Integrand size = 57, antiderivative size = 24 \[ \int \frac {-36 x^2-12 x^3-18 x^2 \log (5)+e^{80} x^{40} (492+240 x+246 \log (5))}{4+4 x+x^2+(4+2 x) \log (5)+\log ^2(5)} \, dx=\frac {6 x \left (e^{40 (2+\log (x))}-x^2\right )}{2+x+\log (5)} \] Output:
6*(exp(40*ln(x)+80)-x^2)/(x+2+ln(5))*x
Leaf count is larger than twice the leaf count of optimal. \(54\) vs. \(2(24)=48\).
Time = 0.28 (sec) , antiderivative size = 54, normalized size of antiderivative = 2.25 \[ \int \frac {-36 x^2-12 x^3-18 x^2 \log (5)+e^{80} x^{40} (492+240 x+246 \log (5))}{4+4 x+x^2+(4+2 x) \log (5)+\log ^2(5)} \, dx=\frac {6 \left (-x^3+x (2+\log (5))^2+(2+\log (5))^3+e^{80} \left (x^{41}-x (2+\log (5))^{40}-(2+\log (5))^{41}\right )\right )}{2+x+\log (5)} \] Input:
Integrate[(-36*x^2 - 12*x^3 - 18*x^2*Log[5] + E^80*x^40*(492 + 240*x + 246 *Log[5]))/(4 + 4*x + x^2 + (4 + 2*x)*Log[5] + Log[5]^2),x]
Output:
(6*(-x^3 + x*(2 + Log[5])^2 + (2 + Log[5])^3 + E^80*(x^41 - x*(2 + Log[5]) ^40 - (2 + Log[5])^41)))/(2 + x + Log[5])
Leaf count is larger than twice the leaf count of optimal. \(591\) vs. \(2(24)=48\).
Time = 7.46 (sec) , antiderivative size = 591, normalized size of antiderivative = 24.62, number of steps used = 4, number of rules used = 4, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.070, Rules used = {6, 2007, 2389, 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.
| \(\displaystyle \int \frac {e^{80} x^{40} (240 x+492+246 \log (5))-12 x^3-36 x^2-18 x^2 \log (5)}{x^2+4 x+(2 x+4) \log (5)+4+\log ^2(5)} \, dx\) |
| \(\Big \downarrow \) 6 |
| \(\displaystyle \int \frac {e^{80} x^{40} (240 x+492+246 \log (5))-12 x^3+x^2 (-36-18 \log (5))}{x^2+4 x+(2 x+4) \log (5)+4+\log ^2(5)}dx\) |
| \(\Big \downarrow \) 2007 |
| \(\displaystyle \int \frac {e^{80} x^{40} (240 x+492+246 \log (5))-12 x^3+x^2 (-36-18 \log (5))}{(x+2+\log (5))^2}dx\) |
| \(\Big \downarrow \) 2389 |
| \(\displaystyle \int \left (240 e^{80} x^{39}-234 e^{80} x^{38} (2+\log (5))+228 e^{80} x^{37} (2+\log (5))^2-222 e^{80} x^{36} (2+\log (5))^3+216 e^{80} x^{35} (2+\log (5))^4-210 e^{80} x^{34} (2+\log (5))^5+204 e^{80} x^{33} (2+\log (5))^6-198 e^{80} x^{32} (2+\log (5))^7+192 e^{80} x^{31} (2+\log (5))^8-186 e^{80} x^{30} (2+\log (5))^9+180 e^{80} x^{29} (2+\log (5))^{10}-174 e^{80} x^{28} (2+\log (5))^{11}+168 e^{80} x^{27} (2+\log (5))^{12}-162 e^{80} x^{26} (2+\log (5))^{13}+156 e^{80} x^{25} (2+\log (5))^{14}-150 e^{80} x^{24} (2+\log (5))^{15}+144 e^{80} x^{23} (2+\log (5))^{16}-138 e^{80} x^{22} (2+\log (5))^{17}+132 e^{80} x^{21} (2+\log (5))^{18}-126 e^{80} x^{20} (2+\log (5))^{19}+120 e^{80} x^{19} (2+\log (5))^{20}-114 e^{80} x^{18} (2+\log (5))^{21}+108 e^{80} x^{17} (2+\log (5))^{22}-102 e^{80} x^{16} (2+\log (5))^{23}+96 e^{80} x^{15} (2+\log (5))^{24}-90 e^{80} x^{14} (2+\log (5))^{25}+84 e^{80} x^{13} (2+\log (5))^{26}-78 e^{80} x^{12} (2+\log (5))^{27}+72 e^{80} x^{11} (2+\log (5))^{28}-66 e^{80} x^{10} (2+\log (5))^{29}+60 e^{80} x^9 (2+\log (5))^{30}-54 e^{80} x^8 (2+\log (5))^{31}+48 e^{80} x^7 (2+\log (5))^{32}-42 e^{80} x^6 (2+\log (5))^{33}+36 e^{80} x^5 (2+\log (5))^{34}-30 e^{80} x^4 (2+\log (5))^{35}+24 e^{80} x^3 (2+\log (5))^{36}-18 e^{80} x^2 (2+\log (5))^{37}+12 x \left (e^{80} (2+\log (5))^{38}-1\right )+\frac {6 (2+\log (5))^3 \left (e^{80} (2+\log (5))^{38}-1\right )}{(x+2+\log (5))^2}+6 (2+\log (5)) \left (1-e^{80} (2+\log (5))^{38}\right )\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle 6 e^{80} x^{40}-6 e^{80} x^{39} (2+\log (5))+6 e^{80} x^{38} (2+\log (5))^2-6 e^{80} x^{37} (2+\log (5))^3+6 e^{80} x^{36} (2+\log (5))^4-6 e^{80} x^{35} (2+\log (5))^5+6 e^{80} x^{34} (2+\log (5))^6-6 e^{80} x^{33} (2+\log (5))^7+6 e^{80} x^{32} (2+\log (5))^8-6 e^{80} x^{31} (2+\log (5))^9+6 e^{80} x^{30} (2+\log (5))^{10}-6 e^{80} x^{29} (2+\log (5))^{11}+6 e^{80} x^{28} (2+\log (5))^{12}-6 e^{80} x^{27} (2+\log (5))^{13}+6 e^{80} x^{26} (2+\log (5))^{14}-6 e^{80} x^{25} (2+\log (5))^{15}+6 e^{80} x^{24} (2+\log (5))^{16}-6 e^{80} x^{23} (2+\log (5))^{17}+6 e^{80} x^{22} (2+\log (5))^{18}-6 e^{80} x^{21} (2+\log (5))^{19}+6 e^{80} x^{20} (2+\log (5))^{20}-6 e^{80} x^{19} (2+\log (5))^{21}+6 e^{80} x^{18} (2+\log (5))^{22}-6 e^{80} x^{17} (2+\log (5))^{23}+6 e^{80} x^{16} (2+\log (5))^{24}-6 e^{80} x^{15} (2+\log (5))^{25}+6 e^{80} x^{14} (2+\log (5))^{26}-6 e^{80} x^{13} (2+\log (5))^{27}+6 e^{80} x^{12} (2+\log (5))^{28}-6 e^{80} x^{11} (2+\log (5))^{29}+6 e^{80} x^{10} (2+\log (5))^{30}-6 e^{80} x^9 (2+\log (5))^{31}+6 e^{80} x^8 (2+\log (5))^{32}-6 e^{80} x^7 (2+\log (5))^{33}+6 e^{80} x^6 (2+\log (5))^{34}-6 e^{80} x^5 (2+\log (5))^{35}+6 e^{80} x^4 (2+\log (5))^{36}-6 e^{80} x^3 (2+\log (5))^{37}-6 x^2 \left (1-e^{80} (2+\log (5))^{38}\right )+6 x (2+\log (5)) \left (1-e^{80} (2+\log (5))^{38}\right )+\frac {6 (2+\log (5))^3 \left (1-e^{80} (2+\log (5))^{38}\right )}{x+2+\log (5)}\) |
Input:
Int[(-36*x^2 - 12*x^3 - 18*x^2*Log[5] + E^80*x^40*(492 + 240*x + 246*Log[5 ]))/(4 + 4*x + x^2 + (4 + 2*x)*Log[5] + Log[5]^2),x]
Output:
6*E^80*x^40 - 6*E^80*x^39*(2 + Log[5]) + 6*E^80*x^38*(2 + Log[5])^2 - 6*E^ 80*x^37*(2 + Log[5])^3 + 6*E^80*x^36*(2 + Log[5])^4 - 6*E^80*x^35*(2 + Log [5])^5 + 6*E^80*x^34*(2 + Log[5])^6 - 6*E^80*x^33*(2 + Log[5])^7 + 6*E^80* x^32*(2 + Log[5])^8 - 6*E^80*x^31*(2 + Log[5])^9 + 6*E^80*x^30*(2 + Log[5] )^10 - 6*E^80*x^29*(2 + Log[5])^11 + 6*E^80*x^28*(2 + Log[5])^12 - 6*E^80* x^27*(2 + Log[5])^13 + 6*E^80*x^26*(2 + Log[5])^14 - 6*E^80*x^25*(2 + Log[ 5])^15 + 6*E^80*x^24*(2 + Log[5])^16 - 6*E^80*x^23*(2 + Log[5])^17 + 6*E^8 0*x^22*(2 + Log[5])^18 - 6*E^80*x^21*(2 + Log[5])^19 + 6*E^80*x^20*(2 + Lo g[5])^20 - 6*E^80*x^19*(2 + Log[5])^21 + 6*E^80*x^18*(2 + Log[5])^22 - 6*E ^80*x^17*(2 + Log[5])^23 + 6*E^80*x^16*(2 + Log[5])^24 - 6*E^80*x^15*(2 + Log[5])^25 + 6*E^80*x^14*(2 + Log[5])^26 - 6*E^80*x^13*(2 + Log[5])^27 + 6 *E^80*x^12*(2 + Log[5])^28 - 6*E^80*x^11*(2 + Log[5])^29 + 6*E^80*x^10*(2 + Log[5])^30 - 6*E^80*x^9*(2 + Log[5])^31 + 6*E^80*x^8*(2 + Log[5])^32 - 6 *E^80*x^7*(2 + Log[5])^33 + 6*E^80*x^6*(2 + Log[5])^34 - 6*E^80*x^5*(2 + L og[5])^35 + 6*E^80*x^4*(2 + Log[5])^36 - 6*E^80*x^3*(2 + Log[5])^37 - 6*x^ 2*(1 - E^80*(2 + Log[5])^38) + 6*x*(2 + Log[5])*(1 - E^80*(2 + Log[5])^38) + (6*(2 + Log[5])^3*(1 - E^80*(2 + Log[5])^38))/(2 + x + Log[5])
Int[(u_.)*((v_.) + (a_.)*(Fx_) + (b_.)*(Fx_))^(p_.), x_Symbol] :> Int[u*(v + (a + b)*Fx)^p, x] /; FreeQ[{a, b}, x] && !FreeQ[Fx, x]
Int[(u_.)*(Px_)^(p_), x_Symbol] :> With[{a = Rt[Coeff[Px, x, 0], Expon[Px, x]], b = Rt[Coeff[Px, x, Expon[Px, x]], Expon[Px, x]]}, Int[u*(a + b*x)^(Ex pon[Px, x]*p), x] /; EqQ[Px, (a + b*x)^Expon[Px, x]]] /; IntegerQ[p] && Pol yQ[Px, x] && GtQ[Expon[Px, x], 1] && NeQ[Coeff[Px, x, 0], 0]
Int[(Pq_)*((a_) + (b_.)*(x_)^(n_.))^(p_.), x_Symbol] :> Int[ExpandIntegrand [Pq*(a + b*x^n)^p, x], x] /; FreeQ[{a, b, n}, x] && PolyQ[Pq, x] && (IGtQ[p , 0] || EqQ[n, 1])
Time = 0.57 (sec) , antiderivative size = 25, normalized size of antiderivative = 1.04
| method | result | size |
| parallelrisch | \(\frac {-6 x^{3}+6 \,{\mathrm e}^{40 \ln \left (x \right )+80} x}{x +2+\ln \left (5\right )}\) | \(25\) |
| default | \(\text {Expression too large to display}\) | \(7339\) |
| parts | \(\text {Expression too large to display}\) | \(7339\) |
| risch | \(\text {Expression too large to display}\) | \(9387\) |
Input:
int(((246*ln(5)+240*x+492)*exp(40*ln(x)+80)-18*x^2*ln(5)-12*x^3-36*x^2)/(l n(5)^2+(4+2*x)*ln(5)+x^2+4*x+4),x,method=_RETURNVERBOSE)
Output:
(-6*x^3+6*exp(40*ln(x)+80)*x)/(x+2+ln(5))
Leaf count of result is larger than twice the leaf count of optimal. 565 vs. \(2 (23) = 46\).
