3.20.86 \(\int \frac {-8 x^2+2 x^3+e^{2 e^{2 x}+2 x} (-16 x+4 x^2)+e^x (-48 x-46 x^2+6 x^3+2 x^4)+e^{2 x} (-40-248 x-28 x^2+14 x^3+2 x^4)+(e^{2 x} (8+88 x-6 x^2-4 x^3)+e^x (8 x+6 x^2-2 x^3)) \log (\frac {-12+3 x}{x})+e^{2 x} (-8 x+2 x^2) \log ^2(\frac {-12+3 x}{x})+e^{e^{2 x}} (-8 x+2 x^2+e^x (-8-48 x+4 x^2+2 x^3)+e^{2 x} (-16 x^2+4 x^3)+e^{3 x} (-80 x+4 x^2+4 x^3)+(e^{3 x} (16 x-4 x^2)+e^x (8 x-2 x^2)) \log (\frac {-12+3 x}{x}))}{-4 x+x^2} \, dx\)

Optimal. Leaf size=29 \[ \left (e^{e^{2 x}}+x+e^x \left (5+x-\log \left (\frac {3 (-4+x)}{x}\right )\right )\right )^2 \]

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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[(-8*x^2 + 2*x^3 + E^(2*E^(2*x) + 2*x)*(-16*x + 4*x^2) + E^x*(-48*x - 46*x^2 + 6*x^3 + 2*x^4) + E^(2*x)*(-4
0 - 248*x - 28*x^2 + 14*x^3 + 2*x^4) + (E^(2*x)*(8 + 88*x - 6*x^2 - 4*x^3) + E^x*(8*x + 6*x^2 - 2*x^3))*Log[(-
12 + 3*x)/x] + E^(2*x)*(-8*x + 2*x^2)*Log[(-12 + 3*x)/x]^2 + E^E^(2*x)*(-8*x + 2*x^2 + E^x*(-8 - 48*x + 4*x^2
+ 2*x^3) + E^(2*x)*(-16*x^2 + 4*x^3) + E^(3*x)*(-80*x + 4*x^2 + 4*x^3) + (E^(3*x)*(16*x - 4*x^2) + E^x*(8*x -
2*x^2))*Log[(-12 + 3*x)/x]))/(-4*x + x^2),x]

[Out]

$Aborted

Rubi steps

Aborted

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Mathematica [A]  time = 0.32, size = 32, normalized size = 1.10 \begin {gather*} \left (e^{e^{2 x}}+x+e^x (5+x)-e^x \log \left (\frac {3 (-4+x)}{x}\right )\right )^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-8*x^2 + 2*x^3 + E^(2*E^(2*x) + 2*x)*(-16*x + 4*x^2) + E^x*(-48*x - 46*x^2 + 6*x^3 + 2*x^4) + E^(2*
x)*(-40 - 248*x - 28*x^2 + 14*x^3 + 2*x^4) + (E^(2*x)*(8 + 88*x - 6*x^2 - 4*x^3) + E^x*(8*x + 6*x^2 - 2*x^3))*
Log[(-12 + 3*x)/x] + E^(2*x)*(-8*x + 2*x^2)*Log[(-12 + 3*x)/x]^2 + E^E^(2*x)*(-8*x + 2*x^2 + E^x*(-8 - 48*x +
4*x^2 + 2*x^3) + E^(2*x)*(-16*x^2 + 4*x^3) + E^(3*x)*(-80*x + 4*x^2 + 4*x^3) + (E^(3*x)*(16*x - 4*x^2) + E^x*(
8*x - 2*x^2))*Log[(-12 + 3*x)/x]))/(-4*x + x^2),x]

[Out]

