Integrand size = 123, antiderivative size = 26 \[ \int \frac {e^2 \left (16 x^6+4 x^7\right )+e^2 \left (28 x^6+6 x^7\right ) \log (x)+e^2 \left (-32 x^6-12 x^7\right ) \log ^2(x)+e^2 \left (-104 x^6-32 x^7\right ) \log ^3(x)+e^2 \left (-80 x^6-24 x^7\right ) \log ^4(x)+\left (-4+e^2 \left (-20 x^6-6 x^7\right )\right ) \log ^5(x)}{e^2 x^2 \log ^5(x)} \, dx=\frac {(4+x) \left (\frac {1}{e^2}-x^2 \left (x+\frac {x}{\log (x)}\right )^4\right )}{x} \] Output:
(exp(-2)-(x+x/ln(x))^4*x^2)*(4+x)/x
Leaf count is larger than twice the leaf count of optimal. \(65\) vs. \(2(26)=52\).
Time = 0.35 (sec) , antiderivative size = 65, normalized size of antiderivative = 2.50 \[ \int \frac {e^2 \left (16 x^6+4 x^7\right )+e^2 \left (28 x^6+6 x^7\right ) \log (x)+e^2 \left (-32 x^6-12 x^7\right ) \log ^2(x)+e^2 \left (-104 x^6-32 x^7\right ) \log ^3(x)+e^2 \left (-80 x^6-24 x^7\right ) \log ^4(x)+\left (-4+e^2 \left (-20 x^6-6 x^7\right )\right ) \log ^5(x)}{e^2 x^2 \log ^5(x)} \, dx=\frac {4}{e^2 x}-x^5 (4+x)-\frac {x^5 (4+x)}{\log ^4(x)}-\frac {4 x^5 (4+x)}{\log ^3(x)}-\frac {6 x^5 (4+x)}{\log ^2(x)}-\frac {4 x^5 (4+x)}{\log (x)} \] Input:
Integrate[(E^2*(16*x^6 + 4*x^7) + E^2*(28*x^6 + 6*x^7)*Log[x] + E^2*(-32*x ^6 - 12*x^7)*Log[x]^2 + E^2*(-104*x^6 - 32*x^7)*Log[x]^3 + E^2*(-80*x^6 - 24*x^7)*Log[x]^4 + (-4 + E^2*(-20*x^6 - 6*x^7))*Log[x]^5)/(E^2*x^2*Log[x]^ 5),x]
Output:
4/(E^2*x) - x^5*(4 + x) - (x^5*(4 + x))/Log[x]^4 - (4*x^5*(4 + x))/Log[x]^ 3 - (6*x^5*(4 + x))/Log[x]^2 - (4*x^5*(4 + x))/Log[x]
Leaf count is larger than twice the leaf count of optimal. \(127\) vs. \(2(26)=52\).
Time = 1.72 (sec) , antiderivative size = 127, normalized size of antiderivative = 4.88, number of steps used = 4, number of rules used = 4, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.033, Rules used = {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.
