3.19.87 \(\int \frac {-162 x+108 x^2+518 x^3-160 x^4-546 x^5-4 x^6+186 x^7+56 x^8+4 x^9+e^{2 x} (-2 x+6 x^3+2 x^4-6 x^5-4 x^6+2 x^7+2 x^8)+e^x (36 x-12 x^2-110 x^3+110 x^5+36 x^6-34 x^7-24 x^8-2 x^9)+(486 x^2-18 x^3-674 x^4-56 x^5+182 x^6+74 x^7+6 x^8+e^{2 x} (6 x^2+2 x^3-8 x^4-6 x^5+2 x^6+4 x^7)+e^x (-108 x^2-16 x^3+144 x^4+60 x^5-32 x^6-44 x^7-4 x^8)) \log (x)+(-324 x^3-90 x^4-6 x^5+18 x^6+2 x^7+e^{2 x} (-4 x^3-2 x^4+2 x^6)+e^x (72 x^3+28 x^4+2 x^5-20 x^6-2 x^7)) \log ^2(x)}{-1+3 x^2-3 x^4+x^6} \, dx\)

Optimal. Leaf size=33 \[ \left (9-e^x+x\right )^2 \left (-x-\log (x)+\frac {\log (x)}{1-x^2}\right )^2 \]

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Rubi [F]  time = 180.00, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \text {\$Aborted} \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-162*x + 108*x^2 + 518*x^3 - 160*x^4 - 546*x^5 - 4*x^6 + 186*x^7 + 56*x^8 + 4*x^9 + E^(2*x)*(-2*x + 6*x^3
+ 2*x^4 - 6*x^5 - 4*x^6 + 2*x^7 + 2*x^8) + E^x*(36*x - 12*x^2 - 110*x^3 + 110*x^5 + 36*x^6 - 34*x^7 - 24*x^8
- 2*x^9) + (486*x^2 - 18*x^3 - 674*x^4 - 56*x^5 + 182*x^6 + 74*x^7 + 6*x^8 + E^(2*x)*(6*x^2 + 2*x^3 - 8*x^4 -
6*x^5 + 2*x^6 + 4*x^7) + E^x*(-108*x^2 - 16*x^3 + 144*x^4 + 60*x^5 - 32*x^6 - 44*x^7 - 4*x^8))*Log[x] + (-324*
x^3 - 90*x^4 - 6*x^5 + 18*x^6 + 2*x^7 + E^(2*x)*(-4*x^3 - 2*x^4 + 2*x^6) + E^x*(72*x^3 + 28*x^4 + 2*x^5 - 20*x
^6 - 2*x^7))*Log[x]^2)/(-1 + 3*x^2 - 3*x^4 + x^6),x]

[Out]

$Aborted

Rubi steps

Aborted

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Mathematica [A]  time = 0.17, size = 32, normalized size = 0.97 \begin {gather*} \frac {x^2 \left (9-e^x+x\right )^2 \left (-1+x^2+x \log (x)\right )^2}{\left (-1+x^2\right )^2} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-162*x + 108*x^2 + 518*x^3 - 160*x^4 - 546*x^5 - 4*x^6 + 186*x^7 + 56*x^8 + 4*x^9 + E^(2*x)*(-2*x +
6*x^3 + 2*x^4 - 6*x^5 - 4*x^6 + 2*x^7 + 2*x^8) + E^x*(36*x - 12*x^2 - 110*x^3 + 110*x^5 + 36*x^6 - 34*x^7 - 2
4*x^8 - 2*x^9) + (486*x^2 - 18*x^3 - 674*x^4 - 56*x^5 + 182*x^6 + 74*x^7 + 6*x^8 + E^(2*x)*(6*x^2 + 2*x^3 - 8*
x^4 - 6*x^5 + 2*x^6 + 4*x^7) + E^x*(-108*x^2 - 16*x^3 + 144*x^4 + 60*x^5 - 32*x^6 - 44*x^7 - 4*x^8))*Log[x] +
(-324*x^3 - 90*x^4 - 6*x^5 + 18*x^6 + 2*x^7 + E^(2*x)*(-4*x^3 - 2*x^4 + 2*x^6) + E^x*(72*x^3 + 28*x^4 + 2*x^5
- 20*x^6 - 2*x^7))*Log[x]^2)/(-1 + 3*x^2 - 3*x^4 + x^6),x]