(E^E^(2*x) + x + E^x*(5 + x) - E^x*Log[(3*(-4 + x))/x])^2

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fricas [B]  time = 0.72, size = 103, normalized size = 3.55 \begin {gather*} e^{\left (2 \, x\right )} \log \left (\frac {3 \, {\left (x - 4\right )}}{x}\right )^{2} + x^{2} + {\left (x^{2} + 10 \, x + 25\right )} e^{\left (2 \, x\right )} + 2 \, {\left (x^{2} + 5 \, x\right )} e^{x} + 2 \, {\left ({\left (x + 5\right )} e^{x} - e^{x} \log \left (\frac {3 \, {\left (x - 4\right )}}{x}\right ) + x\right )} e^{\left (e^{\left (2 \, x\right )}\right )} - 2 \, {\left ({\left (x + 5\right )} e^{\left (2 \, x\right )} + x e^{x}\right )} \log \left (\frac {3 \, {\left (x - 4\right )}}{x}\right ) + e^{\left (2 \, e^{\left (2 \, x\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*x^2-16*x)*exp(x)^2*exp(exp(x)^2)^2+(((-4*x^2+16*x)*exp(x)^3+(-2*x^2+8*x)*exp(x))*log((3*x-12)/x)
+(4*x^3+4*x^2-80*x)*exp(x)^3+(4*x^3-16*x^2)*exp(x)^2+(2*x^3+4*x^2-48*x-8)*exp(x)+2*x^2-8*x)*exp(exp(x)^2)+(2*x
^2-8*x)*exp(x)^2*log((3*x-12)/x)^2+((-4*x^3-6*x^2+88*x+8)*exp(x)^2+(-2*x^3+6*x^2+8*x)*exp(x))*log((3*x-12)/x)+
(2*x^4+14*x^3-28*x^2-248*x-40)*exp(x)^2+(2*x^4+6*x^3-46*x^2-48*x)*exp(x)+2*x^3-8*x^2)/(x^2-4*x),x, algorithm="
fricas")

[Out]

e^(2*x)*log(3*(x - 4)/x)^2 + x^2 + (x^2 + 10*x + 25)*e^(2*x) + 2*(x^2 + 5*x)*e^x + 2*((x + 5)*e^x - e^x*log(3*
(x - 4)/x) + x)*e^(e^(2*x)) - 2*((x + 5)*e^(2*x) + x*e^x)*log(3*(x - 4)/x) + e^(2*e^(2*x))

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {2 \, {\left ({\left (x^{2} - 4 \, x\right )} e^{\left (2 \, x\right )} \log \left (\frac {3 \, {\left (x - 4\right )}}{x}\right )^{2} + x^{3} - 4 \, x^{2} + {\left (x^{4} + 7 \, x^{3} - 14 \, x^{2} - 124 \, x - 20\right )} e^{\left (2 \, x\right )} + 2 \, {\left (x^{2} - 4 \, x\right )} e^{\left (2 \, x + 2 \, e^{\left (2 \, x\right )}\right )} + {\left (x^{4} + 3 \, x^{3} - 23 \, x^{2} - 24 \, x\right )} e^{x} + {\left (x^{2} + 2 \, {\left (x^{3} + x^{2} - 20 \, x\right )} e^{\left (3 \, x\right )} + 2 \, {\left (x^{3} - 4 \, x^{2}\right )} e^{\left (2 \, x\right )} + {\left (x^{3} + 2 \, x^{2} - 24 \, x - 4\right )} e^{x} - {\left (2 \, {\left (x^{2} - 4 \, x\right )} e^{\left (3 \, x\right )} + {\left (x^{2} - 4 \, x\right )} e^{x}\right )} \log \left (\frac {3 \, {\left (x - 4\right )}}{x}\right ) - 4 \, x\right )} e^{\left (e^{\left (2 \, x\right )}\right )} - {\left ({\left (2 \, x^{3} + 3 \, x^{2} - 44 \, x - 4\right )} e^{\left (2 \, x\right )} + {\left (x^{3} - 3 \, x^{2} - 4 \, x\right )} e^{x}\right )} \log \left (\frac {3 \, {\left (x - 4\right )}}{x}\right )\right )}}{x^{2} - 4 \, x}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*x^2-16*x)*exp(x)^2*exp(exp(x)^2)^2+(((-4*x^2+16*x)*exp(x)^3+(-2*x^2+8*x)*exp(x))*log((3*x-12)/x)
+(4*x^3+4*x^2-80*x)*exp(x)^3+(4*x^3-16*x^2)*exp(x)^2+(2*x^3+4*x^2-48*x-8)*exp(x)+2*x^2-8*x)*exp(exp(x)^2)+(2*x
^2-8*x)*exp(x)^2*log((3*x-12)/x)^2+((-4*x^3-6*x^2+88*x+8)*exp(x)^2+(-2*x^3+6*x^2+8*x)*exp(x))*log((3*x-12)/x)+
(2*x^4+14*x^3-28*x^2-248*x-40)*exp(x)^2+(2*x^4+6*x^3-46*x^2-48*x)*exp(x)+2*x^3-8*x^2)/(x^2-4*x),x, algorithm="
giac")