| \(\displaystyle \int \frac {e^2 \left (4 x^7+16 x^6\right )+\left (e^2 \left (-6 x^7-20 x^6\right )-4\right ) \log ^5(x)+e^2 \left (-24 x^7-80 x^6\right ) \log ^4(x)+e^2 \left (-32 x^7-104 x^6\right ) \log ^3(x)+e^2 \left (-12 x^7-32 x^6\right ) \log ^2(x)+e^2 \left (6 x^7+28 x^6\right ) \log (x)}{e^2 x^2 \log ^5(x)} \, dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {\int \frac {2 \left (-\left (\left (e^2 \left (3 x^7+10 x^6\right )+2\right ) \log ^5(x)\right )-4 e^2 \left (3 x^7+10 x^6\right ) \log ^4(x)-4 e^2 \left (4 x^7+13 x^6\right ) \log ^3(x)-2 e^2 \left (3 x^7+8 x^6\right ) \log ^2(x)+e^2 \left (3 x^7+14 x^6\right ) \log (x)+2 e^2 \left (x^7+4 x^6\right )\right )}{x^2 \log ^5(x)}dx}{e^2}\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {2 \int \frac {-\left (\left (e^2 \left (3 x^7+10 x^6\right )+2\right ) \log ^5(x)\right )-4 e^2 \left (3 x^7+10 x^6\right ) \log ^4(x)-4 e^2 \left (4 x^7+13 x^6\right ) \log ^3(x)-2 e^2 \left (3 x^7+8 x^6\right ) \log ^2(x)+e^2 \left (3 x^7+14 x^6\right ) \log (x)+2 e^2 \left (x^7+4 x^6\right )}{x^2 \log ^5(x)}dx}{e^2}\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {2 \int \left (-\frac {4 e^2 (3 x+10) x^4}{\log (x)}-\frac {4 e^2 (4 x+13) x^4}{\log ^2(x)}-\frac {2 e^2 (3 x+8) x^4}{\log ^3(x)}+\frac {e^2 (3 x+14) x^4}{\log ^4(x)}+\frac {2 e^2 (x+4) x^4}{\log ^5(x)}+\frac {-3 e^2 x^7-10 e^2 x^6-2}{x^2}\right )dx}{e^2}\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle \frac {2 \left (-\frac {e^2 x^6}{2}-\frac {e^2 x^6}{2 \log ^4(x)}-\frac {2 e^2 x^6}{\log ^3(x)}-\frac {3 e^2 x^6}{\log ^2(x)}-\frac {2 e^2 x^6}{\log (x)}-2 e^2 x^5-\frac {2 e^2 x^5}{\log ^4(x)}-\frac {8 e^2 x^5}{\log ^3(x)}-\frac {12 e^2 x^5}{\log ^2(x)}-\frac {8 e^2 x^5}{\log (x)}+\frac {2}{x}\right )}{e^2}\) |
Input:
Int[(E^2*(16*x^6 + 4*x^7) + E^2*(28*x^6 + 6*x^7)*Log[x] + E^2*(-32*x^6 - 1 2*x^7)*Log[x]^2 + E^2*(-104*x^6 - 32*x^7)*Log[x]^3 + E^2*(-80*x^6 - 24*x^7 )*Log[x]^4 + (-4 + E^2*(-20*x^6 - 6*x^7))*Log[x]^5)/(E^2*x^2*Log[x]^5),x]
Output:
(2*(2/x - 2*E^2*x^5 - (E^2*x^6)/2 - (2*E^2*x^5)/Log[x]^4 - (E^2*x^6)/(2*Lo g[x]^4) - (8*E^2*x^5)/Log[x]^3 - (2*E^2*x^6)/Log[x]^3 - (12*E^2*x^5)/Log[x ]^2 - (3*E^2*x^6)/Log[x]^2 - (8*E^2*x^5)/Log[x] - (2*E^2*x^6)/Log[x]))/E^2
Int[(a_)*(Fx_), x_Symbol] :> Simp[a Int[Fx, x], x] /; FreeQ[a, x] && !Ma tchQ[Fx, (b_)*(Gx_) /; FreeQ[b, x]]
Leaf count of result is larger than twice the leaf count of optimal. \(70\) vs. \(2(25)=50\).
