3.4.77 \(\int \frac {-40-40 x+110 x^2+120 x^3-98 x^4-112 x^5+16 x^6+36 x^7+8 x^8+e^{3 e^8} (-4-12 x-8 x^2)+e^3 (4+12 x+8 x^2)+e^2 (-26-60 x+60 x^3+24 x^4)+e (56+92 x-88 x^2-180 x^3+12 x^4+84 x^5+24 x^6)+e^{2 e^8} (-26-60 x+60 x^3+24 x^4+e (12+36 x+24 x^2))+e^{e^8} (-56-92 x+88 x^2+180 x^3-12 x^4-84 x^5-24 x^6+e^2 (-12-36 x-24 x^2)+e (52+120 x-120 x^3-48 x^4))+(10+20 x-20 x^3-8 x^4+e (-4-12 x-8 x^2)+e^{e^8} (4+12 x+8 x^2)) \log (1+x)}{1+x} \, dx\)

Optimal. Leaf size=25 \[ \left (-\left (-2+e-e^{e^8}+x+x^2\right )^2+\log (1+x)\right )^2 \]

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Rubi [A]  time = 1.24, antiderivative size = 29, normalized size of antiderivative = 1.16, number of steps used = 3, number of rules used = 3, integrand size = 279, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.011, Rules used = {6688, 12, 6686} \begin {gather*} \left (\left (-x^2-x+e^{e^8}-e+2\right )^2-\log (x+1)\right )^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-40 - 40*x + 110*x^2 + 120*x^3 - 98*x^4 - 112*x^5 + 16*x^6 + 36*x^7 + 8*x^8 + E^(3*E^8)*(-4 - 12*x - 8*x^
2) + E^3*(4 + 12*x + 8*x^2) + E^2*(-26 - 60*x + 60*x^3 + 24*x^4) + E*(56 + 92*x - 88*x^2 - 180*x^3 + 12*x^4 +
84*x^5 + 24*x^6) + E^(2*E^8)*(-26 - 60*x + 60*x^3 + 24*x^4 + E*(12 + 36*x + 24*x^2)) + E^E^8*(-56 - 92*x + 88*
x^2 + 180*x^3 - 12*x^4 - 84*x^5 - 24*x^6 + E^2*(-12 - 36*x - 24*x^2) + E*(52 + 120*x - 120*x^3 - 48*x^4)) + (1
0 + 20*x - 20*x^3 - 8*x^4 + E*(-4 - 12*x - 8*x^2) + E^E^8*(4 + 12*x + 8*x^2))*Log[1 + x])/(1 + x),x]

[Out]

((2 - E + E^E^8 - x - x^2)^2 - Log[1 + x])^2

Rule 12

Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] &&  !MatchQ[u, (b_)*(v_) /; FreeQ[b, x]]

Rule 6686

Int[(u_)*(y_)^(m_.), x_Symbol] :> With[{q = DerivativeDivides[y, u, x]}, Simp[(q*y^(m + 1))/(m + 1), x] /;  !F
alseQ[q]] /; FreeQ[m, x] && NeQ[m, -1]

Rule 6688

Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; SimplerIntegrandQ[v, u, x]]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {2 \left (5-2 e+2 e^{e^8}+2 \left (5-3 e+3 e^{e^8}\right ) x-4 \left (e-e^{e^8}\right ) x^2-10 x^3-4 x^4\right ) \left (-\left (-2+e-e^{e^8}+x+x^2\right )^2+\log (1+x)\right )}{1+x} \, dx\\ &=2 \int \frac {\left (5-2 e+2 e^{e^8}+2 \left (5-3 e+3 e^{e^8}\right ) x-4 \left (e-e^{e^8}\right ) x^2-10 x^3-4 x^4\right ) \left (-\left (-2+e-e^{e^8}+x+x^2\right )^2+\log (1+x)\right )}{1+x} \, dx\\ &=\left (\left (2-e+e^{e^8}-x-x^2\right )^2-\log (1+x)\right )^2\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.10, size = 25, normalized size = 1.00 \begin {gather*} \left (\left (-2+e-e^{e^8}+x+x^2\right )^2-\log (1+x)\right )^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-40 - 40*x + 110*x^2 + 120*x^3 - 98*x^4 - 112*x^5 + 16*x^6 + 36*x^7 + 8*x^8 + E^(3*E^8)*(-4 - 12*x
- 8*x^2) + E^3*(4 + 12*x + 8*x^2) + E^2*(-26 - 60*x + 60*x^3 + 24*x^4) + E*(56 + 92*x - 88*x^2 - 180*x^3 + 12*
x^4 + 84*x^5 + 24*x^6) + E^(2*E^8)*(-26 - 60*x + 60*x^3 + 24*x^4 + E*(12 + 36*x + 24*x^2)) + E^E^8*(-56 - 92*x
+ 88*x^2 + 180*x^3 - 12*x^4 - 84*x^5 - 24*x^6 + E^2*(-12 - 36*x - 24*x^2) + E*(52 + 120*x - 120*x^3 - 48*x^4)
) + (10 + 20*x - 20*x^3 - 8*x^4 + E*(-4 - 12*x - 8*x^2) + E^E^8*(4 + 12*x + 8*x^2))*Log[1 + x])/(1 + x),x]

[Out]