[Out]

integrate(2*((x^2 - 4*x)*e^(2*x)*log(3*(x - 4)/x)^2 + x^3 - 4*x^2 + (x^4 + 7*x^3 - 14*x^2 - 124*x - 20)*e^(2*x
) + 2*(x^2 - 4*x)*e^(2*x + 2*e^(2*x)) + (x^4 + 3*x^3 - 23*x^2 - 24*x)*e^x + (x^2 + 2*(x^3 + x^2 - 20*x)*e^(3*x
) + 2*(x^3 - 4*x^2)*e^(2*x) + (x^3 + 2*x^2 - 24*x - 4)*e^x - (2*(x^2 - 4*x)*e^(3*x) + (x^2 - 4*x)*e^x)*log(3*(
x - 4)/x) - 4*x)*e^(e^(2*x)) - ((2*x^3 + 3*x^2 - 44*x - 4)*e^(2*x) + (x^3 - 3*x^2 - 4*x)*e^x)*log(3*(x - 4)/x)
)/(x^2 - 4*x), x)

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maple [C]  time = 0.65, size = 1246, normalized size = 42.97

method	result	size
risch	\(i \pi x \mathrm {csgn}\left (\frac {i \left (x -4\right )}{x}\right )^{3} {\mathrm e}^{2 x}+i \pi x \mathrm {csgn}\left (\frac {i \left (x -4\right )}{x}\right )^{3} {\mathrm e}^{x}+\frac {{\mathrm e}^{2 x} \pi ^{2} \mathrm {csgn}\left (\frac {i}{x}\right ) \mathrm {csgn}\left (i \left (x -4\right )\right )^{2} \mathrm {csgn}\left (\frac {i \left (x -4\right )}{x}\right )^{3}}{2}-{\mathrm e}^{2 x} \pi ^{2} \mathrm {csgn}\left (\frac {i}{x}\right ) \mathrm {csgn}\left (i \left (x -4\right )\right ) \mathrm {csgn}\left (\frac {i \left (x -4\right )}{x}\right )^{4}-\frac {{\mathrm e}^{2 x} \pi ^{2} \mathrm {csgn}\left (\frac {i}{x}\right )^{2} \mathrm {csgn}\left (i \left (x -4\right )\right )^{2} \mathrm {csgn}\left (\frac {i \left (x -4\right )}{x}\right )^{2}}{4}-\frac {{\mathrm e}^{2 x} \pi ^{2} \mathrm {csgn}\left (\frac {i \left (x -4\right )}{x}\right )^{6}}{4}+2 x \,{\mathrm e}^{x} \ln \relax (x )+25 \,{\mathrm e}^{2 x}+x^{2}+{\mathrm e}^{2 x} x^{2}+10 x \,{\mathrm e}^{2 x}+2 \,{\mathrm e}^{x} x^{2}+10 \,{\mathrm e}^{x} x -\frac {{\mathrm e}^{2 x} \pi ^{2} \mathrm {csgn}\left (\frac {i}{x}\right )^{2} \mathrm {csgn}\left (\frac {i \left (x -4\right )}{x}\right )^{4}}{4}+\frac {{\mathrm e}^{2 x} \pi ^{2} \mathrm {csgn}\left (\frac {i}{x}\right ) \mathrm {csgn}\left (\frac {i \left (x -4\right )}{x}\right )^{5}}{2}-\frac {{\mathrm e}^{2 x} \pi ^{2} \mathrm {csgn}\left (i \left (x -4\right )\right )^{2} \mathrm {csgn}\left (\frac {i \left (x -4\right )}{x}\right )^{4}}{4}+\frac {{\mathrm e}^{2 x} \pi ^{2} \mathrm {csgn}\left (i \left (x -4\right )\right ) \mathrm {csgn}\left (\frac {i \left (x -4\right )}{x}\right )^{5}}{2}+5 i \pi \mathrm {csgn}\left (\frac {i \left (x -4\right )}{x}\right )^{3} {\mathrm e}^{2 x}+\ln \relax (x )^{2} {\mathrm e}^{2 x}-2 x \ln \relax (3) {\mathrm e}^{x}-10 \ln \relax (3) {\mathrm e}^{2 x}+\left (2 x +i \pi \,\mathrm {csgn}\left (\frac {i}{x}\right ) \mathrm {csgn}\left (i \left (x -4\right )\right ) \mathrm {csgn}\left (\frac {i \left (x -4\right )}{x}\right ) {\mathrm e}^{x}-i \pi \,\mathrm {csgn}\left (\frac {i}{x}\right ) \mathrm {csgn}\left (\frac {i \left (x -4\right )}{x}\right )^{2} {\mathrm e}^{x}-i \pi \,\mathrm {csgn}\left (i \left (x -4\right )\right ) \mathrm {csgn}\left (\frac {i \left (x -4\right )}{x}\right )^{2} {\mathrm e}^{x}+i \pi \mathrm {csgn}\left (\frac {i \left (x -4\right )}{x}\right )^{3} {\mathrm e}^{x}-2 \ln \relax (3) {\mathrm e}^{x}+2 \,{\mathrm e}^{x} x +10 \,{\mathrm e}^{x}+2 \,{\mathrm e}^{x} \ln \relax (x )-2 \,{\mathrm e}^{x} \ln \left (x -4\right )\right ) {\mathrm e}^{{\mathrm e}^{2 x}}+\left (-2 \,{\mathrm e}^{2 x} \ln \relax (x )-i \pi \,\mathrm {csgn}\left (\frac {i}{x}\right ) \mathrm {csgn}\left (i \left (x -4\right )\right ) \mathrm {csgn}\left (\frac {i \left (x -4\right )}{x}\right ) {\mathrm e}^{2 x}+i \pi \,\mathrm {csgn}\left (\frac {i}{x}\right ) \mathrm {csgn}\left (\frac {i \left (x -4\right )}{x}\right )^{2} {\mathrm e}^{2 x}+i \pi \,\mathrm {csgn}\left (i \left (x -4\right )\right ) \mathrm {csgn}\left (\frac {i \left (x -4\right )}{x}\right )^{2} {\mathrm e}^{2 x}-i \pi \mathrm {csgn}\left (\frac {i \left (x -4\right )}{x}\right )^{3} {\mathrm e}^{2 x}+2 \ln \relax (3) {\mathrm e}^{2 x}-2 x \,{\mathrm e}^{2 x}-2 \,{\mathrm e}^{x} x -10 \,{\mathrm e}^{2 x}\right ) \ln \left (x -4\right )+{\mathrm e}^{2 \,{\mathrm e}^{2 x}}+i {\mathrm e}^{2 x} \pi \ln \relax (3) \mathrm {csgn}\left (i \left (x -4\right )\right ) \mathrm {csgn}\left (\frac {i \left (x -4\right )}{x}\right )^{2}-i \pi \,\mathrm {csgn}\left (\frac {i}{x}\right ) \mathrm {csgn}\left (\frac {i \left (x -4\right )}{x}\right )^{2} {\mathrm e}^{2 x} \ln \relax (x )-i \pi \,\mathrm {csgn}\left (i \left (x -4\right )\right ) \mathrm {csgn}\left (\frac {i \left (x -4\right )}{x}\right )^{2} {\mathrm e}^{2 x} \ln \relax (x )-i \pi x \,\mathrm {csgn}\left (\frac {i}{x}\right ) \mathrm {csgn}\left (\frac {i \left (x -4\right )}{x}\right )^{2} {\mathrm e}^{2 x}-i \pi x \,\mathrm {csgn}\left (i \left (x -4\right )\right ) \mathrm {csgn}\left (\frac {i \left (x -4\right )}{x}\right )^{2} {\mathrm e}^{2 x}-i \pi x \,\mathrm {csgn}\left (\frac {i}{x}\right ) \mathrm {csgn}\left (\frac {i \left (x -4\right )}{x}\right )^{2} {\mathrm e}^{x}-i \pi x \,\mathrm {csgn}\left (i \left (x -4\right )\right ) \mathrm {csgn}\left (\frac {i \left (x -4\right )}{x}\right )^{2} {\mathrm e}^{x}+\ln \relax (3)^{2} {\mathrm