Time = 28.86 (sec) , antiderivative size = 71, normalized size of antiderivative = 2.73
| method | result | size |
| risch | \(-\frac {{\mathrm e}^{-2} \left ({\mathrm e}^{2} x^{7}+4 \,{\mathrm e}^{2} x^{6}-4\right )}{x}-\frac {x^{5} \left (4 x \ln \left (x \right )^{3}+6 x \ln \left (x \right )^{2}+16 \ln \left (x \right )^{3}+4 x \ln \left (x \right )+24 \ln \left (x \right )^{2}+x +16 \ln \left (x \right )+4\right )}{\ln \left (x \right )^{4}}\) | \(71\) |
| parts | \(-\frac {4 x^{5}}{\ln \left (x \right )^{4}}-\frac {16 x^{5}}{\ln \left (x \right )^{3}}-\frac {24 x^{5}}{\ln \left (x \right )^{2}}-\frac {16 x^{5}}{\ln \left (x \right )}-\frac {x^{6}}{\ln \left (x \right )^{4}}-\frac {4 x^{6}}{\ln \left (x \right )^{3}}-\frac {6 x^{6}}{\ln \left (x \right )^{2}}-\frac {4 x^{6}}{\ln \left (x \right )}-2 \,{\mathrm e}^{-2} \left (\frac {{\mathrm e}^{2} x^{6}}{2}+2 \,{\mathrm e}^{2} x^{5}-\frac {2}{x}\right )\) | \(100\) |
| parallelrisch | \(-\frac {{\mathrm e}^{-2} \left (x^{7} {\mathrm e}^{2} \ln \left (x \right )^{4}+4 x^{7} {\mathrm e}^{2} \ln \left (x \right )^{3}+4 x^{6} {\mathrm e}^{2} \ln \left (x \right )^{4}+6 x^{7} {\mathrm e}^{2} \ln \left (x \right )^{2}+16 x^{6} {\mathrm e}^{2} \ln \left (x \right )^{3}+4 x^{7} {\mathrm e}^{2} \ln \left (x \right )+24 x^{6} {\mathrm e}^{2} \ln \left (x \right )^{2}+{\mathrm e}^{2} x^{7}+16 x^{6} {\mathrm e}^{2} \ln \left (x \right )+4 \,{\mathrm e}^{2} x^{6}-4 \ln \left (x \right )^{4}\right )}{x \ln \left (x \right )^{4}}\) | \(117\) |
| default | \({\mathrm e}^{-2} \left (-{\mathrm e}^{2} x^{6}-4 \,{\mathrm e}^{2} x^{5}+24 \,{\mathrm e}^{2} \operatorname {expIntegral}_{1}\left (-6 \ln \left (x \right )\right )+80 \,{\mathrm e}^{2} \operatorname {expIntegral}_{1}\left (-5 \ln \left (x \right )\right )-32 \,{\mathrm e}^{2} \left (-\frac {x^{6}}{\ln \left (x \right )}-6 \,\operatorname {expIntegral}_{1}\left (-6 \ln \left (x \right )\right )\right )-104 \,{\mathrm e}^{2} \left (-\frac {x^{5}}{\ln \left (x \right )}-5 \,\operatorname {expIntegral}_{1}\left (-5 \ln \left (x \right )\right )\right )-12 \,{\mathrm e}^{2} \left (-\frac {x^{6}}{2 \ln \left (x \right )^{2}}-\frac {3 x^{6}}{\ln \left (x \right )}-18 \,\operatorname {expIntegral}_{1}\left (-6 \ln \left (x \right )\right )\right )-32 \,{\mathrm e}^{2} \left (-\frac {x^{5}}{2 \ln \left (x \right )^{2}}-\frac {5 x^{5}}{2 \ln \left (x \right )}-\frac {25 \,\operatorname {expIntegral}_{1}\left (-5 \ln \left (x \right )\right )}{2}\right )+6 \,{\mathrm e}^{2} \left (-\frac {x^{6}}{3 \ln \left (x \right )^{3}}-\frac {x^{6}}{\ln \left (x \right )^{2}}-\frac {6 x^{6}}{\ln \left (x \right )}-36 \,\operatorname {expIntegral}_{1}\left (-6 \ln \left (x \right )\right )\right )+28 \,{\mathrm e}^{2} \left (-\frac {x^{5}}{3 \ln \left (x \right )^{3}}-\frac {5 x^{5}}{6 \ln \left (x \right )^{2}}-\frac {25 x^{5}}{6 \ln \left (x \right )}-\frac {125 \,\operatorname {expIntegral}_{1}\left (-5 \ln \left (x \right )\right )}{6}\right )+4 \,{\mathrm e}^{2} \left (-\frac {x^{6}}{4 \ln \left (x \right )^{4}}-\frac {x^{6}}{2 \ln \left (x \right )^{3}}-\frac {3 x^{6}}{2 \ln \left (x \right )^{2}}-\frac {9 x^{6}}{\ln \left (x \right )}-54 \,\operatorname {expIntegral}_{1}\left (-6 \ln \left (x \right )\right )\right )+16 \,{\mathrm e}^{2} \left (-\frac {x^{5}}{4 \ln \left (x \right )^{4}}-\frac {5 x^{5}}{12 \ln \left (x \right )^{3}}-\frac {25 x^{5}}{24 \ln \left (x \right )^{2}}-\frac {125 x^{5}}{24 \ln \left (x \right )}-\frac {625 \,\operatorname {expIntegral}_{1}\left (-5 \ln \left (x \right )\right )}{24}\right )+\frac {4}{x}\right )\) | \(330\) |
Input:
int((((-6*x^7-20*x^6)*exp(2)-4)*ln(x)^5+(-24*x^7-80*x^6)*exp(2)*ln(x)^4+(- 32*x^7-104*x^6)*exp(2)*ln(x)^3+(-12*x^7-32*x^6)*exp(2)*ln(x)^2+(6*x^7+28*x ^6)*exp(2)*ln(x)+(4*x^7+16*x^6)*exp(2))/x^2/exp(2)/ln(x)^5,x,method=_RETUR NVERBOSE)
Output:
-exp(-2)*(exp(2)*x^7+4*exp(2)*x^6-4)/x-x^5*(4*x*ln(x)^3+6*x*ln(x)^2+16*ln( x)^3+4*x*ln(x)+24*ln(x)^2+x+16*ln(x)+4)/ln(x)^4
Leaf count of result is larger than twice the leaf count of optimal. 92 vs. \(2 (27) = 54\).
Time = 0.08 (sec) , antiderivative size = 92, normalized size of antiderivative = 3.54 \[ \int \frac {e^2 \left (16 x^6+4 x^7\right )+e^2 \left (28 x^6+6 x^7\right ) \log (x)+e^2 \left (-32 x^6-12 x^7\right ) \log ^2(x)+e^2 \left (-104 x^6-32 x^7\right ) \log ^3(x)+e^2 \left (-80 x^6-24 x^7\right ) \log ^4(x)+\left (-4+e^2 \left (-20 x^6-6 x^7\right )\right ) \log ^5(x)}{e^2 x^2 \log ^5(x)} \, dx=-\frac {{\left (4 \, {\left (x^{7} + 4 \, x^{6}\right )} e^{2} \log \left (x\right )^{3} + {\left ({\left (x^{7} + 4 \, x^{6}\right )} e^{2} - 4\right )} \log \left (x\right )^{4} + 6 \, {\left (x^{7} + 4 \, x^{6}\right )} e^{2} \log \left (x\right )^{2} + 4 \, {\left (x^{7} + 4 \, x^{6}\right )} e^{2} \log \left (x\right ) + {\left (x^{7} + 4 \, x^{6}\right )} e^{2}\right )} e^{\left (-2\right )}}{x \log \left (x\right )^{4}} \] Input:
integrate((((-6*x^7-20*x^6)*exp(2)-4)*log(x)^5+(-24*x^7-80*x^6)*exp(2)*log (x)^4+(-32*x^7-104*x^6)*exp(2)*log(x)^3+(-12*x^7-32*x^6)*exp(2)*log(x)^2+( 6*x^7+28*x^6)*exp(2)*log(x)+(4*x^7+16*x^6)*exp(2))/x^2/exp(2)/log(x)^5,x, algorithm="fricas")
Output:
-(4*(x^7 + 4*x^6)*e^2*log(x)^3 + ((x^7 + 4*x^6)*e^2 - 4)*log(x)^4 + 6*(x^7 + 4*x^6)*e^2*log(x)^2 + 4*(x^7 + 4*x^6)*e^2*log(x) + (x^7 + 4*x^6)*e^2)*e ^(-2)/(x*log(x)^4)
Leaf count of result is larger than twice the leaf count of optimal. 83 vs. \(2 (20) = 40\).