[Out]

(x^2*(9 - E^x + x)^2*(-1 + x^2 + x*Log[x])^2)/(-1 + x^2)^2

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fricas [B]  time = 0.79, size = 200, normalized size = 6.06 \begin {gather*} \frac {x^{8} + 18 \, x^{7} + 79 \, x^{6} - 36 \, x^{5} - 161 \, x^{4} + 18 \, x^{3} + {\left (x^{6} + 18 \, x^{5} + x^{4} e^{\left (2 \, x\right )} + 81 \, x^{4} - 2 \, {\left (x^{5} + 9 \, x^{4}\right )} e^{x}\right )} \log \relax (x)^{2} + 81 \, x^{2} + {\left (x^{6} - 2 \, x^{4} + x^{2}\right )} e^{\left (2 \, x\right )} - 2 \, {\left (x^{7} + 9 \, x^{6} - 2 \, x^{5} - 18 \, x^{4} + x^{3} + 9 \, x^{2}\right )} e^{x} + 2 \, {\left (x^{7} + 18 \, x^{6} + 80 \, x^{5} - 18 \, x^{4} - 81 \, x^{3} + {\left (x^{5} - x^{3}\right )} e^{\left (2 \, x\right )} - 2 \, {\left (x^{6} + 9 \, x^{5} - x^{4} - 9 \, x^{3}\right )} e^{x}\right )} \log \relax (x)}{x^{4} - 2 \, x^{2} + 1} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((2*x^6-2*x^4-4*x^3)*exp(x)^2+(-2*x^7-20*x^6+2*x^5+28*x^4+72*x^3)*exp(x)+2*x^7+18*x^6-6*x^5-90*x^4-
324*x^3)*log(x)^2+((4*x^7+2*x^6-6*x^5-8*x^4+2*x^3+6*x^2)*exp(x)^2+(-4*x^8-44*x^7-32*x^6+60*x^5+144*x^4-16*x^3-
108*x^2)*exp(x)+6*x^8+74*x^7+182*x^6-56*x^5-674*x^4-18*x^3+486*x^2)*log(x)+(2*x^8+2*x^7-4*x^6-6*x^5+2*x^4+6*x^
3-2*x)*exp(x)^2+(-2*x^9-24*x^8-34*x^7+36*x^6+110*x^5-110*x^3-12*x^2+36*x)*exp(x)+4*x^9+56*x^8+186*x^7-4*x^6-54
6*x^5-160*x^4+518*x^3+108*x^2-162*x)/(x^6-3*x^4+3*x^2-1),x, algorithm="fricas")

[Out]

(x^8 + 18*x^7 + 79*x^6 - 36*x^5 - 161*x^4 + 18*x^3 + (x^6 + 18*x^5 + x^4*e^(2*x) + 81*x^4 - 2*(x^5 + 9*x^4)*e^
x)*log(x)^2 + 81*x^2 + (x^6 - 2*x^4 + x^2)*e^(2*x) - 2*(x^7 + 9*x^6 - 2*x^5 - 18*x^4 + x^3 + 9*x^2)*e^x + 2*(x
^7 + 18*x^6 + 80*x^5 - 18*x^4 - 81*x^3 + (x^5 - x^3)*e^(2*x) - 2*(x^6 + 9*x^5 - x^4 - 9*x^3)*e^x)*log(x))/(x^4
- 2*x^2 + 1)