((-2 + E - E^E^8 + x + x^2)^2 - Log[1 + x])^2

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fricas [B]  time = 0.64, size = 263, normalized size = 10.52 \begin {gather*} x^{8} + 4 \, x^{7} - 2 \, x^{6} - 20 \, x^{5} + x^{4} + 40 \, x^{3} - 8 \, x^{2} + 4 \, {\left (x^{2} + x\right )} e^{3} + 6 \, {\left (x^{4} + 2 \, x^{3} - 3 \, x^{2} - 4 \, x\right )} e^{2} + 4 \, {\left (x^{6} + 3 \, x^{5} - 3 \, x^{4} - 11 \, x^{3} + 6 \, x^{2} + 12 \, x\right )} e - 4 \, {\left (x^{2} + x\right )} e^{\left (3 \, e^{8}\right )} + 6 \, {\left (x^{4} + 2 \, x^{3} - 3 \, x^{2} + 2 \, {\left (x^{2} + x\right )} e - 4 \, x\right )} e^{\left (2 \, e^{8}\right )} - 4 \, {\left (x^{6} + 3 \, x^{5} - 3 \, x^{4} - 11 \, x^{3} + 6 \, x^{2} + 3 \, {\left (x^{2} + x\right )} e^{2} + 3 \, {\left (x^{4} + 2 \, x^{3} - 3 \, x^{2} - 4 \, x\right )} e + 12 \, x\right )} e^{\left (e^{8}\right )} - 2 \, {\left (x^{4} + 2 \, x^{3} - 3 \, x^{2} + 2 \, {\left (x^{2} + x - 2\right )} e - 2 \, {\left (x^{2} + x + e - 2\right )} e^{\left (e^{8}\right )} - 4 \, x + e^{2} + e^{\left (2 \, e^{8}\right )} + 4\right )} \log \left (x + 1\right ) + \log \left (x + 1\right )^{2} - 32 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((8*x^2+12*x+4)*exp(exp(4)^2)+(-8*x^2-12*x-4)*exp(1)-8*x^4-20*x^3+20*x+10)*log(x+1)+(-8*x^2-12*x-4)
*exp(exp(4)^2)^3+((24*x^2+36*x+12)*exp(1)+24*x^4+60*x^3-60*x-26)*exp(exp(4)^2)^2+((-24*x^2-36*x-12)*exp(1)^2+(
-48*x^4-120*x^3+120*x+52)*exp(1)-24*x^6-84*x^5-12*x^4+180*x^3+88*x^2-92*x-56)*exp(exp(4)^2)+(8*x^2+12*x+4)*exp
(1)^3+(24*x^4+60*x^3-60*x-26)*exp(1)^2+(24*x^6+84*x^5+12*x^4-180*x^3-88*x^2+92*x+56)*exp(1)+8*x^8+36*x^7+16*x^
6-112*x^5-98*x^4+120*x^3+110*x^2-40*x-40)/(x+1),x, algorithm="fricas")

[Out]

x^8 + 4*x^7 - 2*x^6 - 20*x^5 + x^4 + 40*x^3 - 8*x^2 + 4*(x^2 + x)*e^3 + 6*(x^4 + 2*x^3 - 3*x^2 - 4*x)*e^2 + 4*
(x^6 + 3*x^5 - 3*x^4 - 11*x^3 + 6*x^2 + 12*x)*e - 4*(x^2 + x)*e^(3*e^8) + 6*(x^4 + 2*x^3 - 3*x^2 + 2*(x^2 + x)
*e - 4*x)*e^(2*e^8) - 4*(x^6 + 3*x^5 - 3*x^4 - 11*x^3 + 6*x^2 + 3*(x^2 + x)*e^2 + 3*(x^4 + 2*x^3 - 3*x^2 - 4*x
)*e + 12*x)*e^(e^8) - 2*(x^4 + 2*x^3 - 3*x^2 + 2*(x^2 + x - 2)*e - 2*(x^2 + x + e - 2)*e^(e^8) - 4*x + e^2 + e
^(2*e^8) + 4)*log(x + 1) + log(x + 1)^2 - 32*x

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giac [B]  time = 0.34, size = 428, normalized size = 17.12 \begin {gather*} x^{8} + 4 \, x^{7} + 4 \, x^{6} e - 4 \, x^{6} e^{\left (e^{8}\right )} - 2 \, x^{6} + 12 \, x^{5} e - 12 \, x^{5} e^{\left (e^{8}\right )} - 20 \, x^{5} + 6 \, x^{4} e^{2} - 12 \, x^{4} e + 6 \, x^{4} e^{\left (2 \, e^{8}\right )} - 12 \, x^{4} e^{\left (e^{8} + 1\right )} + 12 \, x^{4} e^{\left (e^{8}\right )} - 2 \, x^{4} \log \left (x + 1\right ) + x^{4} + 12 \, x^{3} e^{2} - 44 \, x^{3} e + 12 \, x^{3} e^{\left (2 \, e^{8}\right )} - 24 \, x^{3} e^{\left (e^{8} + 1\right )} + 44 \, x^{3} e^{\left (e^{8}\right )} - 4 \, x^{3} \log \left (x + 1\right ) - 4 \, x^{2} e \log \left (x + 1\right ) + 4 \, x^{2} e^{\left (e^{8}\right )} \log \left (x + 1\right ) + 40 \, x^{3} + 4 \, x^{2} e^{3} - 18 \, x^{2} e^{2} + 24 \, x^{2} e - 4 \, x^{2} e^{\left (3 \, e^{8}\right )} - 18 \, x^{2} e^{\left (2 \, e^{8}\right )} + 12 \, x^{2} e^{\left (2 \, e^{8} + 1\right )} - 12 \, x^{2} e^{\left (e^{8} + 2\right )} + 36 \, x^{2} e^{\left (e^{8} + 1\right )} - 24 \, x^{2} e^{\left (e^{8}\right )} + 6 \, x^{2} \log \left (x + 1\right ) - 4 \, x e \log \left (x + 1\right ) + 4 \, x e^{\left (e^{8}\right )} \log \left (x + 1\right ) - 8 \, x^{2} + 4 \, x e^{3} - 24 \, x e^{2} + 48 \, x e - 4 \, x e^{\left (3 \, e^{8}\right )} - 24 \, x e^{\left (2 \, e^{8}\right )} + 12 \, x e^{\left (2 \, e^{8} + 1\right )} - 12 \, x e^{\left (e^{8} + 2\right )} + 48 \, x e^{\left (e^{8} + 1\right )} - 48 \, x e^{\left (e^{8}\right )} + 8 \, x \log \left (x + 1\right ) - 2 \, e^{2} \log \left (x + 1\right ) + 8 \, e \log \left (x + 1\right ) - 2 \, e^{\left (2 \, e^{8}\right )} \log \left (x + 1\right ) + 4 \, e^{\left (e^{8} + 1\right )} \log \left (x + 1\right ) - 8 \, e^{\left (e^{8}\right )} \log \left (x + 1\right ) + \log \left (x + 1\right )^{2} - 32 \, x - 8 \, \log \left (x + 1\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((8*x^2+12*x+4)*exp(exp(4)^2)+(-8*x^2-12*x-4)*exp(1)-8*x^4-20*x^3+20*x+10)*log(x+1)+(-8*x^2-12*x-4)
*exp(exp(4)^2)^3+((24*x^2+36*x+12)*exp(1)+24*x^4+60*x^3-60*x-26)*exp(exp(4)^2)^2+((-24*x^2-36*x-12)*exp(1)^2+(
-48*x^4-120*x^3+120*x+52)*exp(1)-24*x^6-84*x^5-12*x^4+180*x^3+88*x^2-92*x-56)*exp(exp(4)^2)+(8*x^2+12*x+4)*exp
(1)^3+(24*x^4+60*x^3-60*x-26)*exp(1)^2+(24*x^6+84*x^5+12*x^4-180*x^3-88*x^2+92*x+56)*exp(1)+8*x^8+36*x^7+16*x^
6-112*x^5-98*x^4+120*x^3+110*x^2-40*x-40)/(x+1),x, algorithm="giac")