Time = 0.11 (sec) , antiderivative size = 83, normalized size of antiderivative = 3.19 \[ \int \frac {e^2 \left (16 x^6+4 x^7\right )+e^2 \left (28 x^6+6 x^7\right ) \log (x)+e^2 \left (-32 x^6-12 x^7\right ) \log ^2(x)+e^2 \left (-104 x^6-32 x^7\right ) \log ^3(x)+e^2 \left (-80 x^6-24 x^7\right ) \log ^4(x)+\left (-4+e^2 \left (-20 x^6-6 x^7\right )\right ) \log ^5(x)}{e^2 x^2 \log ^5(x)} \, dx=\frac {- x^{6} e^{2} - 4 x^{5} e^{2} + \frac {4}{x}}{e^{2}} + \frac {- x^{6} - 4 x^{5} + \left (- 6 x^{6} - 24 x^{5}\right ) \log {\left (x \right )}^{2} + \left (- 4 x^{6} - 16 x^{5}\right ) \log {\left (x \right )}^{3} + \left (- 4 x^{6} - 16 x^{5}\right ) \log {\left (x \right )}}{\log {\left (x \right )}^{4}} \] Input:
integrate((((-6*x**7-20*x**6)*exp(2)-4)*ln(x)**5+(-24*x**7-80*x**6)*exp(2) *ln(x)**4+(-32*x**7-104*x**6)*exp(2)*ln(x)**3+(-12*x**7-32*x**6)*exp(2)*ln (x)**2+(6*x**7+28*x**6)*exp(2)*ln(x)+(4*x**7+16*x**6)*exp(2))/x**2/exp(2)/ ln(x)**5,x)
Output:
(-x**6*exp(2) - 4*x**5*exp(2) + 4/x)*exp(-2) + (-x**6 - 4*x**5 + (-6*x**6 - 24*x**5)*log(x)**2 + (-4*x**6 - 16*x**5)*log(x)**3 + (-4*x**6 - 16*x**5) *log(x))/log(x)**4
Result contains higher order function than in optimal. Order 4 vs. order 3.
Time = 0.09 (sec) , antiderivative size = 121, normalized size of antiderivative = 4.65 \[ \int \frac {e^2 \left (16 x^6+4 x^7\right )+e^2 \left (28 x^6+6 x^7\right ) \log (x)+e^2 \left (-32 x^6-12 x^7\right ) \log ^2(x)+e^2 \left (-104 x^6-32 x^7\right ) \log ^3(x)+e^2 \left (-80 x^6-24 x^7\right ) \log ^4(x)+\left (-4+e^2 \left (-20 x^6-6 x^7\right )\right ) \log ^5(x)}{e^2 x^2 \log ^5(x)} \, dx=-{\left (x^{6} e^{2} + 4 \, x^{5} e^{2} + 24 \, {\rm Ei}\left (6 \, \log \left (x\right )\right ) e^{2} + 80 \, {\rm Ei}\left (5 \, \log \left (x\right )\right ) e^{2} + 520 \, e^{2} \Gamma \left (-1, -5 \, \log \left (x\right )\right ) + 192 \, e^{2} \Gamma \left (-1, -6 \, \log \left (x\right )\right ) - 800 \, e^{2} \Gamma \left (-2, -5 \, \log \left (x\right )\right ) - 432 \, e^{2} \Gamma \left (-2, -6 \, \log \left (x\right )\right ) - 3500 \, e^{2} \Gamma \left (-3, -5 \, \log \left (x\right )\right ) - 1296 \, e^{2} \Gamma \left (-3, -6 \, \log \left (x\right )\right ) + 10000 \, e^{2} \Gamma \left (-4, -5 \, \log \left (x\right )\right ) + 5184 \, e^{2} \Gamma \left (-4, -6 \, \log \left (x\right )\right ) - \frac {4}{x}\right )} e^{\left (-2\right )} \] Input:
integrate((((-6*x^7-20*x^6)*exp(2)-4)*log(x)^5+(-24*x^7-80*x^6)*exp(2)*log (x)^4+(-32*x^7-104*x^6)*exp(2)*log(x)^3+(-12*x^7-32*x^6)*exp(2)*log(x)^2+( 6*x^7+28*x^6)*exp(2)*log(x)+(4*x^7+16*x^6)*exp(2))/x^2/exp(2)/log(x)^5,x, algorithm="maxima")
Output:
-(x^6*e^2 + 4*x^5*e^2 + 24*Ei(6*log(x))*e^2 + 80*Ei(5*log(x))*e^2 + 520*e^ 2*gamma(-1, -5*log(x)) + 192*e^2*gamma(-1, -6*log(x)) - 800*e^2*gamma(-2, -5*log(x)) - 432*e^2*gamma(-2, -6*log(x)) - 3500*e^2*gamma(-3, -5*log(x)) - 1296*e^2*gamma(-3, -6*log(x)) + 10000*e^2*gamma(-4, -5*log(x)) + 5184*e^ 2*gamma(-4, -6*log(x)) - 4/x)*e^(-2)
Leaf count of result is larger than twice the leaf count of optimal. 114 vs. \(2 (27) = 54\).
