3.88.16 \(\int \frac {(-30 x-24 x^2-6 x^3+e^{4 x} (-10 x-8 x^2-2 x^3)+(10 x+8 x^2+2 x^3) \log (x)) \log (\frac {-4+8 x+4 x^2}{2+x})+(4-6 x-8 x^2-2 x^3+e^{4 x} (-16 x+24 x^2+32 x^3+8 x^4)) \log ^2(\frac {-4+8 x+4 x^2}{2+x})}{54 x-81 x^2-108 x^3-27 x^4+e^{4 x} (54 x-81 x^2-108 x^3-27 x^4)+e^{8 x} (18 x-27 x^2-36 x^3-9 x^4)+e^{12 x} (2 x-3 x^2-4 x^3-x^4)+(-54 x+81 x^2+108 x^3+27 x^4+e^{8 x} (-6 x+9 x^2+12 x^3+3 x^4)+e^{4 x} (-36 x+54 x^2+72 x^3+18 x^4)) \log (x)+(18 x-27 x^2-36 x^3-9 x^4+e^{4 x} (6 x-9 x^2-12 x^3-3 x^4)) \log ^2(x)+(-2 x+3 x^2+4 x^3+x^4) \log ^3(x)} \, dx\)

Optimal. Leaf size=28 \[ \frac {\log ^2\left (4 \left (x-\frac {1}{2+x}\right )\right )}{\left (3+e^{4 x}-\log (x)\right )^2} \]

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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[((-30*x - 24*x^2 - 6*x^3 + E^(4*x)*(-10*x - 8*x^2 - 2*x^3) + (10*x + 8*x^2 + 2*x^3)*Log[x])*Log[(-4 + 8*x
+ 4*x^2)/(2 + x)] + (4 - 6*x - 8*x^2 - 2*x^3 + E^(4*x)*(-16*x + 24*x^2 + 32*x^3 + 8*x^4))*Log[(-4 + 8*x + 4*x^
2)/(2 + x)]^2)/(54*x - 81*x^2 - 108*x^3 - 27*x^4 + E^(4*x)*(54*x - 81*x^2 - 108*x^3 - 27*x^4) + E^(8*x)*(18*x
- 27*x^2 - 36*x^3 - 9*x^4) + E^(12*x)*(2*x - 3*x^2 - 4*x^3 - x^4) + (-54*x + 81*x^2 + 108*x^3 + 27*x^4 + E^(8*
x)*(-6*x + 9*x^2 + 12*x^3 + 3*x^4) + E^(4*x)*(-36*x + 54*x^2 + 72*x^3 + 18*x^4))*Log[x] + (18*x - 27*x^2 - 36*
x^3 - 9*x^4 + E^(4*x)*(6*x - 9*x^2 - 12*x^3 - 3*x^4))*Log[x]^2 + (-2*x + 3*x^2 + 4*x^3 + x^4)*Log[x]^3),x]

[Out]