[Out]

x^8 + 4*x^7 + 4*x^6*e - 4*x^6*e^(e^8) - 2*x^6 + 12*x^5*e - 12*x^5*e^(e^8) - 20*x^5 + 6*x^4*e^2 - 12*x^4*e + 6*
x^4*e^(2*e^8) - 12*x^4*e^(e^8 + 1) + 12*x^4*e^(e^8) - 2*x^4*log(x + 1) + x^4 + 12*x^3*e^2 - 44*x^3*e + 12*x^3*
e^(2*e^8) - 24*x^3*e^(e^8 + 1) + 44*x^3*e^(e^8) - 4*x^3*log(x + 1) - 4*x^2*e*log(x + 1) + 4*x^2*e^(e^8)*log(x
+ 1) + 40*x^3 + 4*x^2*e^3 - 18*x^2*e^2 + 24*x^2*e - 4*x^2*e^(3*e^8) - 18*x^2*e^(2*e^8) + 12*x^2*e^(2*e^8 + 1)
- 12*x^2*e^(e^8 + 2) + 36*x^2*e^(e^8 + 1) - 24*x^2*e^(e^8) + 6*x^2*log(x + 1) - 4*x*e*log(x + 1) + 4*x*e^(e^8)
*log(x + 1) - 8*x^2 + 4*x*e^3 - 24*x*e^2 + 48*x*e - 4*x*e^(3*e^8) - 24*x*e^(2*e^8) + 12*x*e^(2*e^8 + 1) - 12*x
*e^(e^8 + 2) + 48*x*e^(e^8 + 1) - 48*x*e^(e^8) + 8*x*log(x + 1) - 2*e^2*log(x + 1) + 8*e*log(x + 1) - 2*e^(2*e
^8)*log(x + 1) + 4*e^(e^8 + 1)*log(x + 1) - 8*e^(e^8)*log(x + 1) + log(x + 1)^2 - 32*x - 8*log(x + 1)

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maple [B]  time = 0.29, size = 386, normalized size = 15.44