e}^{2 x}+10 \,{\mathrm e}^{2 x} \ln \relax (x )+{\mathrm e}^{2 x} \ln \left (x -4\right )^{2}+5 i \pi \,\mathrm {csgn}\left (\frac {i}{x}\right ) \mathrm {csgn}\left (i \left (x -4\right )\right ) \mathrm {csgn}\left (\frac {i \left (x -4\right )}{x}\right ) {\mathrm e}^{2 x}+i {\mathrm e}^{2 x} \pi \ln \relax (3) \mathrm {csgn}\left (\frac {i}{x}\right ) \mathrm {csgn}\left (\frac {i \left (x -4\right )}{x}\right )^{2}-2 \ln \relax (3) {\mathrm e}^{2 x} x -i {\mathrm e}^{2 x} \pi \ln \relax (3) \mathrm {csgn}\left (\frac {i \left (x -4\right )}{x}\right )^{3}+\frac {{\mathrm e}^{2 x} \pi ^{2} \mathrm {csgn}\left (\frac {i}{x}\right )^{2} \mathrm {csgn}\left (i \left (x -4\right )\right ) \mathrm {csgn}\left (\frac {i \left (x -4\right )}{x}\right )^{3}}{2}-5 i \pi \,\mathrm {csgn}\left (\frac {i}{x}\right ) \mathrm {csgn}\left (\frac {i \left (x -4\right )}{x}\right )^{2} {\mathrm e}^{2 x}-5 i \pi \,\mathrm {csgn}\left (i \left (x -4\right )\right ) \mathrm {csgn}\left (\frac {i \left (x -4\right )}{x}\right )^{2} {\mathrm e}^{2 x}+i \pi \mathrm {csgn}\left (\frac {i \left (x -4\right )}{x}\right )^{3} {\mathrm e}^{2 x} \ln \relax (x )-2 \ln \relax (3) {\mathrm e}^{2 x} \ln \relax (x )+2 x \,{\mathrm e}^{2 x} \ln \relax (x )-i {\mathrm e}^{2 x} \pi \ln \relax (3) \mathrm {csgn}\left (\frac {i}{x}\right ) \mathrm {csgn}\left (i \left (x -4\right )\right ) \mathrm {csgn}\left (\frac {i \left (x -4\right )}{x}\right )+i \pi x \,\mathrm {csgn}\left (\frac {i}{x}\right ) \mathrm {csgn}\left (i \left (x -4\right )\right ) \mathrm {csgn}\left (\frac {i \left (x -4\right )}{x}\right ) {\mathrm e}^{x}+i \pi x \,\mathrm {csgn}\left (\frac {i}{x}\right ) \mathrm {csgn}\left (i \left (x -4\right )\right ) \mathrm {csgn}\left (\frac {i \left (x -4\right )}{x}\right ) {\mathrm e}^{2 x}+i \pi \,\mathrm {csgn}\left (\frac {i}{x}\right ) \mathrm {csgn}\left (i \left (x -4\right )\right ) \mathrm {csgn}\left (\frac {i \left (x -4\right )}{x}\right ) {\mathrm e}^{2 x} \ln \relax (x )\)	\(1246\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((4*x^2-16*x)*exp(x)^2*exp(exp(x)^2)^2+(((-4*x^2+16*x)*exp(x)^3+(-2*x^2+8*x)*exp(x))*ln((3*x-12)/x)+(4*x^3
+4*x^2-80*x)*exp(x)^3+(4*x^3-16*x^2)*exp(x)^2+(2*x^3+4*x^2-48*x-8)*exp(x)+2*x^2-8*x)*exp(exp(x)^2)+(2*x^2-8*x)
*exp(x)^2*ln((3*x-12)/x)^2+((-4*x^3-6*x^2+88*x+8)*exp(x)^2+(-2*x^3+6*x^2+8*x)*exp(x))*ln((3*x-12)/x)+(2*x^4+14
*x^3-28*x^2-248*x-40)*exp(x)^2+(2*x^4+6*x^3-46*x^2-48*x)*exp(x)+2*x^3-8*x^2)/(x^2-4*x),x,method=_RETURNVERBOSE
)