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {2 \, {\left (2 \, x^{9} + 28 \, x^{8} + 93 \, x^{7} - 2 \, x^{6} - 273 \, x^{5} - 80 \, x^{4} + 259 \, x^{3} + {\left (x^{7} + 9 \, x^{6} - 3 \, x^{5} - 45 \, x^{4} - 162 \, x^{3} + {\left (x^{6} - x^{4} - 2 \, x^{3}\right )} e^{\left (2 \, x\right )} - {\left (x^{7} + 10 \, x^{6} - x^{5} - 14 \, x^{4} - 36 \, x^{3}\right )} e^{x}\right )} \log \relax (x)^{2} + 54 \, x^{2} + {\left (x^{8} + x^{7} - 2 \, x^{6} - 3 \, x^{5} + x^{4} + 3 \, x^{3} - x\right )} e^{\left (2 \, x\right )} - {\left (x^{9} + 12 \, x^{8} + 17 \, x^{7} - 18 \, x^{6} - 55 \, x^{5} + 55 \, x^{3} + 6 \, x^{2} - 18 \, x\right )} e^{x} + {\left (3 \, x^{8} + 37 \, x^{7} + 91 \, x^{6} - 28 \, x^{5} - 337 \, x^{4} - 9 \, x^{3} + 243 \, x^{2} + {\left (2 \, x^{7} + x^{6} - 3 \, x^{5} - 4 \, x^{4} + x^{3} + 3 \, x^{2}\right )} e^{\left (2 \, x\right )} - 2 \, {\left (x^{8} + 11 \, x^{7} + 8 \, x^{6} - 15 \, x^{5} - 36 \, x^{4} + 4 \, x^{3} + 27 \, x^{2}\right )} e^{x}\right )} \log \relax (x) - 81 \, x\right )}}{x^{6} - 3 \, x^{4} + 3 \, x^{2} - 1}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((2*x^6-2*x^4-4*x^3)*exp(x)^2+(-2*x^7-20*x^6+2*x^5+28*x^4+72*x^3)*exp(x)+2*x^7+18*x^6-6*x^5-90*x^4-
324*x^3)*log(x)^2+((4*x^7+2*x^6-6*x^5-8*x^4+2*x^3+6*x^2)*exp(x)^2+(-4*x^8-44*x^7-32*x^6+60*x^5+144*x^4-16*x^3-
108*x^2)*exp(x)+6*x^8+74*x^7+182*x^6-56*x^5-674*x^4-18*x^3+486*x^2)*log(x)+(2*x^8+2*x^7-4*x^6-6*x^5+2*x^4+6*x^
3-2*x)*exp(x)^2+(-2*x^9-24*x^8-34*x^7+36*x^6+110*x^5-110*x^3-12*x^2+36*x)*exp(x)+4*x^9+56*x^8+186*x^7-4*x^6-54
6*x^5-160*x^4+518*x^3+108*x^2-162*x)/(x^6-3*x^4+3*x^2-1),x, algorithm="giac")

[Out]

integrate(2*(2*x^9 + 28*x^8 + 93*x^7 - 2*x^6 - 273*x^5 - 80*x^4 + 259*x^3 + (x^7 + 9*x^6 - 3*x^5 - 45*x^4 - 16
2*x^3 + (x^6 - x^4 - 2*x^3)*e^(2*x) - (x^7 + 10*x^6 - x^5 - 14*x^4 - 36*x^3)*e^x)*log(x)^2 + 54*x^2 + (x^8 + x
^7 - 2*x^6 - 3*x^5 + x^4 + 3*x^3 - x)*e^(2*x) - (x^9 + 12*x^8 + 17*x^7 - 18*x^6 - 55*x^5 + 55*x^3 + 6*x^2 - 18
*x)*e^x + (3*x^8 + 37*x^7 + 91*x^6 - 28*x^5 - 337*x^4 - 9*x^3 + 243*x^2 + (2*x^7 + x^6 - 3*x^5 - 4*x^4 + x^3 +
3*x^2)*e^(2*x) - 2*(x^8 + 11*x^7 + 8*x^6 - 15*x^5 - 36*x^4 + 4*x^3 + 27*x^2)*e^x)*log(x) - 81*x)/(x^6 - 3*x^4
+ 3*x^2 - 1), x)

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maple [B]  time = 0.12, size = 130, normalized size = 3.94