method	result	size
norman	\(x^{8}+\ln \left (x +1\right )^{2}+\left (-20+12 \,{\mathrm e}-12 \,{\mathrm e}^{{\mathrm e}^{8}}\right ) x^{5}+\left (-2+4 \,{\mathrm e}-4 \,{\mathrm e}^{{\mathrm e}^{8}}\right ) x^{6}+\left (1-12 \,{\mathrm e}+12 \,{\mathrm e}^{{\mathrm e}^{8}}+6 \,{\mathrm e}^{2}+6 \,{\mathrm e}^{2 \,{\mathrm e}^{8}}-12 \,{\mathrm e} \,{\mathrm e}^{{\mathrm e}^{8}}\right ) x^{4}+\left (40-44 \,{\mathrm e}+44 \,{\mathrm e}^{{\mathrm e}^{8}}+12 \,{\mathrm e}^{2}+12 \,{\mathrm e}^{2 \,{\mathrm e}^{8}}-24 \,{\mathrm e} \,{\mathrm e}^{{\mathrm e}^{8}}\right ) x^{3}+\left (-2 \,{\mathrm e}^{2}+4 \,{\mathrm e} \,{\mathrm e}^{{\mathrm e}^{8}}-2 \,{\mathrm e}^{2 \,{\mathrm e}^{8}}+8 \,{\mathrm e}-8 \,{\mathrm e}^{{\mathrm e}^{8}}-8\right ) \ln \left (x +1\right )+\left (-32+48 \,{\mathrm e}-48 \,{\mathrm e}^{{\mathrm e}^{8}}-24 \,{\mathrm e}^{2}-24 \,{\mathrm e}^{2 \,{\mathrm e}^{8}}+48 \,{\mathrm e} \,{\mathrm e}^{{\mathrm e}^{8}}-4 \,{\mathrm e}^{3 \,{\mathrm e}^{8}}+4 \,{\mathrm e}^{3}-12 \,{\mathrm e}^{2} {\mathrm e}^{{\mathrm e}^{8}}+12 \,{\mathrm e} \,{\mathrm e}^{2 \,{\mathrm e}^{8}}\right ) x +\left (-8+24 \,{\mathrm e}-24 \,{\mathrm e}^{{\mathrm e}^{8}}-18 \,{\mathrm e}^{2}-18 \,{\mathrm e}^{2 \,{\mathrm e}^{8}}+36 \,{\mathrm e} \,{\mathrm e}^{{\mathrm e}^{8}}-4 \,{\mathrm e}^{3 \,{\mathrm e}^{8}}+4 \,{\mathrm e}^{3}-12 \,{\mathrm e}^{2} {\mathrm e}^{{\mathrm e}^{8}}+12 \,{\mathrm e} \,{\mathrm e}^{2 \,{\mathrm e}^{8}}\right ) x^{2}+\left (6-4 \,{\mathrm e}+4 \,{\mathrm e}^{{\mathrm e}^{8}}\right ) x^{2} \ln \left (x +1\right )+\left (8-4 \,{\mathrm e}+4 \,{\mathrm e}^{{\mathrm e}^{8}}\right ) x \ln \left (x +1\right )+4 x^{7}-4 \ln \left (x +1\right ) x^{3}-2 \ln \left (x +1\right ) x^{4}\)	\(386\)
risch	\(-32 x -24 \,{\mathrm e}^{2} x +\ln \left (x +1\right )^{2}-8 \ln \left (x +1\right )+4 x^{7}+x^{8}-2 x^{6}-20 x^{5}+x^{4}+40 x^{3}-8 x^{2}+12 x^{5} {\mathrm e}+12 x^{3} {\mathrm e}^{2}-18 x^{2} {\mathrm e}^{2}+6 x^{4} {\mathrm e}^{2}+48 x \,{\mathrm e}+4 x \,{\mathrm e}^{3}+24 x^{2} {\mathrm e}-44 x^{3} {\mathrm e}+4 x^{2} {\mathrm e}^{3}-12 x^{4} {\mathrm e}+48 x \,{\mathrm e}^{1+{\mathrm e}^{8}}+36 x^{2} {\mathrm e}^{1+{\mathrm e}^{8}}+4 \ln \left (x +1\right ) {\mathrm e}^{1+{\mathrm e}^{8}}-24 x^{3} {\mathrm e}^{1+{\mathrm e}^{8}}-12 x \,{\mathrm e}^{2+{\mathrm e}^{8}}+12 x \,{\mathrm e}^{1+2 \,{\mathrm e}^{8}}-12 x^{2} {\mathrm e}^{2+{\mathrm e}^{8}}+12 x^{2} {\mathrm e}^{1+2 \,{\mathrm e}^{8}}-12 x^{4} {\mathrm e}^{1+{\mathrm e}^{8}}-2 \,{\mathrm e}^{2} \ln \left (x +1\right )-2 \ln \left (x +1\right ) {\mathrm e}^{2 \,{\mathrm e}^{8}}-8 \ln \left (x +1\right ) {\mathrm e}^{{\mathrm e}^{8}}-48 \,{\mathrm e}^{{\mathrm e}^{8}} x -24 \,{\mathrm e}^{2 \,{\mathrm e}^{8}} x +\left (-2 x^{4}-4 x^{2} {\mathrm e}+4 \,{\mathrm e}^{{\mathrm e}^{8}} x^{2}-4 x^{3}-4 x \,{\mathrm e}+4 \,{\mathrm e}^{{\mathrm e}^{8}} x +6 x^{2}+8 x \right ) \ln \left (x +1\right )-24 \,{\mathrm e}^{{\mathrm e}^{8}} x^{2}-4 \,{\mathrm e}^{3 \,{\mathrm e}^{8}} x +44 \,{\mathrm e}^{{\mathrm e}^{8}} x^{3}+12 \,{\mathrm e}^{2 \,{\mathrm e}^{8}} x^{3}+12 \,{\mathrm e}^{{\mathrm e}^{8}} x^{4}-12 \,{\mathrm e}^{{\mathrm e}^{8}} x^{5}-4 \,{\mathrm e}^{3 \,{\mathrm e}^{8}} x^{2}-4 \,{\mathrm e}^{{\mathrm e}^{8}} x^{6}+6 \,{\mathrm e}^{2 \,{\mathrm e}^{8}} x^{4}-18 \,{\mathrm e}^{2 \,{\mathrm e}^{8}} x^{2}+8 \,{\mathrm e} \ln \left (x +1\right )+4 x^{6} {\mathrm e}\)	\(403\)
derivativedivides	\(32+32 x +\ln \left (x +1\right )^{2}+\left (x +1\right )^{4}-8 \left (x +1\right )^{2}-8 \ln \left (x +1\right )-2 \,{\mathrm e}^{2} \ln \left (x +1\right )-2 \ln \left (x +1\right ) {\mathrm e}^{2 \,{\mathrm e}^{8}}-8 \ln \left (x +1\right ) {\mathrm e}^{{\mathrm e}^{8}}+4 \ln \left (x +1\right ) \left (x +1\right )^{3}+22 \,{\mathrm e} \left (x +1\right )^{2}+4 \,{\mathrm e} \left (\left (x +1\right ) \ln \left (x +1\right )-x -1\right )+6 \ln \left (x +1\right ) \left (x +1\right )^{2}-8 \,{\mathrm e} \left (\frac {\ln \left (x +1\right ) \left (x +1\right )^{2}}{2}-\frac {\left (x +1\right )^{2}}{4}\right )+4 \,{\mathrm e} \left (x +1\right )^{6}-12 \,{\mathrm e} \left (x +1\right )^{5}-12 \,{\mathrm e} \left (x +1\right )^{4}-2 \ln \left (x +1\right ) \left (x +1\right )^{4}+44 \,{\mathrm e} \left (x +1\right )^{3}+8 \,{\mathrm e} \ln \left (x +1\right )-44 \left (x +1\right ) {\mathrm e}-8 \left (x +1\right ) \ln \left (x +1\right )+24 \left (x +1\right ) {\mathrm e}^{2}-4 \left (x +1\right ) {\mathrm e}^{3}+\left (x +1\right )^{8}-4 \left (x +1\right )^{7}-2 \left (x +1\right )^{6}+20 \left (x +1\right )^{5}-40 \left (x +1\right )^{3}-18 \,{\mathrm e}^{2} \left (x +1\right )^{2}+4 \,{\mathrm e}^{3 \,{\mathrm e}^{8}} \left (x +1\right )-18 \,{\mathrm e}^{2 \,{\mathrm e}^{8}} \left (x +1\right )^{2}-44 \,{\mathrm e}^{{\mathrm e}^{8}} \left (x +1\right )^{3}+24 \,{\mathrm e}^{2 \,{\mathrm e}^{8}} \left (x +1\right )-22 \,{\mathrm e}^{{\mathrm e}^{8}} \left (x +1\right )^{2}+44 \,{\mathrm e}^{{\mathrm