$Aborted

Rubi steps

Aborted

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Mathematica [F]  time = 0.32, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\left (-30 x-24 x^2-6 x^3+e^{4 x} \left (-10 x-8 x^2-2 x^3\right )+\left (10 x+8 x^2+2 x^3\right ) \log (x)\right ) \log \left (\frac {-4+8 x+4 x^2}{2+x}\right )+\left (4-6 x-8 x^2-2 x^3+e^{4 x} \left (-16 x+24 x^2+32 x^3+8 x^4\right )\right ) \log ^2\left (\frac {-4+8 x+4 x^2}{2+x}\right )}{54 x-81 x^2-108 x^3-27 x^4+e^{4 x} \left (54 x-81 x^2-108 x^3-27 x^4\right )+e^{8 x} \left (18 x-27 x^2-36 x^3-9 x^4\right )+e^{12 x} \left (2 x-3 x^2-4 x^3-x^4\right )+\left (-54 x+81 x^2+108 x^3+27 x^4+e^{8 x} \left (-6 x+9 x^2+12 x^3+3 x^4\right )+e^{4 x} \left (-36 x+54 x^2+72 x^3+18 x^4\right )\right ) \log (x)+\left (18 x-27 x^2-36 x^3-9 x^4+e^{4 x} \left (6 x-9 x^2-12 x^3-3 x^4\right )\right ) \log ^2(x)+\left (-2 x+3 x^2+4 x^3+x^4\right ) \log ^3(x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[((-30*x - 24*x^2 - 6*x^3 + E^(4*x)*(-10*x - 8*x^2 - 2*x^3) + (10*x + 8*x^2 + 2*x^3)*Log[x])*Log[(-4
+ 8*x + 4*x^2)/(2 + x)] + (4 - 6*x - 8*x^2 - 2*x^3 + E^(4*x)*(-16*x + 24*x^2 + 32*x^3 + 8*x^4))*Log[(-4 + 8*x
+ 4*x^2)/(2 + x)]^2)/(54*x - 81*x^2 - 108*x^3 - 27*x^4 + E^(4*x)*(54*x - 81*x^2 - 108*x^3 - 27*x^4) + E^(8*x)*
(18*x - 27*x^2 - 36*x^3 - 9*x^4) + E^(12*x)*(2*x - 3*x^2 - 4*x^3 - x^4) + (-54*x + 81*x^2 + 108*x^3 + 27*x^4 +
E^(8*x)*(-6*x + 9*x^2 + 12*x^3 + 3*x^4) + E^(4*x)*(-36*x + 54*x^2 + 72*x^3 + 18*x^4))*Log[x] + (18*x - 27*x^2
- 36*x^3 - 9*x^4 + E^(4*x)*(6*x - 9*x^2 - 12*x^3 - 3*x^4))*Log[x]^2 + (-2*x + 3*x^2 + 4*x^3 + x^4)*Log[x]^3),
x]

[Out]

Integrate[((-30*x - 24*x^2 - 6*x^3 + E^(4*x)*(-10*x - 8*x^2 - 2*x^3) + (10*x + 8*x^2 + 2*x^3)*Log[x])*Log[(-4
+ 8*x + 4*x^2)/(2 + x)] + (4 - 6*x - 8*x^2 - 2*x^3 + E^(4*x)*(-16*x + 24*x^2 + 32*x^3 + 8*x^4))*Log[(-4 + 8*x
+ 4*x^2)/(2 + x)]^2)/(54*x - 81*x^2 - 108*x^3 - 27*x^4 + E^(4*x)*(54*x - 81*x^2 - 108*x^3 - 27*x^4) + E^(8*x)*
(18*x - 27*x^2 - 36*x^3 - 9*x^4) + E^(12*x)*(2*x - 3*x^2 - 4*x^3 - x^4) + (-54*x + 81*x^2 + 108*x^3 + 27*x^4 +
E^(8*x)*(-6*x + 9*x^2 + 12*x^3 + 3*x^4) + E^(4*x)*(-36*x + 54*x^2 + 72*x^3 + 18*x^4))*Log[x] + (18*x - 27*x^2
- 36*x^3 - 9*x^4 + E^(4*x)*(6*x - 9*x^2 - 12*x^3 - 3*x^4))*Log[x]^2 + (-2*x + 3*x^2 + 4*x^3 + x^4)*Log[x]^3),
x]

