] Input:
integrate(1/25*((-25*exp(x)-25)*exp(exp(x)+x)*log(5*exp(-3+x))^3+(8*x^7-56 *x^6+144*x^5-160*x^4+64*x^3)*log(5*exp(-3+x))-2*x^8+16*x^7-48*x^6+64*x^5-3 2*x^4)/log(5*exp(-3+x))^3,x, algorithm="giac")
Output:
1/25*(x^8*e^(2*x) - 7*x^2*e^(2*x)*log(5)^6 - 14*x*e^(2*x)*log(5)^7 - 7*e^( 2*x)*log(5)^8 - 8*x^7*e^(2*x) + 78*x^2*e^(2*x)*log(5)^5 + 198*x*e^(2*x)*lo g(5)^6 + 120*e^(2*x)*log(5)^7 + 24*x^6*e^(2*x) - 345*x^2*e^(2*x)*log(5)^4 - 1158*x*e^(2*x)*log(5)^5 - 876*e^(2*x)*log(5)^6 - 32*x^5*e^(2*x) + 772*x^ 2*e^(2*x)*log(5)^3 + 3614*x*e^(2*x)*log(5)^4 + 3544*e^(2*x)*log(5)^5 + 16* x^4*e^(2*x) - 921*x^2*e^(2*x)*log(5)^2 - 6474*x*e^(2*x)*log(5)^3 - 8658*e^ (2*x)*log(5)^4 + 558*x^2*e^(2*x)*log(5) + 6642*x*e^(2*x)*log(5)^2 + 13032* e^(2*x)*log(5)^3 - 135*x^2*e^(2*x) - 25*x^2*e^(3*x + e^x) - 3618*x*e^(2*x) *log(5) - 50*x*e^(3*x + e^x)*log(5) - 11772*e^(2*x)*log(5)^2 - 25*e^(3*x + e^x)*log(5)^2 + 810*x*e^(2*x) + 150*x*e^(3*x + e^x) + 5832*e^(2*x)*log(5) + 150*e^(3*x + e^x)*log(5) - 1215*e^(2*x) - 225*e^(3*x + e^x))/(x^2*e^(2* x) + 2*x*e^(2*x)*log(5) + e^(2*x)*log(5)^2 - 6*x*e^(2*x) - 6*e^(2*x)*log(5 ) + 9*e^(2*x))
Time = 2.24 (sec) , antiderivative size = 586, normalized size of antiderivative = 18.31 \[ \int \frac {-32 x^4+64 x^5-48 x^6+16 x^7-2 x^8+\left (64 x^3-160 x^4+144 x^5-56 x^6+8 x^7\right ) \log \left (5 e^{-3+x}\right )+e^{e^x+x} \left (-25-25 e^x\right ) \log ^3\left (5 e^{-3+x}\right )}{25 \log ^3\left (5 e^{-3+x}\right )} \, dx=\text {Too large to display} \] Input:
int(-((32*x^4)/25 - (64*x^5)/25 + (48*x^6)/25 - (16*x^7)/25 + (2*x^8)/25 - (log(5*exp(x - 3))*(64*x^3 - 160*x^4 + 144*x^5 - 56*x^6 + 8*x^7))/25 + (l og(5*exp(x - 3))^3*exp(x + exp(x))*(25*exp(x) + 25))/25)/log(5*exp(x - 3)) ^3,x)
Output:
x^2*((3*(log(5) - 3)^2*((56*log(5))/25 + (18*(log(5) - 3)^2)/25 - 3*((2*lo g(5))/5 + 2/5)*(log(5) - 3) - 264/25))/2 - (16*log(5))/5 + (((2*log(5))/5 + 2/5)*(log(5) - 3)^3)/2 - (3*(log(5) - 3)*((144*log(5))/25 - (6*(log(5) - 3)^3)/25 + 3*(log(5) - 3)*((56*log(5))/25 + (18*(log(5) - 3)^2)/25 - 3*(( 2*log(5))/5 + 2/5)*(log(5) - 3) - 264/25) + 3*((2*log(5))/5 + 2/5)*(log(5) - 3)^2 - 528/25))/2 + 256/25) - x*(3*(log(5) - 3)^2*((144*log(5))/25 - (6 *(log(5) - 3)^3)/25 + 3*(log(5) - 3)*((56*log(5))/25 + (18*(log(5) - 3)^2) /25 - 3*((2*log(5))/5 + 2/5)*(log(5) - 3) - 264/25) + 3*((2*log(5))/5 + 2/ 5)*(log(5) - 3)^2 - 528/25) - (64*log(5))/25 + 3*(log(5) - 3)*(3*(log(5) - 3)^2*((56*log(5))/25 + (18*(log(5) - 3)^2)/25 - 3*((2*log(5))/5 + 2/5)*(l og(5) - 3) - 264/25) - (32*log(5))/5 + ((2*log(5))/5 + 2/5)*(log(5) - 3)^3 - 3*(log(5) - 3)*((144*log(5))/25 - (6*(log(5) - 3)^3)/25 + 3*(log(5) - 3 )*((56*log(5))/25 + (18*(log(5) - 3)^2)/25 - 3*((2*log(5))/5 + 2/5)*(log(5 ) - 3) - 264/25) + 3*((2*log(5))/5 + 2/5)*(log(5) - 3)^2 - 528/25) + 512/2 5) - (log(5) - 3)^3*((56*log(5))/25 + (18*(log(5) - 3)^2)/25 - 3*((2*log(5 ))/5 + 2/5)*(log(5) - 3) - 264/25) + 192/25) - x^4*((14*log(5))/25 + (9*(l og(5) - 3)^2)/50 - (3*((2*log(5))/5 + 2/5)*(log(5) - 3))/4 - 66/25) - x^5* ((2*log(5))/25 + 2/25) - exp(x + exp(x)) - (48*(log(5) - 3)^4 + 128*(log(5 ) - 3)^5 + 120*(log(5) - 3)^6 + 48*(log(5) - 3)^7 + 7*(log(5) - 3)^8 + x*( 64*(log(5) - 3)^3 + 160*(log(5) - 3)^4 + 144*(log(5) - 3)^5 + 56*(log(5...
Time = 0.19 (sec) , antiderivative size = 57, normalized size of antiderivative = 1.78 \[ \int \frac {-32 x^4+64 x^5-48 x^6+16 x^7-2 x^8+\left (64 x^3-160 x^4+144 x^5-56 x^6+8 x^7\right ) \log \left (5 e^{-3+x}\right )+e^{e^x+x} \left (-25-25 e^x\right ) \log ^3\left (5 e^{-3+x}\right )}{25 \log ^3\left (5 e^{-3+x}\right )} \, dx=\frac {-25 e^{e^{x}+x} \mathrm {log}\left (\frac {5 e^{x}}{e^{3}}\right )^{2}+x^{8}-8 x^{7}+24 x^{6}-32 x^{5}+16 x^{4}}{25 \mathrm {log}\left (\frac {5 e^{x}}{e^{3}}\right )^{2}} \] Input:
int(1/25*((-25*exp(x)-25)*exp(exp(x)+x)*log(5*exp(-3+x))^3+(8*x^7-56*x^6+1 44*x^5-160*x^4+64*x^3)*log(5*exp(-3+x))-2*x^8+16*x^7-48*x^6+64*x^5-32*x^4) /log(5*exp(-3+x))^3,x)
Output:
( - 25*e**(e**x + x)*log((5*e**x)/e**3)**2 + x**8 - 8*x**7 + 24*x**6 - 32* x**5 + 16*x**4)/(25*log((5*e**x)/e**3)**2)