e}^{8}} \left (x +1\right )-4 \,{\mathrm e}^{{\mathrm e}^{8}} \left (\left (x +1\right ) \ln \left (x +1\right )-x -1\right )+8 \,{\mathrm e}^{{\mathrm e}^{8}} \left (\frac {\ln \left (x +1\right ) \left (x +1\right )^{2}}{2}-\frac {\left (x +1\right )^{2}}{4}\right )-4 \,{\mathrm e}^{{\mathrm e}^{8}} \left (x +1\right )^{6}+6 \,{\mathrm e}^{2} \left (x +1\right )^{4}+6 \,{\mathrm e}^{2 \,{\mathrm e}^{8}} \left (x +1\right )^{4}+12 \,{\mathrm e}^{{\mathrm e}^{8}} \left (x +1\right )^{5}+4 \,{\mathrm e}^{3} \left (x +1\right )^{2}-12 \,{\mathrm e}^{2} \left (x +1\right )^{3}-4 \,{\mathrm e}^{3 \,{\mathrm e}^{8}} \left (x +1\right )^{2}-12 \,{\mathrm e}^{2 \,{\mathrm e}^{8}} \left (x +1\right )^{3}+12 \,{\mathrm e}^{{\mathrm e}^{8}} \left (x +1\right )^{4}-12 \,{\mathrm e} \,{\mathrm e}^{{\mathrm e}^{8}} \left (x +1\right )^{4}-12 \,{\mathrm e}^{2} {\mathrm e}^{{\mathrm e}^{8}} \left (x +1\right )^{2}+12 \,{\mathrm e} \,{\mathrm e}^{2 \,{\mathrm e}^{8}} \left (x +1\right )^{2}+24 \,{\mathrm e} \,{\mathrm e}^{{\mathrm e}^{8}} \left (x +1\right )^{3}+12 \,{\mathrm e}^{2} {\mathrm e}^{{\mathrm e}^{8}} \left (x +1\right )-12 \,{\mathrm e} \,{\mathrm e}^{2 \,{\mathrm e}^{8}} \left (x +1\right )+36 \,{\mathrm e} \,{\mathrm e}^{{\mathrm e}^{8}} \left (x +1\right )^{2}-48 \,{\mathrm e} \,{\mathrm e}^{{\mathrm e}^{8}} \left (x +1\right )+4 \,{\mathrm e} \ln \left (x +1\right ) {\mathrm e}^{{\mathrm e}^{8}}\)	\(624\)
default	\(32+32 x +\ln \left (x +1\right )^{2}+\left (x +1\right )^{4}-8 \left (x +1\right )^{2}-8 \ln \left (x +1\right )-2 \,{\mathrm e}^{2} \ln \left (x +1\right )-2 \ln \left (x +1\right ) {\mathrm e}^{2 \,{\mathrm e}^{8}}-8 \ln \left (x +1\right ) {\mathrm e}^{{\mathrm e}^{8}}+4 \ln \left (x +1\right ) \left (x +1\right )^{3}+22 \,{\mathrm e} \left (x +1\right )^{2}+4 \,{\mathrm e} \left (\left (x +1\right ) \ln \left (x +1\right )-x -1\right )+6 \ln \left (x +1\right ) \left (x +1\right )^{2}-8 \,{\mathrm e} \left (\frac {\ln \left (x +1\right ) \left (x +1\right )^{2}}{2}-\frac {\left (x +1\right )^{2}}{4}\right )+4 \,{\mathrm e} \left (x +1\right )^{6}-12 \,{\mathrm e} \left (x +1\right )^{5}-12 \,{\mathrm e} \left (x +1\right )^{4}-2 \ln \left (x +1\right ) \left (x +1\right )^{4}+44 \,{\mathrm e} \left (x +1\right )^{3}+8 \,{\mathrm e} \ln \left (x +1\right )-44 \left (x +1\right ) {\mathrm e}-8 \left (x +1\right ) \ln \left (x +1\right )+24 \left (x +1\right ) {\mathrm e}^{2}-4 \left (x +1\right ) {\mathrm e}^{3}+\left (x +1\right )^{8}-4 \left (x +1\right )^{7}-2 \left (x +1\right )^{6}+20 \left (x +1\right )^{5}-40 \left (x +1\right )^{3}-18 \,{\mathrm e}^{2} \left (x +1\right )^{2}+4 \,{\mathrm e}^{3 \,{\mathrm e}^{8}} \left (x +1\right )-18 \,{\mathrm e}^{2 \,{\mathrm e}^{8}} \left (x +1\right )^{2}-44 \,{\mathrm e}^{{\mathrm e}^{8}} \left (x +1\right )^{3}+24 \,{\mathrm e}^{2 \,{\mathrm e}^{8}} \left (x +1\right )-22 \,{\mathrm e}^{{\mathrm e}^{8}} \left (x +1\right )^{2}+44 \,{\mathrm e}^{{\mathrm e}^{8}} \left (x +1\right )-4 \,{\mathrm e}^{{\mathrm e}^{8}} \left (\left (x +1\right ) \ln \left (x +1\right )-x -1\right )+8 \,{\mathrm e}^{{\mathrm e}^{8}} \left (\frac {\ln \left (x +1\right ) \left (x +1\right )^{2}}{2}-\frac {\left (x +1\right )^{2}}{4}\right )-4 \,{\mathrm e}^{{\mathrm e}^{8}} \left (x +1\right )^{6}+6 \,{\mathrm e}^{2} \left (x +1\right )^{4}+6 \,{\mathrm e}^{2 \,{\mathrm e}^{8}} \left (x +1\right )^{4}+12 \,{\mathrm e}^{{\mathrm e}^{8}} \left (x +1\right )^{5}+4 \,{\mathrm e}^{3} \left (x +1\right )^{2}-12 \,{\mathrm e}^{2} \left (x +1\right )^{3}-4 \,{\mathrm e}^{3 \,{\mathrm e}^{8}} \left (x +1\right )^{2}-12 \,{\mathrm e}^{2 \,{\mathrm e}^{8}} \left (x +1\right )^{3}+12 \,{\mathrm e}^{{\mathrm e}^{8}} \left (x +1\right )^{4}-12 \,{\mathrm e} \,{\mathrm e}^{{\mathrm e}^{8}} \left (x +1\right )^{4}-12 \,{\mathrm e}^{2} {\mathrm e}^{{\mathrm e}^{8}} \left (x +1\right )^{2}+12 \,{\mathrm e} \,{\mathrm e}^{2 \,{\mathrm e}^{8}} \left (x +1\right )^{2}+24 \,{\mathrm e} \,{\mathrm e}^{{\mathrm e}^{8}} \left (x +1\right )^{3}+12 \,{\mathrm e}^{2} {\mathrm e}^{{\mathrm e}^{8}} \left (x +1\right )-12 \,{\mathrm e} \,{\mathrm e}^{2 \,{\mathrm e}^{8}} \left (x +1\right )+36 \,{\mathrm e} \,{\mathrm e}^{{\mathrm e}^{8}} \left (x +1\right )^{2}-48 \,{\mathrm e} \,{\mathrm e}^{{\mathrm e}^{8}} \left (x +1\right )+4 \,{\mathrm e} \ln \left (x +1\right ) {\mathrm e}^{{\mathrm e}^{8}}\)	\(624\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((8*x^2+12*x+4)*exp(exp(4)^2)+(-8*x^2-12*x-4)*exp(1)-8*x^4-20*x^3+20*x+10)*ln(x+1)+(-8*x^2-12*x-4)*exp(ex
p(4)^2)^3+((24*x^2+36*x+12)*exp(1)+24*x^4+60*x^3-60*x-26)*exp(exp(4)^2)^2+((-24*x^2-36*x-12)*exp(1)^2+(-48*x^4
-120*x^3+120*x+52)*exp(1)-24*x^6-84*x^5-12*x^4+180*x^3+88*x^2-92*x-56)*exp(exp(4)^2)+(8*x^2+12*x+4)*exp(1)^3+(
24*x^4+60*x^3-60*x-26)*exp(1)^2+(24*x^6+84*x^5+12*x^4-180*x^3-88*x^2+92*x+56)*exp(1)+8*x^8+36*x^7+16*x^6-112*x
^5-98*x^4+120*x^3+110*x^2-40*x-40)/(x+1),x,method=_RETURNVERBOSE)