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fricas [A]  time = 0.76, size = 52, normalized size = 1.86 \begin {gather*} -\frac {\log \left (\frac {4 \, {\left (x^{2} + 2 \, x - 1\right )}}{x + 2}\right )^{2}}{2 \, {\left (e^{\left (4 \, x\right )} + 3\right )} \log \relax (x) - \log \relax (x)^{2} - e^{\left (8 \, x\right )} - 6 \, e^{\left (4 \, x\right )} - 9} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((8*x^4+32*x^3+24*x^2-16*x)*exp(4*x)-2*x^3-8*x^2-6*x+4)*log((4*x^2+8*x-4)/(2+x))^2+((2*x^3+8*x^2+10
*x)*log(x)+(-2*x^3-8*x^2-10*x)*exp(4*x)-6*x^3-24*x^2-30*x)*log((4*x^2+8*x-4)/(2+x)))/((x^4+4*x^3+3*x^2-2*x)*lo
g(x)^3+((-3*x^4-12*x^3-9*x^2+6*x)*exp(4*x)-9*x^4-36*x^3-27*x^2+18*x)*log(x)^2+((3*x^4+12*x^3+9*x^2-6*x)*exp(4*
x)^2+(18*x^4+72*x^3+54*x^2-36*x)*exp(4*x)+27*x^4+108*x^3+81*x^2-54*x)*log(x)+(-x^4-4*x^3-3*x^2+2*x)*exp(4*x)^3
+(-9*x^4-36*x^3-27*x^2+18*x)*exp(4*x)^2+(-27*x^4-108*x^3-81*x^2+54*x)*exp(4*x)-27*x^4-108*x^3-81*x^2+54*x),x,
algorithm="fricas")

[Out]

-log(4*(x^2 + 2*x - 1)/(x + 2))^2/(2*(e^(4*x) + 3)*log(x) - log(x)^2 - e^(8*x) - 6*e^(4*x) - 9)

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giac [B]  time = 0.91, size = 96, normalized size = 3.43 \begin {gather*} -\frac {4 \, \log \relax (2)^{2} + 4 \, \log \relax (2) \log \left (x^{2} + 2 \, x - 1\right ) + \log \left (x^{2} + 2 \, x - 1\right )^{2} - 4 \, \log \relax (2) \log \left (x + 2\right ) - 2 \, \log \left (x^{2} + 2 \, x - 1\right ) \log \left (x + 2\right ) + \log \left (x + 2\right )^{2}}{2 \, e^{\left (4 \, x\right )} \log \relax (x) - \log \relax (x)^{2} - e^{\left (8 \, x\right )} - 6 \, e^{\left (4 \, x\right )} + 6 \, \log \relax (x) - 9} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((8*x^4+32*x^3+24*x^2-16*x)*exp(4*x)-2*x^3-8*x^2-6*x+4)*log((4*x^2+8*x-4)/(2+x))^2+((2*x^3+8*x^2+10
*x)*log(x)+(-2*x^3-8*x^2-10*x)*exp(4*x)-6*x^3-24*x^2-30*x)*log((4*x^2+8*x-4)/(2+x)))/((x^4+4*x^3+3*x^2-2*x)*lo
g(x)^3+((-3*x^4-12*x^3-9*x^2+6*x)*exp(4*x)-9*x^4-36*x^3-27*x^2+18*x)*log(x)^2+((3*x^4+12*x^3+9*x^2-6*x)*exp(4*
x)^2+(18*x^4+72*x^3+54*x^2-36*x)*exp(4*x)+27*x^4+108*x^3+81*x^2-54*x)*log(x)+(-x^4-4*x^3-3*x^2+2*x)*exp(4*x)^3
+(-9*x^4-36*x^3-27*x^2+18*x)*exp(4*x)^2+(-27*x^4-108*x^3-81*x^2+54*x)*exp(4*x)-27*x^4-108*x^3-81*x^2+54*x),x,
algorithm="giac")

[Out]

-(4*log(2)^2 + 4*log(2)*log(x^2 + 2*x - 1) + log(x^2 + 2*x - 1)^2 - 4*log(2)*log(x + 2) - 2*log(x^2 + 2*x - 1)
*log(x + 2) + log(x + 2)^2)/(2*e^(4*x)*log(x) - log(x)^2 - e^(8*x) - 6*e^(4*x) + 6*log(x) - 9)