method	result	size
risch	\(\frac {\left (x^{2}-2 \,{\mathrm e}^{x} x +{\mathrm e}^{2 x}+18 x -18 \,{\mathrm e}^{x}+81\right ) x^{4} \ln \relax (x )^{2}}{\left (x^{2}-1\right )^{2}}+\frac {2 \left (x^{5}-2 \,{\mathrm e}^{x} x^{4}+{\mathrm e}^{2 x} x^{3}+18 x^{4}-18 \,{\mathrm e}^{x} x^{3}+81 x^{3}-18 x^{2}+18\right ) \ln \relax (x )}{x^{2}-1}+x^{4}-2 \,{\mathrm e}^{x} x^{3}+{\mathrm e}^{2 x} x^{2}+18 x^{3}-18 \,{\mathrm e}^{x} x^{2}+81 x^{2}+36 \ln \relax (x )\)	\(130\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((2*x^6-2*x^4-4*x^3)*exp(x)^2+(-2*x^7-20*x^6+2*x^5+28*x^4+72*x^3)*exp(x)+2*x^7+18*x^6-6*x^5-90*x^4-324*x^
3)*ln(x)^2+((4*x^7+2*x^6-6*x^5-8*x^4+2*x^3+6*x^2)*exp(x)^2+(-4*x^8-44*x^7-32*x^6+60*x^5+144*x^4-16*x^3-108*x^2
)*exp(x)+6*x^8+74*x^7+182*x^6-56*x^5-674*x^4-18*x^3+486*x^2)*ln(x)+(2*x^8+2*x^7-4*x^6-6*x^5+2*x^4+6*x^3-2*x)*e
xp(x)^2+(-2*x^9-24*x^8-34*x^7+36*x^6+110*x^5-110*x^3-12*x^2+36*x)*exp(x)+4*x^9+56*x^8+186*x^7-4*x^6-546*x^5-16
0*x^4+518*x^3+108*x^2-162*x)/(x^6-3*x^4+3*x^2-1),x,method=_RETURNVERBOSE)

[Out]

(x^2-2*exp(x)*x+exp(2*x)+18*x-18*exp(x)+81)*x^4/(x^2-1)^2*ln(x)^2+2*(x^5-2*exp(x)*x^4+exp(2*x)*x^3+18*x^4-18*e
xp(x)*x^3+81*x^3-18*x^2+18)/(x^2-1)*ln(x)+x^4-2*exp(x)*x^3+exp(2*x)*x^2+18*x^3-18*exp(x)*x^2+81*x^2+36*ln(x)

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maxima [B]  time = 0.73, size = 436, normalized size = 13.21 \begin {gather*} x^{4} + \frac {56}{3} \, x^{3} + 99 \, x^{2} + 164 \, x - \frac {2 \, x^{7} + 54 \, x^{6} + 488 \, x^{5} - 108 \, x^{4} - 982 \, x^{3} - 3 \, {\left (x^{6} + 18 \, x^{5} + 81 \, x^{4}\right )} \log \relax (x)^{2} + 54 \, x^{2} - 3 \, {\left (x^{6} + x^{4} \log \relax (x)^{2} - 2 \, x^{4} + x^{2} + 2 \, {\left (x^{5} - x^{3}\right )} \log \relax (x)\right )} e^{\left (2 \, x\right )} + 6 \, {\left (x^{7} + 9 \, x^{6} - 2 \, x^{5} - 18 \, x^{4} + x^{3} + {\left (x^{5} + 9 \, x^{4}\right )} \log \relax (x)^{2} + 9 \, x^{2} + 2 \, {\left (x^{6} + 9 \, x^{5} - x^{4} - 9 \, x^{3}\right )} \log \relax (x)\right )} e^{x} - 6 \, {\left (x^{7} + 18 \, x^{6} + 80 \, x^{5} - 36 \, x^{4} - 81 \, x^{3} + 36 \, x^{2} - 18\right )} \log \relax (x) + 492 \, x}{3 \, {\left (x^{4} - 2 \, x^{2} + 1\right )}} - \frac {7 \, {\left (13 \, x^{3} - 11 \, x\right )}}{x^{4} - 2 \, x^{2} + 1} + \frac {9 \, x^{3} - 7 \, x}{2 \, {\left (x^{4} - 2 \, x^{2} + 1\right )}} + \frac {20 \, {\left (5 \, x^{3} - 3 \, x\right )}}{x^{4} - 2 \, x^{2} + 1} - \frac {27 \, {\left (x^{3} + x\right )}}{2 \, {\left (x^{4} - 2 \, x^{2} + 1\right )}} - \frac {8 \, x^{2} - 7}{x^{4} - 2 \, x^{2} + 1} - \frac {93 \, {\left (6 \, x^{2} - 5\right )}}{2 \, {\left (x^{4} - 2 \, x^{2} + 1\right )}} + \frac {273 \, {\left (4 \, x^{2} - 3\right )}}{2 \, {\left (x^{4} - 2 \, x^{2} + 1\right )}} - \frac {259 \, {\left (2 \, x^{2} - 1\right )}}{2 \, {\left (x^{4} - 2 \, x^{2} + 1\right )}} + \frac {81}{2 \, {\left (x^{4} - 2 \, x^{2} + 1\right )}} + 18 \, \log \left (x^{2} - 1\right ) - 18 \, \log \left (x + 1\right ) - 18 \, \log \left (x - 1\right ) + 36 \, \log \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((2*x^6-2*x^4-4*x^3)*exp(x)^2+(-2*x^7-20*x^6+2*x^5+28*x^4+72*x^3)*exp(x)+2*x^7+18*x^6-6*x^5-90*x^4-
324*x^3)*log(x)^2+((4*x^7+2*x^6-6*x^5-8*x^4+2*x^3+6*x^2)*exp(x)^2+(-4*x^8-44*x^7-32*x^6+60*x^5+144*x^4-16*x^3-
108*x^2)*exp(x)+6*x^8+74*x^7+182*x^6-56*x^5-674*x^4-18*x^3+486*x^2)*log(x)+(2*x^8+2*x^7-4*x^6-6*x^5+2*x^4+6*x^
3-2*x)*exp(x)^2+(-2*x^9-24*x^8-34*x^7+36*x^6+110*x^5-110*x^3-12*x^2+36*x)*exp(x)+4*x^9+56*x^8+186*x^7-4*x^6-54
6*x^5-160*x^4+518*x^3+108*x^2-162*x)/(x^6-3*x^4+3*x^2-1),x, algorithm="maxima")