Time = 0.12 (sec) , antiderivative size = 565, normalized size of antiderivative = 23.54 \[ \int \frac {-36 x^2-12 x^3-18 x^2 \log (5)+e^{80} x^{40} (492+240 x+246 \log (5))}{4+4 x+x^2+(4+2 x) \log (5)+\log ^2(5)} \, dx=\text {Too large to display} \] Input:
integrate(((246*log(5)+240*x+492)*exp(40*log(x)+80)-18*x^2*log(5)-12*x^3-3 6*x^2)/(log(5)^2+(4+2*x)*log(5)+x^2+4*x+4),x, algorithm="fricas")
Output:
-6*((x + 82)*e^80*log(5)^40 + e^80*log(5)^41 + 80*(x + 41)*e^80*log(5)^39 + 1040*(3*x + 82)*e^80*log(5)^38 + 39520*(2*x + 41)*e^80*log(5)^37 + 29244 8*(5*x + 82)*e^80*log(5)^36 + 7018752*(3*x + 41)*e^80*log(5)^35 + 35093760 *(7*x + 82)*e^80*log(5)^34 + 596593920*(4*x + 41)*e^80*log(5)^33 + 2187511 040*(9*x + 82)*e^80*log(5)^32 + 28000141312*(5*x + 41)*e^80*log(5)^31 + 78 909489152*(11*x + 82)*e^80*log(5)^30 + 789094891520*(6*x + 41)*e^80*log(5) ^29 + 1760288604160*(13*x + 82)*e^80*log(5)^28 + 14082308833280*(7*x + 41) *e^80*log(5)^27 + 25348155899904*(15*x + 82)*e^80*log(5)^26 + 164763013349 376*(8*x + 41)*e^80*log(5)^25 + 242298549043200*(17*x + 82)*e^80*log(5)^24 + 1292258928230400*(9*x + 41)*e^80*log(5)^23 + 1564313439436800*(19*x + 8 2)*e^80*log(5)^22 + 6882979133521920*(10*x + 41)*e^80*log(5)^21 + 68829791 33521920*(21*x + 82)*e^80*log(5)^20 + 25029015030988800*(11*x + 41)*e^80*l og(5)^19 + 20676142851686400*(23*x + 82)*e^80*log(5)^18 + 6202842855505920 0*(12*x + 41)*e^80*log(5)^17 + 42179331417440256*(25*x + 82)*e^80*log(5)^1 6 + 103826046566006784*(13*x + 41)*e^80*log(5)^15 + 57681136981114880*(27* x + 82)*e^80*log(5)^14 + 115362273962229760*(14*x + 41)*e^80*log(5)^13 + 5 1714122810654720*(29*x + 82)*e^80*log(5)^12 + 82742596497047552*(15*x + 41 )*e^80*log(5)^11 + 29360276176371712*(31*x + 82)*e^80*log(5)^10 + 36700345 220464640*(16*x + 41)*e^80*log(5)^9 + 10009185060126720*(33*x + 82)*e^80*l og(5)^8 + 9420409468354560*(17*x + 41)*e^80*log(5)^7 + 1884081893670912...
Leaf count of result is larger than twice the leaf count of optimal. 8716 vs. \(2 (20) = 40\).