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maple [C]  time = 0.62, size = 870, normalized size = 31.07

method	result	size
risch	\(\frac {\ln \left (x^{2}+2 x -1\right )^{2}}{\left (3+{\mathrm e}^{4 x}-\ln \relax (x )\right )^{2}}+\frac {\left (i \pi \,\mathrm {csgn}\left (i \left (x^{2}+2 x -1\right )\right ) \mathrm {csgn}\left (\frac {i \left (x^{2}+2 x -1\right )}{2+x}\right )^{2}-i \pi \,\mathrm {csgn}\left (i \left (x^{2}+2 x -1\right )\right ) \mathrm {csgn}\left (\frac {i \left (x^{2}+2 x -1\right )}{2+x}\right ) \mathrm {csgn}\left (\frac {i}{2+x}\right )+i \pi \mathrm {csgn}\left (\frac {i \left (x^{2}+2 x -1\right )}{2+x}\right )^{2} \mathrm {csgn}\left (\frac {i}{2+x}\right )-i \pi \mathrm {csgn}\left (\frac {i \left (x^{2}+2 x -1\right )}{2+x}\right )^{3}+4 \ln \relax (2)-2 \ln \left (2+x \right )\right ) \ln \left (x^{2}+2 x -1\right )}{\left (3+{\mathrm e}^{4 x}-\ln \relax (x )\right )^{2}}+\frac {16 \ln \relax (2)^{2}+4 \ln \left (2+x \right )^{2}-\pi ^{2} \mathrm {csgn}\left (i \left (x^{2}+2 x -1\right )\right )^{2} \mathrm {csgn}\left (\frac {i \left (x^{2}+2 x -1\right )}{2+x}\right )^{2} \mathrm {csgn}\left (\frac {i}{2+x}\right )^{2}-16 \ln \relax (2) \ln \left (2+x \right )+4 i \ln \left (2+x \right ) \pi \,\mathrm {csgn}\left (i \left (x^{2}+2 x -1\right )\right ) \mathrm {csgn}\left (\frac {i \left (x^{2}+2 x -1\right )}{2+x}\right ) \mathrm {csgn}\left (\frac {i}{2+x}\right )+8 i \ln \relax (2) \pi \,\mathrm {csgn}\left (i \left (x^{2}+2 x -1\right )\right ) \mathrm {csgn}\left (\frac {i \left (x^{2}+2 x -1\right )}{2+x}\right )^{2}+2 \pi ^{2} \mathrm {csgn}\left (i \left (x^{2}+2 x -1\right )\right ) \mathrm {csgn}\left (\frac {i \left (x^{2}+2 x -1\right )}{2+x}\right )^{3} \mathrm {csgn}\left (\frac {i}{2+x}\right )^{2}+2 \pi ^{2} \mathrm {csgn}\left (i \left (x^{2}+2 x -1\right )\right )^{2} \mathrm {csgn}\left (\frac {i \left (x^{2}+2 x -1\right )}{2+x}\right )^{3} \mathrm {csgn}\left (\frac {i}{2+x}\right )-4 \pi ^{2} \mathrm {csgn}\left (i \left (x^{2}+2 x -1\right )\right ) \mathrm {csgn}\left (\frac {i \left (x^{2}+2 x -1\right )}{2+x}\right )^{4} \mathrm {csgn}\left (\frac {i}{2+x}\right )-8 i \ln \relax (2) \pi \mathrm {csgn}\left (\frac {i \left (x^{2}+2 x -1\right )}{2+x}\right )^{3}+8 i \ln \relax (2) \pi \mathrm {csgn}\left (\frac {i \left (x^{2}+2 x -1\right )}{2+x}\right )^{2} \mathrm {csgn}\left (\frac {i}{2+x}\right )-8 i \ln \relax (2) \pi \,\mathrm {csgn}\left (i \left (x^{2}+2 x -1\right )\right ) \mathrm {csgn}\left (\frac {i \left (x^{2}+2 x -1\right )}{2+x}\right ) \mathrm {csgn}\left (\frac {i}{2+x}\right )-4 i \ln \left (2+x \right ) \pi \,\mathrm {csgn}\left (i \left (x^{2}+2 x -1\right )\right ) \mathrm {csgn}\left (\frac {i \left (x^{2}+2 x -1\right )}{2+x}\right )^{2}+4 i \ln \left (2+x \right ) \pi \mathrm {csgn}\left (\frac {i \left (x^{2}+2 x -1\right )}{2+x}\right )^{3}-4 i \ln \left (2+x \right ) \pi \mathrm {csgn}\left (\frac {i \left (x^{2}+2 x -1\right )}{2+x}\right )^{2} \mathrm {csgn}\left (\frac {i}{2+x}\right )+2 \pi ^{2} \mathrm {csgn}\left (\frac {i \left (x^{2}+2 x -1\right )}{2+x}\right )^{5} \mathrm {csgn}\left (\frac {i}{2+x}\right )-\pi ^{2} \mathrm {csgn}\left (\frac {i \left (x^{2}+2 x -1\right )}{2+x}\right )^{6}-\pi ^{2} \mathrm {csgn}\left (\frac {i \left (x^{2}+2 x -1\right )}{2+x}\right )^{4} \mathrm {csgn}\left (\frac {i}{2+x}\right )^{2}-\pi ^{2} \mathrm {csgn}\left (i \left (x^{2}+2 x -1\right )\right )^{2} \mathrm {csgn}\left (\frac {i \left (x^{2}+2 x -1\right )}{2+x}\right )^{4}+2 \pi ^{2} \mathrm {csgn}\left (i \left (x^{2}+2 x -1\right )\right ) \mathrm {csgn}\left (\frac {i \left (x^{2}+2 x -1\right )}{2+x}\right )^{5}}{4 \left (3+{\mathrm e}^{4 x}-\ln \relax (x )\right )^{2}}\)	\(870\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((8*x^4+32*x^3+24*x^2-16*x)*exp(4*x)-2*x^3-8*x^2-6*x+4)*ln((4*x^2+8*x-4)/(2+x))^2+((2*x^3+8*x^2+10*x)*ln(
x)+(-2*x^3-8*x^2-10*x)*exp(4*x)-6*x^3-24*x^2-30*x)*ln((4*x^2+8*x-4)/(2+x)))/((x^4+4*x^3+3*x^2-2*x)*ln(x)^3+((-
3*x^4-12*x^3-9*x^2+6*x)*exp(4*x)-9*x^4-36*x^3-27*x^2+18*x)*ln(x)^2+((3*x^4+12*x^3+9*x^2-6*x)*exp(4*x)^2+(18*x^
4+72*x^3+54*x^2-36*x)*exp(4*x)+27*x^4+108*x^3+81*x^2-54*x)*ln(x)+(-x^4-4*x^3-3*x^2+2*x)*exp(4*x)^3+(-9*x^4-36*
x^3-27*x^2+18*x)*exp(4*x)^2+(-27*x^4-108*x^3-81*x^2+54*x)*exp(4*x)-27*x^4-108*x^3-81*x^2+54*x),x,method=_RETUR
NVERBOSE)