[Out]

x^8+ln(x+1)^2+(-20+12*exp(1)-12*exp(exp(4)^2))*x^5+(-2+4*exp(1)-4*exp(exp(4)^2))*x^6+(1-12*exp(1)+12*exp(exp(4
)^2)+6*exp(1)^2+6*exp(exp(4)^2)^2-12*exp(1)*exp(exp(4)^2))*x^4+(40-44*exp(1)+44*exp(exp(4)^2)+12*exp(1)^2+12*e
xp(exp(4)^2)^2-24*exp(1)*exp(exp(4)^2))*x^3+(-2*exp(1)^2+4*exp(1)*exp(exp(4)^2)-2*exp(exp(4)^2)^2+8*exp(1)-8*e
xp(exp(4)^2)-8)*ln(x+1)+(-32+48*exp(1)-48*exp(exp(4)^2)-24*exp(1)^2-24*exp(exp(4)^2)^2+48*exp(1)*exp(exp(4)^2)
-4*exp(exp(4)^2)^3+4*exp(1)^3-12*exp(1)^2*exp(exp(4)^2)+12*exp(1)*exp(exp(4)^2)^2)*x+(-8+24*exp(1)-24*exp(exp(
4)^2)-18*exp(1)^2-18*exp(exp(4)^2)^2+36*exp(1)*exp(exp(4)^2)-4*exp(exp(4)^2)^3+4*exp(1)^3-12*exp(1)^2*exp(exp(
4)^2)+12*exp(1)*exp(exp(4)^2)^2)*x^2+(6-4*exp(1)+4*exp(exp(4)^2))*x^2*ln(x+1)+(8-4*exp(1)+4*exp(exp(4)^2))*x*l
n(x+1)+4*x^7-4*ln(x+1)*x^3-2*ln(x+1)*x^4

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maxima [B]  time = 0.59, size = 1065, normalized size = 42.60 result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((8*x^2+12*x+4)*exp(exp(4)^2)+(-8*x^2-12*x-4)*exp(1)-8*x^4-20*x^3+20*x+10)*log(x+1)+(-8*x^2-12*x-4)
*exp(exp(4)^2)^3+((24*x^2+36*x+12)*exp(1)+24*x^4+60*x^3-60*x-26)*exp(exp(4)^2)^2+((-24*x^2-36*x-12)*exp(1)^2+(
-48*x^4-120*x^3+120*x+52)*exp(1)-24*x^6-84*x^5-12*x^4+180*x^3+88*x^2-92*x-56)*exp(exp(4)^2)+(8*x^2+12*x+4)*exp
(1)^3+(24*x^4+60*x^3-60*x-26)*exp(1)^2+(24*x^6+84*x^5+12*x^4-180*x^3-88*x^2+92*x+56)*exp(1)+8*x^8+36*x^7+16*x^
6-112*x^5-98*x^4+120*x^3+110*x^2-40*x-40)/(x+1),x, algorithm="maxima")

[Out]

x^8 + 4*x^7 - 2*x^6 - 20*x^5 + x^4 + 40*x^3 - 4*(x^2 - 2*x + 2*log(x + 1))*e*log(x + 1) - 12*(x - log(x + 1))*
e*log(x + 1) + 4*(x^2 - 2*x + 2*log(x + 1))*e^(e^8)*log(x + 1) + 12*(x - log(x + 1))*e^(e^8)*log(x + 1) - 2*e*
log(x + 1)^2 + 2*e^(e^8)*log(x + 1)^2 - 8*x^2 + 4*(x^2 - 2*x + 2*log(x + 1))*e^3 + 12*(x - log(x + 1))*e^3 + 2
*(3*x^4 - 4*x^3 + 6*x^2 - 12*x + 12*log(x + 1))*e^2 + 10*(2*x^3 - 3*x^2 + 6*x - 6*log(x + 1))*e^2 - 60*(x - lo
g(x + 1))*e^2 + 2/5*(10*x^6 - 12*x^5 + 15*x^4 - 20*x^3 + 30*x^2 - 60*x + 60*log(x + 1))*e + 7/5*(12*x^5 - 15*x
^4 + 20*x^3 - 30*x^2 + 60*x - 60*log(x + 1))*e + (3*x^4 - 4*x^3 + 6*x^2 - 12*x + 12*log(x + 1))*e - 30*(2*x^3
- 3*x^2 + 6*x - 6*log(x + 1))*e + 2*(x^2 + 2*log(x + 1)^2 - 6*x + 6*log(x + 1))*e - 44*(x^2 - 2*x + 2*log(x +
1))*e - 6*(log(x + 1)^2 - 2*x + 2*log(x + 1))*e + 92*(x - log(x + 1))*e - 4*(x^2 - 2*x + 2*log(x + 1))*e^(3*e^
8) - 12*(x - log(x + 1))*e^(3*e^8) + 2*(3*x^4 - 4*x^3 + 6*x^2 - 12*x + 12*log(x + 1))*e^(2*e^8) + 10*(2*x^3 -
3*x^2 + 6*x - 6*log(x + 1))*e^(2*e^8) - 60*(x - log(x + 1))*e^(2*e^8) + 12*(x^2 - 2*x + 2*log(x + 1))*e^(2*e^8
+ 1) + 36*(x - log(x + 1))*e^(2*e^8 + 1) - 12*(x^2 - 2*x + 2*log(x + 1))*e^(e^8 + 2) - 36*(x - log(x + 1))*e^
(e^8 + 2) - 4*(3*x^4 - 4*x^3 + 6*x^2 - 12*x + 12*log(x + 1))*e^(e^8 + 1) - 20*(2*x^3 - 3*x^2 + 6*x - 6*log(x +
1))*e^(e^8 + 1) + 120*(x - log(x + 1))*e^(e^8 + 1) - 2/5*(10*x^6 - 12*x^5 + 15*x^4 - 20*x^3 + 30*x^2 - 60*x +
60*log(x + 1))*e^(e^8) - 7/5*(12*x^5 - 15*x^4 + 20*x^3 - 30*x^2 + 60*x - 60*log(x + 1))*e^(e^8) - (3*x^4 - 4*
x^3 + 6*x^2 - 12*x + 12*log(x + 1))*e^(e^8) + 30*(2*x^3 - 3*x^2 + 6*x - 6*log(x + 1))*e^(e^8) - 2*(x^2 + 2*log
(x + 1)^2 - 6*x + 6*log(x + 1))*e^(e^8) + 44*(x^2 - 2*x + 2*log(x + 1))*e^(e^8) + 6*(log(x + 1)^2 - 2*x + 2*lo
g(x + 1))*e^(e^8) - 92*(x - log(x + 1))*e^(e^8) - 2/3*(3*x^4 - 4*x^3 + 6*x^2 - 12*x + 12*log(x + 1))*log(x + 1
) - 10/3*(2*x^3 - 3*x^2 + 6*x - 6*log(x + 1))*log(x + 1) + 20*(x - log(x + 1))*log(x + 1) + 4*e^3*log(x + 1) -
26*e^2*log(x + 1) + 56*e*log(x + 1) - 4*e^(3*e^8)*log(x + 1) - 26*e^(2*e^8)*log(x + 1) + 12*e^(2*e^8 + 1)*log
(x + 1) - 12*e^(e^8 + 2)*log(x + 1) + 52*e^(e^8 + 1)*log(x + 1) - 56*e^(e^8)*log(x + 1) + 9*log(x + 1)^2 - 32*
x - 8*log(x + 1)