[Out]

x^4 + 56/3*x^3 + 99*x^2 + 164*x - 1/3*(2*x^7 + 54*x^6 + 488*x^5 - 108*x^4 - 982*x^3 - 3*(x^6 + 18*x^5 + 81*x^4
)*log(x)^2 + 54*x^2 - 3*(x^6 + x^4*log(x)^2 - 2*x^4 + x^2 + 2*(x^5 - x^3)*log(x))*e^(2*x) + 6*(x^7 + 9*x^6 - 2
*x^5 - 18*x^4 + x^3 + (x^5 + 9*x^4)*log(x)^2 + 9*x^2 + 2*(x^6 + 9*x^5 - x^4 - 9*x^3)*log(x))*e^x - 6*(x^7 + 18
*x^6 + 80*x^5 - 36*x^4 - 81*x^3 + 36*x^2 - 18)*log(x) + 492*x)/(x^4 - 2*x^2 + 1) - 7*(13*x^3 - 11*x)/(x^4 - 2*
x^2 + 1) + 1/2*(9*x^3 - 7*x)/(x^4 - 2*x^2 + 1) + 20*(5*x^3 - 3*x)/(x^4 - 2*x^2 + 1) - 27/2*(x^3 + x)/(x^4 - 2*
x^2 + 1) - (8*x^2 - 7)/(x^4 - 2*x^2 + 1) - 93/2*(6*x^2 - 5)/(x^4 - 2*x^2 + 1) + 273/2*(4*x^2 - 3)/(x^4 - 2*x^2
+ 1) - 259/2*(2*x^2 - 1)/(x^4 - 2*x^2 + 1) + 81/2/(x^4 - 2*x^2 + 1) + 18*log(x^2 - 1) - 18*log(x + 1) - 18*lo
g(x - 1) + 36*log(x)