Time = 6.57 (sec) , antiderivative size = 8716, normalized size of antiderivative = 363.17 \[ \int \frac {-36 x^2-12 x^3-18 x^2 \log (5)+e^{80} x^{40} (492+240 x+246 \log (5))}{4+4 x+x^2+(4+2 x) \log (5)+\log ^2(5)} \, dx=\text {Too large to display} \] Input:
integrate(((246*ln(5)+240*x+492)*exp(40*ln(x)+80)-18*x**2*ln(5)-12*x**3-36 *x**2)/(ln(5)**2+(4+2*x)*ln(5)+x**2+4*x+4),x)
Output:
6*x**40*exp(80) + x**39*(-12*exp(80) - 6*exp(80)*log(5)) + x**38*(6*exp(80 )*log(5)**2 + 24*exp(80) + 24*exp(80)*log(5)) + x**37*(-72*exp(80)*log(5) - 36*exp(80)*log(5)**2 - 48*exp(80) - 6*exp(80)*log(5)**3) + x**36*(6*exp( 80)*log(5)**4 + 96*exp(80) + 48*exp(80)*log(5)**3 + 192*exp(80)*log(5) + 1 44*exp(80)*log(5)**2) + x**35*(-480*exp(80)*log(5)**2 - 240*exp(80)*log(5) **3 - 480*exp(80)*log(5) - 60*exp(80)*log(5)**4 - 192*exp(80) - 6*exp(80)* log(5)**5) + x**34*(6*exp(80)*log(5)**6 + 384*exp(80) + 72*exp(80)*log(5)* *5 + 1152*exp(80)*log(5) + 360*exp(80)*log(5)**4 + 1440*exp(80)*log(5)**2 + 960*exp(80)*log(5)**3) + x**33*(-3360*exp(80)*log(5)**3 - 1680*exp(80)*l og(5)**4 - 4032*exp(80)*log(5)**2 - 504*exp(80)*log(5)**5 - 2688*exp(80)*l og(5) - 84*exp(80)*log(5)**6 - 768*exp(80) - 6*exp(80)*log(5)**7) + x**32* (6*exp(80)*log(5)**8 + 1536*exp(80) + 96*exp(80)*log(5)**7 + 6144*exp(80)* log(5) + 672*exp(80)*log(5)**6 + 10752*exp(80)*log(5)**2 + 2688*exp(80)*lo g(5)**5 + 10752*exp(80)*log(5)**3 + 6720*exp(80)*log(5)**4) + x**31*(-2419 2*exp(80)*log(5)**4 - 32256*exp(80)*log(5)**3 - 12096*exp(80)*log(5)**5 - 27648*exp(80)*log(5)**2 - 4032*exp(80)*log(5)**6 - 864*exp(80)*log(5)**7 - 13824*exp(80)*log(5) - 108*exp(80)*log(5)**8 - 3072*exp(80) - 6*exp(80)*l og(5)**9) + x**30*(6*exp(80)*log(5)**10 + 6144*exp(80) + 120*exp(80)*log(5 )**9 + 1080*exp(80)*log(5)**8 + 30720*exp(80)*log(5) + 5760*exp(80)*log(5) **7 + 69120*exp(80)*log(5)**2 + 20160*exp(80)*log(5)**6 + 92160*exp(80)...
Leaf count of result is larger than twice the leaf count of optimal. 6875 vs. \(2 (23) = 46\).