Time = 0.13 (sec) , antiderivative size = 114, normalized size of antiderivative = 4.38 \[ \int \frac {e^2 \left (16 x^6+4 x^7\right )+e^2 \left (28 x^6+6 x^7\right ) \log (x)+e^2 \left (-32 x^6-12 x^7\right ) \log ^2(x)+e^2 \left (-104 x^6-32 x^7\right ) \log ^3(x)+e^2 \left (-80 x^6-24 x^7\right ) \log ^4(x)+\left (-4+e^2 \left (-20 x^6-6 x^7\right )\right ) \log ^5(x)}{e^2 x^2 \log ^5(x)} \, dx=-\frac {{\left (x^{7} e^{2} \log \left (x\right )^{4} + 4 \, x^{7} e^{2} \log \left (x\right )^{3} + 4 \, x^{6} e^{2} \log \left (x\right )^{4} + 6 \, x^{7} e^{2} \log \left (x\right )^{2} + 16 \, x^{6} e^{2} \log \left (x\right )^{3} + 4 \, x^{7} e^{2} \log \left (x\right ) + 24 \, x^{6} e^{2} \log \left (x\right )^{2} + x^{7} e^{2} + 16 \, x^{6} e^{2} \log \left (x\right ) + 4 \, x^{6} e^{2} - 4 \, \log \left (x\right )^{4}\right )} e^{\left (-2\right )}}{x \log \left (x\right )^{4}} \] Input:
integrate((((-6*x^7-20*x^6)*exp(2)-4)*log(x)^5+(-24*x^7-80*x^6)*exp(2)*log (x)^4+(-32*x^7-104*x^6)*exp(2)*log(x)^3+(-12*x^7-32*x^6)*exp(2)*log(x)^2+( 6*x^7+28*x^6)*exp(2)*log(x)+(4*x^7+16*x^6)*exp(2))/x^2/exp(2)/log(x)^5,x, algorithm="giac")
Output:
-(x^7*e^2*log(x)^4 + 4*x^7*e^2*log(x)^3 + 4*x^6*e^2*log(x)^4 + 6*x^7*e^2*l og(x)^2 + 16*x^6*e^2*log(x)^3 + 4*x^7*e^2*log(x) + 24*x^6*e^2*log(x)^2 + x ^7*e^2 + 16*x^6*e^2*log(x) + 4*x^6*e^2 - 4*log(x)^4)*e^(-2)/(x*log(x)^4)
Time = 0.64 (sec) , antiderivative size = 84, normalized size of antiderivative = 3.23 \[ \int \frac {e^2 \left (16 x^6+4 x^7\right )+e^2 \left (28 x^6+6 x^7\right ) \log (x)+e^2 \left (-32 x^6-12 x^7\right ) \log ^2(x)+e^2 \left (-104 x^6-32 x^7\right ) \log ^3(x)+e^2 \left (-80 x^6-24 x^7\right ) \log ^4(x)+\left (-4+e^2 \left (-20 x^6-6 x^7\right )\right ) \log ^5(x)}{e^2 x^2 \log ^5(x)} \, dx=-\frac {x^8+4\,x^7-4\,{\mathrm {e}}^{-2}\,x}{x^2}-\frac {\ln \left (x\right )\,\left (4\,x^8+16\,x^7\right )+{\ln \left (x\right )}^3\,\left (4\,x^8+16\,x^7\right )+{\ln \left (x\right )}^2\,\left (6\,x^8+24\,x^7\right )+4\,x^7+x^8}{x^2\,{\ln \left (x\right )}^4} \] Input:
int(-(exp(-2)*(log(x)^5*(exp(2)*(20*x^6 + 6*x^7) + 4) - exp(2)*(16*x^6 + 4 *x^7) - exp(2)*log(x)*(28*x^6 + 6*x^7) + exp(2)*log(x)^2*(32*x^6 + 12*x^7) + exp(2)*log(x)^4*(80*x^6 + 24*x^7) + exp(2)*log(x)^3*(104*x^6 + 32*x^7)) )/(x^2*log(x)^5),x)
Output:
- (4*x^7 - 4*x*exp(-2) + x^8)/x^2 - (log(x)*(16*x^7 + 4*x^8) + log(x)^3*(1 6*x^7 + 4*x^8) + log(x)^2*(24*x^7 + 6*x^8) + 4*x^7 + x^8)/(x^2*log(x)^4)
Time = 0.21 (sec) , antiderivative size = 126, normalized size of antiderivative = 4.85 \[ \int \frac {e^2 \left (16 x^6+4 x^7\right )+e^2 \left (28 x^6+6 x^7\right ) \log (x)+e^2 \left (-32 x^6-12 x^7\right ) \log ^2(x)+e^2 \left (-104 x^6-32 x^7\right ) \log ^3(x)+e^2 \left (-80 x^6-24 x^7\right ) \log ^4(x)+\left (-4+e^2 \left (-20 x^6-6 x^7\right )\right ) \log ^5(x)}{e^2 x^2 \log ^5(x)} \, dx=\frac {-\mathrm {log}\left (x \right )^{4} e^{2} x^{7}-4 \mathrm {log}\left (x \right )^{4} e^{2} x^{6}+4 \mathrm {log}\left (x \right )^{4}-4 \mathrm {log}\left (x \right )^{3} e^{2} x^{7}-16 \mathrm {log}\left (x \right )^{3} e^{2} x^{6}-6 \mathrm {log}\left (x \right )^{2} e^{2} x^{7}-24 \mathrm {log}\left (x \right )^{2} e^{2} x^{6}-4 \,\mathrm {log}\left (x \right ) e^{2} x^{7}-16 \,\mathrm {log}\left (x \right ) e^{2} x^{6}-e^{2} x^{7}-4 e^{2} x^{6}}{\mathrm {log}\left (x \right )^{4} e^{2} x} \] Input:
int((((-6*x^7-20*x^6)*exp(2)-4)*log(x)^5+(-24*x^7-80*x^6)*exp(2)*log(x)^4+ (-32*x^7-104*x^6)*exp(2)*log(x)^3+(-12*x^7-32*x^6)*exp(2)*log(x)^2+(6*x^7+ 28*x^6)*exp(2)*log(x)+(4*x^7+16*x^6)*exp(2))/x^2/exp(2)/log(x)^5,x)
Output:
( - log(x)**4*e**2*x**7 - 4*log(x)**4*e**2*x**6 + 4*log(x)**4 - 4*log(x)** 3*e**2*x**7 - 16*log(x)**3*e**2*x**6 - 6*log(x)**2*e**2*x**7 - 24*log(x)** 2*e**2*x**6 - 4*log(x)*e**2*x**7 - 16*log(x)*e**2*x**6 - e**2*x**7 - 4*e** 2*x**6)/(log(x)**4*e**2*x)