[Out]

-I*exp(2*x)*Pi*ln(3)*csgn(I/x*(x-4))^3-I*exp(2*x)*Pi*ln(3)*csgn(I/x)*csgn(I*(x-4))*csgn(I/x*(x-4))+1/2*exp(2*x
)*Pi^2*csgn(I/x)^2*csgn(I*(x-4))*csgn(I/x*(x-4))^3+I*Pi*x*csgn(I/x)*csgn(I*(x-4))*csgn(I/x*(x-4))*exp(x)+2*x*e
xp(x)*ln(x)+25*exp(2*x)+x^2+exp(2*x)*x^2+10*x*exp(2*x)+2*exp(x)*x^2+10*exp(x)*x-1/4*exp(2*x)*Pi^2*csgn(I/x)^2*
csgn(I/x*(x-4))^4+1/2*exp(2*x)*Pi^2*csgn(I/x)*csgn(I/x*(x-4))^5-1/4*exp(2*x)*Pi^2*csgn(I*(x-4))^2*csgn(I/x*(x-
4))^4+1/2*exp(2*x)*Pi^2*csgn(I*(x-4))*csgn(I/x*(x-4))^5+5*I*Pi*csgn(I/x*(x-4))^3*exp(2*x)+ln(x)^2*exp(2*x)-2*x
*ln(3)*exp(x)+(2*x+I*Pi*csgn(I/x)*csgn(I*(x-4))*csgn(I/x*(x-4))*exp(x)-I*Pi*csgn(I/x)*csgn(I/x*(x-4))^2*exp(x)
-I*Pi*csgn(I*(x-4))*csgn(I/x*(x-4))^2*exp(x)+I*Pi*csgn(I/x*(x-4))^3*exp(x)-2*ln(3)*exp(x)+2*exp(x)*x+10*exp(x)
+2*exp(x)*ln(x)-2*exp(x)*ln(x-4))*exp(exp(2*x))-10*ln(3)*exp(2*x)+exp(2*exp(2*x))+ln(3)^2*exp(2*x)+10*exp(2*x)
*ln(x)+I*Pi*x*csgn(I/x)*csgn(I*(x-4))*csgn(I/x*(x-4))*exp(2*x)+(-2*exp(2*x)*ln(x)-I*Pi*csgn(I/x)*csgn(I*(x-4))
*csgn(I/x*(x-4))*exp(2*x)+I*Pi*csgn(I/x)*csgn(I/x*(x-4))^2*exp(2*x)+I*Pi*csgn(I*(x-4))*csgn(I/x*(x-4))^2*exp(2
*x)-I*Pi*csgn(I/x*(x-4))^3*exp(2*x)+2*ln(3)*exp(2*x)-2*x*exp(2*x)-2*exp(x)*x-10*exp(2*x))*ln(x-4)+exp(2*x)*ln(
x-4)^2+I*exp(2*x)*Pi*ln(3)*csgn(I/x)*csgn(I/x*(x-4))^2+I*exp(2*x)*Pi*ln(3)*csgn(I*(x-4))*csgn(I/x*(x-4))^2+I*P
i*csgn(I/x*(x-4))^3*exp(2*x)*ln(x)+I*Pi*x*csgn(I/x*(x-4))^3*exp(2*x)-2*ln(3)*exp(2*x)*x+5*I*Pi*csgn(I/x)*csgn(
I*(x-4))*csgn(I/x*(x-4))*exp(2*x)-I*Pi*csgn(I/x)*csgn(I/x*(x-4))^2*exp(2*x)*ln(x)-I*Pi*csgn(I*(x-4))*csgn(I/x*
(x-4))^2*exp(2*x)*ln(x)-I*Pi*x*csgn(I/x)*csgn(I/x*(x-4))^2*exp(2*x)-I*Pi*x*csgn(I*(x-4))*csgn(I/x*(x-4))^2*exp
(2*x)-I*Pi*x*csgn(I/x)*csgn(I/x*(x-4))^2*exp(x)-I*Pi*x*csgn(I*(x-4))*csgn(I/x*(x-4))^2*exp(x)-1/4*exp(2*x)*Pi^
2*csgn(I/x*(x-4))^6+I*Pi*x*csgn(I/x*(x-4))^3*exp(x)+1/2*exp(2*x)*Pi^2*csgn(I/x)*csgn(I*(x-4))^2*csgn(I/x*(x-4)
)^3-exp(2*x)*Pi^2*csgn(I/x)*csgn(I*(x-4))*csgn(I/x*(x-4))^4-1/4*exp(2*x)*Pi^2*csgn(I/x)^2*csgn(I*(x-4))^2*csgn
(I/x*(x-4))^2-5*I*Pi*csgn(I/x)*csgn(I/x*(x-4))^2*exp(2*x)-5*I*Pi*csgn(I*(x-4))*csgn(I/x*(x-4))^2*exp(2*x)-2*ln
(3)*exp(2*x)*ln(x)+2*x*exp(2*x)*ln(x)+I*Pi*csgn(I/x)*csgn(I*(x-4))*csgn(I/x*(x-4))*exp(2*x)*ln(x)