Time = 0.11 (sec) , antiderivative size = 6875, normalized size of antiderivative = 286.46 \[ \int \frac {-36 x^2-12 x^3-18 x^2 \log (5)+e^{80} x^{40} (492+240 x+246 \log (5))}{4+4 x+x^2+(4+2 x) \log (5)+\log ^2(5)} \, dx=\text {Too large to display} \] Input:
integrate(((246*log(5)+240*x+492)*exp(40*log(x)+80)-18*x^2*log(5)-12*x^3-3 6*x^2)/(log(5)^2+(4+2*x)*log(5)+x^2+4*x+4),x, algorithm="maxima")
Output:
6*x^40*e^80 - 6*(e^80*log(5) + 2*e^80)*x^39 + 6*(e^80*log(5)^2 + 4*e^80*lo g(5) + 4*e^80)*x^38 - 6*(e^80*log(5)^3 + 6*e^80*log(5)^2 + 12*e^80*log(5) + 8*e^80)*x^37 + 6*(e^80*log(5)^4 + 8*e^80*log(5)^3 + 24*e^80*log(5)^2 + 3 2*e^80*log(5) + 16*e^80)*x^36 - 6*(e^80*log(5)^5 + 10*e^80*log(5)^4 + 40*e ^80*log(5)^3 + 80*e^80*log(5)^2 + 80*e^80*log(5) + 32*e^80)*x^35 + 6*(e^80 *log(5)^6 + 12*e^80*log(5)^5 + 60*e^80*log(5)^4 + 160*e^80*log(5)^3 + 240* e^80*log(5)^2 + 192*e^80*log(5) + 64*e^80)*x^34 - 6*(e^80*log(5)^7 + 14*e^ 80*log(5)^6 + 84*e^80*log(5)^5 + 280*e^80*log(5)^4 + 560*e^80*log(5)^3 + 6 72*e^80*log(5)^2 + 448*e^80*log(5) + 128*e^80)*x^33 + 6*(e^80*log(5)^8 + 1 6*e^80*log(5)^7 + 112*e^80*log(5)^6 + 448*e^80*log(5)^5 + 1120*e^80*log(5) ^4 + 1792*e^80*log(5)^3 + 1792*e^80*log(5)^2 + 1024*e^80*log(5) + 256*e^80 )*x^32 - 6*(e^80*log(5)^9 + 18*e^80*log(5)^8 + 144*e^80*log(5)^7 + 672*e^8 0*log(5)^6 + 2016*e^80*log(5)^5 + 4032*e^80*log(5)^4 + 5376*e^80*log(5)^3 + 4608*e^80*log(5)^2 + 2304*e^80*log(5) + 512*e^80)*x^31 + 6*(e^80*log(5)^ 10 + 20*e^80*log(5)^9 + 180*e^80*log(5)^8 + 960*e^80*log(5)^7 + 3360*e^80* log(5)^6 + 8064*e^80*log(5)^5 + 13440*e^80*log(5)^4 + 15360*e^80*log(5)^3 + 11520*e^80*log(5)^2 + 5120*e^80*log(5) + 1024*e^80)*x^30 - 6*(e^80*log(5 )^11 + 22*e^80*log(5)^10 + 220*e^80*log(5)^9 + 1320*e^80*log(5)^8 + 5280*e ^80*log(5)^7 + 14784*e^80*log(5)^6 + 29568*e^80*log(5)^5 + 42240*e^80*log( 5)^4 + 42240*e^80*log(5)^3 + 28160*e^80*log(5)^2 + 11264*e^80*log(5) + ...
Leaf count of result is larger than twice the leaf count of optimal. 9072 vs. \(2 (23) = 46\).