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mupad [B]  time = 2.06, size = 316, normalized size = 9.58 \begin {gather*} 81\,{\ln \relax (x)}^2-2\,x^3\,{\mathrm {e}}^x-18\,x^2\,{\mathrm {e}}^x-\frac {81\,{\ln \relax (x)}^2}{x^4-2\,x^2+1}+x^2\,{\mathrm {e}}^{2\,x}+81\,x^2+18\,x^3+x^4+{\mathrm {e}}^{2\,x}\,{\ln \relax (x)}^2+\frac {162\,x^2\,{\ln \relax (x)}^2}{x^4-2\,x^2+1}+\frac {18\,x^5\,{\ln \relax (x)}^2}{x^4-2\,x^2+1}+\frac {x^6\,{\ln \relax (x)}^2}{x^4-2\,x^2+1}-\frac {{\mathrm {e}}^{2\,x}\,{\ln \relax (x)}^2}{x^4-2\,x^2+1}+\frac {162\,x^3\,\ln \relax (x)}{x^2-1}+\frac {36\,x^4\,\ln \relax (x)}{x^2-1}+\frac {2\,x^5\,\ln \relax (x)}{x^2-1}-\frac {18\,x^4\,{\mathrm {e}}^x\,{\ln \relax (x)}^2}{x^4-2\,x^2+1}-\frac {2\,x^5\,{\mathrm {e}}^x\,{\ln \relax (x)}^2}{x^4-2\,x^2+1}+\frac {2\,x^2\,{\mathrm {e}}^{2\,x}\,{\ln \relax (x)}^2}{x^4-2\,x^2+1}-\frac {36\,x^3\,{\mathrm {e}}^x\,\ln \relax (x)}{x^2-1}-\frac {4\,x^4\,{\mathrm {e}}^x\,\ln \relax (x)}{x^2-1}+\frac {2\,x^3\,{\mathrm {e}}^{2\,x}\,\ln \relax (x)}{x^2-1} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(2*x)*(6*x^3 - 2*x + 2*x^4 - 6*x^5 - 4*x^6 + 2*x^7 + 2*x^8) - 162*x - log(x)^2*(exp(2*x)*(4*x^3 + 2*x^
4 - 2*x^6) - exp(x)*(72*x^3 + 28*x^4 + 2*x^5 - 20*x^6 - 2*x^7) + 324*x^3 + 90*x^4 + 6*x^5 - 18*x^6 - 2*x^7) +
log(x)*(exp(2*x)*(6*x^2 + 2*x^3 - 8*x^4 - 6*x^5 + 2*x^6 + 4*x^7) - exp(x)*(108*x^2 + 16*x^3 - 144*x^4 - 60*x^5
+ 32*x^6 + 44*x^7 + 4*x^8) + 486*x^2 - 18*x^3 - 674*x^4 - 56*x^5 + 182*x^6 + 74*x^7 + 6*x^8) + 108*x^2 + 518*
x^3 - 160*x^4 - 546*x^5 - 4*x^6 + 186*x^7 + 56*x^8 + 4*x^9 - exp(x)*(12*x^2 - 36*x + 110*x^3 - 110*x^5 - 36*x^
6 + 34*x^7 + 24*x^8 + 2*x^9))/(3*x^2 - 3*x^4 + x^6 - 1),x)

[Out]

81*log(x)^2 - 2*x^3*exp(x) - 18*x^2*exp(x) - (81*log(x)^2)/(x^4 - 2*x^2 + 1) + x^2*exp(2*x) + 81*x^2 + 18*x^3
+ x^4 + exp(2*x)*log(x)^2 + (162*x^2*log(x)^2)/(x^4 - 2*x^2 + 1) + (18*x^5*log(x)^2)/(x^4 - 2*x^2 + 1) + (x^6*
log(x)^2)/(x^4 - 2*x^2 + 1) - (exp(2*x)*log(x)^2)/(x^4 - 2*x^2 + 1) + (162*x^3*log(x))/(x^2 - 1) + (36*x^4*log
(x))/(x^2 - 1) + (2*x^5*log(x))/(x^2 - 1) - (18*x^4*exp(x)*log(x)^2)/(x^4 - 2*x^2 + 1) - (2*x^5*exp(x)*log(x)^
2)/(x^4 - 2*x^2 + 1) + (2*x^2*exp(2*x)*log(x)^2)/(x^4 - 2*x^2 + 1) - (36*x^3*exp(x)*log(x))/(x^2 - 1) - (4*x^4
*exp(x)*log(x))/(x^2 - 1) + (2*x^3*exp(2*x)*log(x))/(x^2 - 1)