[Out]

1/(3+exp(4*x)-ln(x))^2*ln(x^2+2*x-1)^2+(I*Pi*csgn(I*(x^2+2*x-1))*csgn(I/(2+x)*(x^2+2*x-1))^2-I*Pi*csgn(I*(x^2+
2*x-1))*csgn(I/(2+x)*(x^2+2*x-1))*csgn(I/(2+x))+I*Pi*csgn(I/(2+x)*(x^2+2*x-1))^2*csgn(I/(2+x))-I*Pi*csgn(I/(2+
x)*(x^2+2*x-1))^3+4*ln(2)-2*ln(2+x))/(3+exp(4*x)-ln(x))^2*ln(x^2+2*x-1)+1/4*(16*ln(2)^2+4*ln(2+x)^2-Pi^2*csgn(
I*(x^2+2*x-1))^2*csgn(I/(2+x)*(x^2+2*x-1))^2*csgn(I/(2+x))^2-16*ln(2)*ln(2+x)+4*I*ln(2+x)*Pi*csgn(I*(x^2+2*x-1
))*csgn(I/(2+x)*(x^2+2*x-1))*csgn(I/(2+x))+8*I*ln(2)*Pi*csgn(I*(x^2+2*x-1))*csgn(I/(2+x)*(x^2+2*x-1))^2+2*Pi^2
*csgn(I*(x^2+2*x-1))*csgn(I/(2+x)*(x^2+2*x-1))^3*csgn(I/(2+x))^2+2*Pi^2*csgn(I*(x^2+2*x-1))^2*csgn(I/(2+x)*(x^
2+2*x-1))^3*csgn(I/(2+x))-4*Pi^2*csgn(I*(x^2+2*x-1))*csgn(I/(2+x)*(x^2+2*x-1))^4*csgn(I/(2+x))-8*I*ln(2)*Pi*cs
gn(I/(2+x)*(x^2+2*x-1))^3+8*I*ln(2)*Pi*csgn(I/(2+x)*(x^2+2*x-1))^2*csgn(I/(2+x))-8*I*ln(2)*Pi*csgn(I*(x^2+2*x-
1))*csgn(I/(2+x)*(x^2+2*x-1))*csgn(I/(2+x))-4*I*ln(2+x)*Pi*csgn(I*(x^2+2*x-1))*csgn(I/(2+x)*(x^2+2*x-1))^2+4*I
*ln(2+x)*Pi*csgn(I/(2+x)*(x^2+2*x-1))^3-4*I*ln(2+x)*Pi*csgn(I/(2+x)*(x^2+2*x-1))^2*csgn(I/(2+x))+2*Pi^2*csgn(I
/(2+x)*(x^2+2*x-1))^5*csgn(I/(2+x))-Pi^2*csgn(I/(2+x)*(x^2+2*x-1))^6-Pi^2*csgn(I/(2+x)*(x^2+2*x-1))^4*csgn(I/(
2+x))^2-Pi^2*csgn(I*(x^2+2*x-1))^2*csgn(I/(2+x)*(x^2+2*x-1))^4+2*Pi^2*csgn(I*(x^2+2*x-1))*csgn(I/(2+x)*(x^2+2*
x-1))^5)/(3+exp(4*x)-ln(x))^2

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maxima [B]  time = 1.21, size = 86, normalized size = 3.07 \begin {gather*} -\frac {4 \, \log \relax (2)^{2} + 2 \, {\left (2 \, \log \relax (2) - \log \left (x + 2\right )\right )} \log \left (x^{2} + 2 \, x - 1\right ) + \log \left (x^{2} + 2 \, x - 1\right )^{2} - 4 \, \log \relax (2) \log \left (x + 2\right ) + \log \left (x + 2\right )^{2}}{2 \, {\left (\log \relax (x) - 3\right )} e^{\left (4 \, x\right )} - \log \relax (x)^{2} - e^{\left (8 \, x\right )} + 6 \, \log \relax (x) - 9} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((8*x^4+32*x^3+24*x^2-16*x)*exp(4*x)-2*x^3-8*x^2-6*x+4)*log((4*x^2+8*x-4)/(2+x))^2+((2*x^3+8*x^2+10
*x)*log(x)+(-2*x^3-8*x^2-10*x)*exp(4*x)-6*x^3-24*x^2-30*x)*log((4*x^2+8*x-4)/(2+x)))/((x^4+4*x^3+3*x^2-2*x)*lo
g(x)^3+((-3*x^4-12*x^3-9*x^2+6*x)*exp(4*x)-9*x^4-36*x^3-27*x^2+18*x)*log(x)^2+((3*x^4+12*x^3+9*x^2-6*x)*exp(4*
x)^2+(18*x^4+72*x^3+54*x^2-36*x)*exp(4*x)+27*x^4+108*x^3+81*x^2-54*x)*log(x)+(-x^4-4*x^3-3*x^2+2*x)*exp(4*x)^3
+(-9*x^4-36*x^3-27*x^2+18*x)*exp(4*x)^2+(-27*x^4-108*x^3-81*x^2+54*x)*exp(4*x)-27*x^4-108*x^3-81*x^2+54*x),x,
algorithm="maxima")

[Out]

-(4*log(2)^2 + 2*(2*log(2) - log(x + 2))*log(x^2 + 2*x - 1) + log(x^2 + 2*x - 1)^2 - 4*log(2)*log(x + 2) + log
(x + 2)^2)/(2*(log(x) - 3)*e^(4*x) - log(x)^2 - e^(8*x) + 6*log(x) - 9)