________________________________________________________________________________________

mupad [B]  time = 4.72, size = 428, normalized size = 17.12 \begin {gather*} 48\,x\,{\mathrm {e}}^{{\mathrm {e}}^8+1}-8\,\ln \left (x+1\right )-24\,x\,{\mathrm {e}}^{2\,{\mathrm {e}}^8}-4\,x\,{\mathrm {e}}^{3\,{\mathrm {e}}^8}-32\,x-12\,x\,{\mathrm {e}}^{{\mathrm {e}}^8+2}-24\,x^2\,{\mathrm {e}}^{{\mathrm {e}}^8}+44\,x^3\,{\mathrm {e}}^{{\mathrm {e}}^8}+12\,x^4\,{\mathrm {e}}^{{\mathrm {e}}^8}-12\,x^5\,{\mathrm {e}}^{{\mathrm {e}}^8}-4\,x^6\,{\mathrm {e}}^{{\mathrm {e}}^8}+8\,\ln \left (x+1\right )\,\mathrm {e}-2\,\ln \left (x+1\right )\,{\mathrm {e}}^2+8\,x\,\ln \left (x+1\right )+48\,x\,\mathrm {e}-24\,x\,{\mathrm {e}}^2+4\,x\,{\mathrm {e}}^3+12\,x\,{\mathrm {e}}^{2\,{\mathrm {e}}^8+1}-18\,x^2\,{\mathrm {e}}^{2\,{\mathrm {e}}^8}-4\,x^2\,{\mathrm {e}}^{3\,{\mathrm {e}}^8}+12\,x^3\,{\mathrm {e}}^{2\,{\mathrm {e}}^8}+6\,x^4\,{\mathrm {e}}^{2\,{\mathrm {e}}^8}+36\,x^2\,{\mathrm {e}}^{{\mathrm {e}}^8+1}-12\,x^2\,{\mathrm {e}}^{{\mathrm {e}}^8+2}-24\,x^3\,{\mathrm {e}}^{{\mathrm {e}}^8+1}-12\,x^4\,{\mathrm {e}}^{{\mathrm {e}}^8+1}-8\,\ln \left (x+1\right )\,{\mathrm {e}}^{{\mathrm {e}}^8}+6\,x^2\,\ln \left (x+1\right )-4\,x^3\,\ln \left (x+1\right )-2\,x^4\,\ln \left (x+1\right )+24\,x^2\,\mathrm {e}-18\,x^2\,{\mathrm {e}}^2-44\,x^3\,\mathrm {e}+4\,x^2\,{\mathrm {e}}^3+12\,x^3\,{\mathrm {e}}^2-12\,x^4\,\mathrm {e}+6\,x^4\,{\mathrm {e}}^2+12\,x^5\,\mathrm {e}+4\,x^6\,\mathrm {e}-48\,x\,{\mathrm {e}}^{{\mathrm {e}}^8}+{\ln \left (x+1\right )}^2+12\,x^2\,{\mathrm {e}}^{2\,{\mathrm {e}}^8+1}-2\,\ln \left (x+1\right )\,{\mathrm {e}}^{2\,{\mathrm {e}}^8}+4\,\ln \left (x+1\right )\,{\mathrm {e}}^{{\mathrm {e}}^8+1}-8\,x^2+40\,x^3+x^4-20\,x^5-2\,x^6+4\,x^7+x^8+4\,x^2\,\ln \left (x+1\right )\,{\mathrm {e}}^{{\mathrm {e}}^8}-4\,x\,\ln \left (x+1\right )\,\mathrm {e}-4\,x^2\,\ln \left (x+1\right )\,\mathrm {e}+4\,x\,\ln \left (x+1\right )\,{\mathrm {e}}^{{\mathrm {e}}^8} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(1)*(92*x - 88*x^2 - 180*x^3 + 12*x^4 + 84*x^5 + 24*x^6 + 56) - 40*x - exp(exp(8))*(92*x + exp(2)*(36*
x + 24*x^2 + 12) - exp(1)*(120*x - 120*x^3 - 48*x^4 + 52) - 88*x^2 - 180*x^3 + 12*x^4 + 84*x^5 + 24*x^6 + 56)
+ log(x + 1)*(20*x - exp(1)*(12*x + 8*x^2 + 4) + exp(exp(8))*(12*x + 8*x^2 + 4) - 20*x^3 - 8*x^4 + 10) + exp(3
)*(12*x + 8*x^2 + 4) + exp(2*exp(8))*(exp(1)*(36*x + 24*x^2 + 12) - 60*x + 60*x^3 + 24*x^4 - 26) - exp(2)*(60*
x - 60*x^3 - 24*x^4 + 26) + 110*x^2 + 120*x^3 - 98*x^4 - 112*x^5 + 16*x^6 + 36*x^7 + 8*x^8 - exp(3*exp(8))*(12
*x + 8*x^2 + 4) - 40)/(x + 1),x)