Time = 0.15 (sec) , antiderivative size = 9072, normalized size of antiderivative = 378.00 \[ \int \frac {-36 x^2-12 x^3-18 x^2 \log (5)+e^{80} x^{40} (492+240 x+246 \log (5))}{4+4 x+x^2+(4+2 x) \log (5)+\log ^2(5)} \, dx=\text {Too large to display} \] Input:
integrate(((246*log(5)+240*x+492)*exp(40*log(x)+80)-18*x^2*log(5)-12*x^3-3 6*x^2)/(log(5)^2+(4+2*x)*log(5)+x^2+4*x+4),x, algorithm="giac")
Output:
6*x^40*e^80 - 6*x^39*e^80*log(5) + 6*x^38*e^80*log(5)^2 - 6*x^37*e^80*log( 5)^3 + 6*x^36*e^80*log(5)^4 - 6*x^35*e^80*log(5)^5 + 6*x^34*e^80*log(5)^6 - 6*x^33*e^80*log(5)^7 + 6*x^32*e^80*log(5)^8 - 6*x^31*e^80*log(5)^9 + 6*x ^30*e^80*log(5)^10 - 6*x^29*e^80*log(5)^11 + 6*x^28*e^80*log(5)^12 - 6*x^2 7*e^80*log(5)^13 + 6*x^26*e^80*log(5)^14 - 6*x^25*e^80*log(5)^15 + 6*x^24* e^80*log(5)^16 - 6*x^23*e^80*log(5)^17 + 6*x^22*e^80*log(5)^18 - 6*x^21*e^ 80*log(5)^19 + 6*x^20*e^80*log(5)^20 - 6*x^19*e^80*log(5)^21 + 6*x^18*e^80 *log(5)^22 - 6*x^17*e^80*log(5)^23 + 6*x^16*e^80*log(5)^24 - 6*x^15*e^80*l og(5)^25 + 6*x^14*e^80*log(5)^26 - 6*x^13*e^80*log(5)^27 + 6*x^12*e^80*log (5)^28 - 6*x^11*e^80*log(5)^29 + 6*x^10*e^80*log(5)^30 - 6*x^9*e^80*log(5) ^31 + 6*x^8*e^80*log(5)^32 - 6*x^7*e^80*log(5)^33 + 6*x^6*e^80*log(5)^34 - 6*x^5*e^80*log(5)^35 + 6*x^4*e^80*log(5)^36 - 6*x^3*e^80*log(5)^37 + 6*x^ 2*e^80*log(5)^38 - 6*x*e^80*log(5)^39 - 12*x^39*e^80 + 24*x^38*e^80*log(5) - 36*x^37*e^80*log(5)^2 + 48*x^36*e^80*log(5)^3 - 60*x^35*e^80*log(5)^4 + 72*x^34*e^80*log(5)^5 - 84*x^33*e^80*log(5)^6 + 96*x^32*e^80*log(5)^7 - 1 08*x^31*e^80*log(5)^8 + 120*x^30*e^80*log(5)^9 - 132*x^29*e^80*log(5)^10 + 144*x^28*e^80*log(5)^11 - 156*x^27*e^80*log(5)^12 + 168*x^26*e^80*log(5)^ 13 - 180*x^25*e^80*log(5)^14 + 192*x^24*e^80*log(5)^15 - 204*x^23*e^80*log (5)^16 + 216*x^22*e^80*log(5)^17 - 228*x^21*e^80*log(5)^18 + 240*x^20*e^80 *log(5)^19 - 252*x^19*e^80*log(5)^20 + 264*x^18*e^80*log(5)^21 - 276*x^...
Time = 3.60 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.83 \[ \int \frac {-36 x^2-12 x^3-18 x^2 \log (5)+e^{80} x^{40} (492+240 x+246 \log (5))}{4+4 x+x^2+(4+2 x) \log (5)+\log ^2(5)} \, dx=\frac {6\,x^3\,\left (x^{38}\,{\mathrm {e}}^{80}-1\right )}{x+\ln \left (5\right )+2} \] Input:
int(-(18*x^2*log(5) - exp(40*log(x) + 80)*(240*x + 246*log(5) + 492) + 36* x^2 + 12*x^3)/(4*x + log(5)*(2*x + 4) + log(5)^2 + x^2 + 4),x)
Output:
(6*x^3*(x^38*exp(80) - 1))/(x + log(5) + 2)
Time = 0.16 (sec) , antiderivative size = 21, normalized size of antiderivative = 0.88 \[ \int \frac {-36 x^2-12 x^3-18 x^2 \log (5)+e^{80} x^{40} (492+240 x+246 \log (5))}{4+4 x+x^2+(4+2 x) \log (5)+\log ^2(5)} \, dx=\frac {6 x^{3} \left (e^{80} x^{38}-1\right )}{\mathrm {log}\left (5\right )+x +2} \] Input:
int(((246*log(5)+240*x+492)*exp(40*log(x)+80)-18*x^2*log(5)-12*x^3-36*x^2) /(log(5)^2+(4+2*x)*log(5)+x^2+4*x+4),x)
Output:
(6*x**3*(e**80*x**38 - 1))/(log(5) + x + 2)