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mupad [B]  time = 5.87, size = 50, normalized size = 1.79 \begin {gather*} \frac {{\ln \left (\frac {4\,x^2+8\,x-4}{x+2}\right )}^2}{{\ln \relax (x)}^2+\left (-2\,{\mathrm {e}}^{4\,x}-6\right )\,\ln \relax (x)+6\,{\mathrm {e}}^{4\,x}+{\mathrm {e}}^{8\,x}+9} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((log((8*x + 4*x^2 - 4)/(x + 2))^2*(6*x - exp(4*x)*(24*x^2 - 16*x + 32*x^3 + 8*x^4) + 8*x^2 + 2*x^3 - 4) +
log((8*x + 4*x^2 - 4)/(x + 2))*(30*x + exp(4*x)*(10*x + 8*x^2 + 2*x^3) + 24*x^2 + 6*x^3 - log(x)*(10*x + 8*x^2
+ 2*x^3)))/(exp(12*x)*(3*x^2 - 2*x + 4*x^3 + x^4) - log(x)*(exp(8*x)*(9*x^2 - 6*x + 12*x^3 + 3*x^4) - 54*x +
exp(4*x)*(54*x^2 - 36*x + 72*x^3 + 18*x^4) + 81*x^2 + 108*x^3 + 27*x^4) - 54*x - log(x)^3*(3*x^2 - 2*x + 4*x^3
+ x^4) + exp(8*x)*(27*x^2 - 18*x + 36*x^3 + 9*x^4) + exp(4*x)*(81*x^2 - 54*x + 108*x^3 + 27*x^4) + 81*x^2 + 1
08*x^3 + 27*x^4 + log(x)^2*(exp(4*x)*(9*x^2 - 6*x + 12*x^3 + 3*x^4) - 18*x + 27*x^2 + 36*x^3 + 9*x^4)),x)

[Out]

log((8*x + 4*x^2 - 4)/(x + 2))^2/(6*exp(4*x) + exp(8*x) - log(x)*(2*exp(4*x) + 6) + log(x)^2 + 9)

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sympy [A]  time = 0.76, size = 44, normalized size = 1.57 \begin {gather*} \frac {\log {\left (\frac {4 x^{2} + 8 x - 4}{x + 2} \right )}^{2}}{\left (6 - 2 \log {\relax (x )}\right ) e^{4 x} + e^{8 x} + \log {\relax (x )}^{2} - 6 \log {\relax (x )} + 9} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((8*x**4+32*x**3+24*x**2-16*x)*exp(4*x)-2*x**3-8*x**2-6*x+4)*ln((4*x**2+8*x-4)/(2+x))**2+((2*x**3+8
*x**2+10*x)*ln(x)+(-2*x**3-8*x**2-10*x)*exp(4*x)-6*x**3-24*x**2-30*x)*ln((4*x**2+8*x-4)/(2+x)))/((x**4+4*x**3+
3*x**2-2*x)*ln(x)**3+((-3*x**4-12*x**3-9*x**2+6*x)*exp(4*x)-9*x**4-36*x**3-27*x**2+18*x)*ln(x)**2+((3*x**4+12*
x**3+9*x**2-6*x)*exp(4*x)**2+(18*x**4+72*x**3+54*x**2-36*x)*exp(4*x)+27*x**4+108*x**3+81*x**2-54*x)*ln(x)+(-x*
*4-4*x**3-3*x**2+2*x)*exp(4*x)**3+(-9*x**4-36*x**3-27*x**2+18*x)*exp(4*x)**2+(-27*x**4-108*x**3-81*x**2+54*x)*
exp(4*x)-27*x**4-108*x**3-81*x**2+54*x),x)

[Out]

log((4*x**2 + 8*x - 4)/(x + 2))**2/((6 - 2*log(x))*exp(4*x) + exp(8*x) + log(x)**2 - 6*log(x) + 9)

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