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maxima [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} e^{\left (2 \, x\right )} \log \left (x - 4\right )^{2} + 2 \, x e^{x} \log \relax (x) + x^{2} + {\left (x^{2} - 2 \, x {\left (\log \relax (3) - 5\right )} + \log \relax (3)^{2} + 2 \, {\left (x - \log \relax (3) + 5\right )} \log \relax (x) + \log \relax (x)^{2} - 10 \, \log \relax (3) + 25\right )} e^{\left (2 \, x\right )} + 2 \, {\left ({\left (x - \log \relax (3) + \log \relax (x) + 5\right )} e^{x} - e^{x} \log \left (x - 4\right ) + x\right )} e^{\left (e^{\left (2 \, x\right )}\right )} + 48 \, e^{4} E_{1}\left (-x + 4\right ) - 2 \, {\left ({\left (x - \log \relax (3) + \log \relax (x) + 5\right )} e^{\left (2 \, x\right )} + x e^{x}\right )} \log \left (x - 4\right ) + e^{\left (2 \, e^{\left (2 \, x\right )}\right )} + 2 \, \int \frac {{\left (x^{3} - x^{2} {\left (\log \relax (3) - 3\right )} + x {\left (3 \, \log \relax (3) - 23\right )} + 4 \, \log \relax (3) + 4\right )} e^{x}}{x - 4}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*x^2-16*x)*exp(x)^2*exp(exp(x)^2)^2+(((-4*x^2+16*x)*exp(x)^3+(-2*x^2+8*x)*exp(x))*log((3*x-12)/x)
+(4*x^3+4*x^2-80*x)*exp(x)^3+(4*x^3-16*x^2)*exp(x)^2+(2*x^3+4*x^2-48*x-8)*exp(x)+2*x^2-8*x)*exp(exp(x)^2)+(2*x
^2-8*x)*exp(x)^2*log((3*x-12)/x)^2+((-4*x^3-6*x^2+88*x+8)*exp(x)^2+(-2*x^3+6*x^2+8*x)*exp(x))*log((3*x-12)/x)+
(2*x^4+14*x^3-28*x^2-248*x-40)*exp(x)^2+(2*x^4+6*x^3-46*x^2-48*x)*exp(x)+2*x^3-8*x^2)/(x^2-4*x),x, algorithm="
maxima")

[Out]

e^(2*x)*log(x - 4)^2 + 2*x*e^x*log(x) + x^2 + (x^2 - 2*x*(log(3) - 5) + log(3)^2 + 2*(x - log(3) + 5)*log(x) +
log(x)^2 - 10*log(3) + 25)*e^(2*x) + 2*((x - log(3) + log(x) + 5)*e^x - e^x*log(x - 4) + x)*e^(e^(2*x)) + 48*
e^4*exp_integral_e(1, -x + 4) - 2*((x - log(3) + log(x) + 5)*e^(2*x) + x*e^x)*log(x - 4) + e^(2*e^(2*x)) + 2*i
ntegrate((x^3 - x^2*(log(3) - 3) + x*(3*log(3) - 23) + 4*log(3) + 4)*e^x/(x - 4), x)

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mupad [F]  time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int \frac {{\mathrm {e}}^x\,\left (-2\,x^4-6\,x^3+46\,x^2+48\,x\right )+{\mathrm {e}}^{{\mathrm {e}}^{2\,x}}\,\left (8\,x-{\mathrm {e}}^{3\,x}\,\left (4\,x^3+4\,x^2-80\,x\right )-\ln \left (\frac {3\,x-12}{x}\right )\,\left ({\mathrm {e}}^{3\,x}\,\left (16\,x-4\,x^2\right )+{\mathrm {e}}^x\,\left (8\,x-2\,x^2\right )\right )+{\mathrm {e}}^{2\,x}\,\left (16\,x^2-4\,x^3\right )-2\,x^2+{\mathrm {e}}^x\,\left (-2\,x^3-4\,x^2+48\,x+8\right )\right )+{\mathrm {e}}^{2\,x}\,\left (-2\,x^4-14\,x^3+28\,x^2+248\,x+40\right )-\ln \left (\frac {3\,x-12}{x}\right )\,\left ({\mathrm {e}}^{2\,x}\,\left (-4\,x^3-6\,x^2+88\,x+8\right )+{\mathrm {e}}^x\,\left (-2\,x^3+6\,x^2+8\,x\right )\right )+8\,x^2-2\,x^3+{\mathrm {e}}^{2\,{\mathrm {e}}^{2\,x}}\,{\mathrm {e}}^{2\,x}\,\left (16\,x-4\,x^2\right )+{\mathrm {e}}^{2\,x}\,{\ln \left (\frac {3\,x-12}{x}\right )}^2\,\left (8\,x-2\,x^2\right )}{4\,x-x^2} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(x)*(48*x + 46*x^2 - 6*x^3 - 2*x^4) + exp(exp(2*x))*(8*x - exp(3*x)*(4*x^2 - 80*x + 4*x^3) - log((3*x
- 12)/x)*(exp(3*x)*(16*x - 4*x^2) + exp(x)*(8*x - 2*x^2)) + exp(2*x)*(16*x^2 - 4*x^3) - 2*x^2 + exp(x)*(48*x -
4*x^2 - 2*x^3 + 8)) + exp(2*x)*(248*x + 28*x^2 - 14*x^3 - 2*x^4 + 40) - log((3*x - 12)/x)*(exp(2*x)*(88*x - 6
*x^2 - 4*x^3 + 8) + exp(x)*(8*x + 6*x^2 - 2*x^3)) + 8*x^2 - 2*x^3 + exp(2*exp(2*x))*exp(2*x)*(16*x - 4*x^2) +
exp(2*x)*log((3*x - 12)/x)^2*(8*x - 2*x^2))/(4*x - x^2),x)