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sympy [B]  time = 0.96, size = 369, normalized size = 11.18 \begin {gather*} x^{4} + 18 x^{3} + 81 x^{2} + \frac {\left (x^{10} + 2 x^{9} \log {\relax (x )} + x^{8} \log {\relax (x )}^{2} - 4 x^{8} - 6 x^{7} \log {\relax (x )} - 2 x^{6} \log {\relax (x )}^{2} + 6 x^{6} + 6 x^{5} \log {\relax (x )} + x^{4} \log {\relax (x )}^{2} - 4 x^{4} - 2 x^{3} \log {\relax (x )} + x^{2}\right ) e^{2 x} + \left (- 2 x^{11} - 4 x^{10} \log {\relax (x )} - 18 x^{10} - 2 x^{9} \log {\relax (x )}^{2} - 36 x^{9} \log {\relax (x )} + 8 x^{9} - 18 x^{8} \log {\relax (x )}^{2} + 12 x^{8} \log {\relax (x )} + 72 x^{8} + 4 x^{7} \log {\relax (x )}^{2} + 108 x^{7} \log {\relax (x )} - 12 x^{7} + 36 x^{6} \log {\relax (x )}^{2} - 12 x^{6} \log {\relax (x )} - 108 x^{6} - 2 x^{5} \log {\relax (x )}^{2} - 108 x^{5} \log {\relax (x )} + 8 x^{5} - 18 x^{4} \log {\relax (x )}^{2} + 4 x^{4} \log {\relax (x )} + 72 x^{4} + 36 x^{3} \log {\relax (x )} - 2 x^{3} - 18 x^{2}\right ) e^{x}}{x^{8} - 4 x^{6} + 6 x^{4} - 4 x^{2} + 1} + 36 \log {\relax (x )} + \frac {\left (x^{6} + 18 x^{5} + 81 x^{4}\right ) \log {\relax (x )}^{2}}{x^{4} - 2 x^{2} + 1} + \frac {\left (2 x^{5} + 36 x^{4} + 162 x^{3} - 36 x^{2} + 36\right ) \log {\relax (x )}}{x^{2} - 1} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((2*x**6-2*x**4-4*x**3)*exp(x)**2+(-2*x**7-20*x**6+2*x**5+28*x**4+72*x**3)*exp(x)+2*x**7+18*x**6-6*
x**5-90*x**4-324*x**3)*ln(x)**2+((4*x**7+2*x**6-6*x**5-8*x**4+2*x**3+6*x**2)*exp(x)**2+(-4*x**8-44*x**7-32*x**
6+60*x**5+144*x**4-16*x**3-108*x**2)*exp(x)+6*x**8+74*x**7+182*x**6-56*x**5-674*x**4-18*x**3+486*x**2)*ln(x)+(
2*x**8+2*x**7-4*x**6-6*x**5+2*x**4+6*x**3-2*x)*exp(x)**2+(-2*x**9-24*x**8-34*x**7+36*x**6+110*x**5-110*x**3-12
*x**2+36*x)*exp(x)+4*x**9+56*x**8+186*x**7-4*x**6-546*x**5-160*x**4+518*x**3+108*x**2-162*x)/(x**6-3*x**4+3*x*
*2-1),x)

[Out]

x**4 + 18*x**3 + 81*x**2 + ((x**10 + 2*x**9*log(x) + x**8*log(x)**2 - 4*x**8 - 6*x**7*log(x) - 2*x**6*log(x)**
2 + 6*x**6 + 6*x**5*log(x) + x**4*log(x)**2 - 4*x**4 - 2*x**3*log(x) + x**2)*exp(2*x) + (-2*x**11 - 4*x**10*lo
g(x) - 18*x**10 - 2*x**9*log(x)**2 - 36*x**9*log(x) + 8*x**9 - 18*x**8*log(x)**2 + 12*x**8*log(x) + 72*x**8 +
4*x**7*log(x)**2 + 108*x**7*log(x) - 12*x**7 + 36*x**6*log(x)**2 - 12*x**6*log(x) - 108*x**6 - 2*x**5*log(x)**
2 - 108*x**5*log(x) + 8*x**5 - 18*x**4*log(x)**2 + 4*x**4*log(x) + 72*x**4 + 36*x**3*log(x) - 2*x**3 - 18*x**2
)*exp(x))/(x**8 - 4*x**6 + 6*x**4 - 4*x**2 + 1) + 36*log(x) + (x**6 + 18*x**5 + 81*x**4)*log(x)**2/(x**4 - 2*x
**2 + 1) + (2*x**5 + 36*x**4 + 162*x**3 - 36*x**2 + 36)*log(x)/(x**2 - 1)

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