[Out]

48*x*exp(exp(8) + 1) - 8*log(x + 1) - 24*x*exp(2*exp(8)) - 4*x*exp(3*exp(8)) - 32*x - 12*x*exp(exp(8) + 2) - 2
4*x^2*exp(exp(8)) + 44*x^3*exp(exp(8)) + 12*x^4*exp(exp(8)) - 12*x^5*exp(exp(8)) - 4*x^6*exp(exp(8)) + 8*log(x
+ 1)*exp(1) - 2*log(x + 1)*exp(2) + 8*x*log(x + 1) + 48*x*exp(1) - 24*x*exp(2) + 4*x*exp(3) + 12*x*exp(2*exp(
8) + 1) - 18*x^2*exp(2*exp(8)) - 4*x^2*exp(3*exp(8)) + 12*x^3*exp(2*exp(8)) + 6*x^4*exp(2*exp(8)) + 36*x^2*exp
(exp(8) + 1) - 12*x^2*exp(exp(8) + 2) - 24*x^3*exp(exp(8) + 1) - 12*x^4*exp(exp(8) + 1) - 8*log(x + 1)*exp(exp
(8)) + 6*x^2*log(x + 1) - 4*x^3*log(x + 1) - 2*x^4*log(x + 1) + 24*x^2*exp(1) - 18*x^2*exp(2) - 44*x^3*exp(1)
+ 4*x^2*exp(3) + 12*x^3*exp(2) - 12*x^4*exp(1) + 6*x^4*exp(2) + 12*x^5*exp(1) + 4*x^6*exp(1) - 48*x*exp(exp(8)
) + log(x + 1)^2 + 12*x^2*exp(2*exp(8) + 1) - 2*log(x + 1)*exp(2*exp(8)) + 4*log(x + 1)*exp(exp(8) + 1) - 8*x^
2 + 40*x^3 + x^4 - 20*x^5 - 2*x^6 + 4*x^7 + x^8 + 4*x^2*log(x + 1)*exp(exp(8)) - 4*x*log(x + 1)*exp(1) - 4*x^2
*log(x + 1)*exp(1) + 4*x*log(x + 1)*exp(exp(8))

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sympy [B]  time = 0.97, size = 357, normalized size = 14.28 \begin {gather*} x^{8} + 4 x^{7} + x^{6} \left (-2 + 4 e - 4 e^{e^{8}}\right ) + x^{5} \left (-20 + 12 e - 12 e^{e^{8}}\right ) + x^{4} \left (- 12 e + 1 + 6 e^{2} + 6 e^{2 e^{8}} + 12 e^{e^{8}} - 12 e e^{e^{8}}\right ) + x^{3} \left (- 44 e + 40 + 12 e^{2} + 12 e^{2 e^{8}} + 44 e^{e^{8}} - 24 e e^{e^{8}}\right ) + x^{2} \left (- 18 e^{2} - 8 + 24 e + 4 e^{3} - 24 e^{e^{8}} - 18 e^{2 e^{8}} - 4 e^{3 e^{8}} - 12 e^{2} e^{e^{8}} + 12 e e^{2 e^{8}} + 36 e e^{e^{8}}\right ) + x \left (- 24 e^{2} - 32 + 4 e^{3} + 48 e - 48 e^{e^{8}} - 24 e^{2 e^{8}} - 4 e^{3 e^{8}} - 12 e^{2} e^{e^{8}} + 12 e e^{2 e^{8}} + 48 e e^{e^{8}}\right ) + \left (- 2 x^{4} - 4 x^{3} - 4 e x^{2} + 6 x^{2} + 4 x^{2} e^{e^{8}} - 4 e x + 8 x + 4 x e^{e^{8}}\right ) \log {\left (x + 1 \right )} + \log {\left (x + 1 \right )}^{2} - 2 \left (-2 + e - e^{e^{8}}\right )^{2} \log {\left (x + 1 \right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((8*x**2+12*x+4)*exp(exp(4)**2)+(-8*x**2-12*x-4)*exp(1)-8*x**4-20*x**3+20*x+10)*ln(x+1)+(-8*x**2-12
*x-4)*exp(exp(4)**2)**3+((24*x**2+36*x+12)*exp(1)+24*x**4+60*x**3-60*x-26)*exp(exp(4)**2)**2+((-24*x**2-36*x-1
2)*exp(1)**2+(-48*x**4-120*x**3+120*x+52)*exp(1)-24*x**6-84*x**5-12*x**4+180*x**3+88*x**2-92*x-56)*exp(exp(4)*
*2)+(8*x**2+12*x+4)*exp(1)**3+(24*x**4+60*x**3-60*x-26)*exp(1)**2+(24*x**6+84*x**5+12*x**4-180*x**3-88*x**2+92
*x+56)*exp(1)+8*x**8+36*x**7+16*x**6-112*x**5-98*x**4+120*x**3+110*x**2-40*x-40)/(x+1),x)

[Out]

x**8 + 4*x**7 + x**6*(-2 + 4*E - 4*exp(exp(8))) + x**5*(-20 + 12*E - 12*exp(exp(8))) + x**4*(-12*E + 1 + 6*exp
(2) + 6*exp(2*exp(8)) + 12*exp(exp(8)) - 12*E*exp(exp(8))) + x**3*(-44*E + 40 + 12*exp(2) + 12*exp(2*exp(8)) +
44*exp(exp(8)) - 24*E*exp(exp(8))) + x**2*(-18*exp(2) - 8 + 24*E + 4*exp(3) - 24*exp(exp(8)) - 18*exp(2*exp(8
)) - 4*exp(3*exp(8)) - 12*exp(2)*exp(exp(8)) + 12*E*exp(2*exp(8)) + 36*E*exp(exp(8))) + x*(-24*exp(2) - 32 + 4
*exp(3) + 48*E - 48*exp(exp(8)) - 24*exp(2*exp(8)) - 4*exp(3*exp(8)) - 12*exp(2)*exp(exp(8)) + 12*E*exp(2*exp(
8)) + 48*E*exp(exp(8))) + (-2*x**4 - 4*x**3 - 4*E*x**2 + 6*x**2 + 4*x**2*exp(exp(8)) - 4*E*x + 8*x + 4*x*exp(e
xp(8)))*log(x + 1) + log(x + 1)**2 - 2*(-2 + E - exp(exp(8)))**2*log(x + 1)

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