[Out]

int((exp(x)*(48*x + 46*x^2 - 6*x^3 - 2*x^4) + exp(exp(2*x))*(8*x - exp(3*x)*(4*x^2 - 80*x + 4*x^3) - log((3*x
- 12)/x)*(exp(3*x)*(16*x - 4*x^2) + exp(x)*(8*x - 2*x^2)) + exp(2*x)*(16*x^2 - 4*x^3) - 2*x^2 + exp(x)*(48*x -
4*x^2 - 2*x^3 + 8)) + exp(2*x)*(248*x + 28*x^2 - 14*x^3 - 2*x^4 + 40) - log((3*x - 12)/x)*(exp(2*x)*(88*x - 6
*x^2 - 4*x^3 + 8) + exp(x)*(8*x + 6*x^2 - 2*x^3)) + 8*x^2 - 2*x^3 + exp(2*exp(2*x))*exp(2*x)*(16*x - 4*x^2) +
exp(2*x)*log((3*x - 12)/x)^2*(8*x - 2*x^2))/(4*x - x^2), x)

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sympy [B]  time = 141.15, size = 116, normalized size = 4.00 \begin {gather*} x^{2} + \left (2 x^{2} - 2 x \log {\left (\frac {3 x - 12}{x} \right )} + 10 x\right ) e^{x} + \left (2 x e^{x} + 2 x - 2 e^{x} \log {\left (\frac {3 x - 12}{x} \right )} + 10 e^{x}\right ) e^{e^{2 x}} + \left (x^{2} - 2 x \log {\left (\frac {3 x - 12}{x} \right )} + 10 x + \log {\left (\frac {3 x - 12}{x} \right )}^{2} - 10 \log {\left (\frac {3 x - 12}{x} \right )} + 25\right ) e^{2 x} + e^{2 e^{2 x}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*x**2-16*x)*exp(x)**2*exp(exp(x)**2)**2+(((-4*x**2+16*x)*exp(x)**3+(-2*x**2+8*x)*exp(x))*ln((3*x-
12)/x)+(4*x**3+4*x**2-80*x)*exp(x)**3+(4*x**3-16*x**2)*exp(x)**2+(2*x**3+4*x**2-48*x-8)*exp(x)+2*x**2-8*x)*exp
(exp(x)**2)+(2*x**2-8*x)*exp(x)**2*ln((3*x-12)/x)**2+((-4*x**3-6*x**2+88*x+8)*exp(x)**2+(-2*x**3+6*x**2+8*x)*e
xp(x))*ln((3*x-12)/x)+(2*x**4+14*x**3-28*x**2-248*x-40)*exp(x)**2+(2*x**4+6*x**3-46*x**2-48*x)*exp(x)+2*x**3-8
*x**2)/(x**2-4*x),x)

[Out]

x**2 + (2*x**2 - 2*x*log((3*x - 12)/x) + 10*x)*exp(x) + (2*x*exp(x) + 2*x - 2*exp(x)*log((3*x - 12)/x) + 10*ex
p(x))*exp(exp(2*x)) + (x**2 - 2*x*log((3*x - 12)/x) + 10*x + log((3*x - 12)/x)**2 - 10*log((3*x - 12)/x) + 25)
*exp(2*x) + exp(2*exp(2*x))

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