3.53.49 \(\int \frac {-6-6 e^x+(2+2 e^x) \log (x)+e^{\frac {1}{2} (9+12 \log (e^3 x+e^{3+x} x)+4 \log ^2(e^3 x+e^{3+x} x))} (96+e^x (96+96 x)+(64+e^x (64+64 x)) \log (e^3 x+e^{3+x} x))+e^{\frac {1}{4} (9+12 \log (e^3 x+e^{3+x} x)+4 \log ^2(e^3 x+e^{3+x} x))} (64+e^x (64+72 x)+(-24+e^x (-24-24 x)) \log (x)+(48+e^x (48+48 x)+(-16+e^x (-16-16 x)) \log (x)) \log (e^3 x+e^{3+x} x))}{x+e^x x} \, dx\)

Optimal. Leaf size=29 \[ \left (3+4 e^{\left (\frac {3}{2}+\log \left (e^3 \left (1+e^x\right ) x\right )\right )^2}-\log (x)\right )^2 \]

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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[(-6 - 6*E^x + (2 + 2*E^x)*Log[x] + E^((9 + 12*Log[E^3*x + E^(3 + x)*x] + 4*Log[E^3*x + E^(3 + x)*x]^2)/2)*
(96 + E^x*(96 + 96*x) + (64 + E^x*(64 + 64*x))*Log[E^3*x + E^(3 + x)*x]) + E^((9 + 12*Log[E^3*x + E^(3 + x)*x]
+ 4*Log[E^3*x + E^(3 + x)*x]^2)/4)*(64 + E^x*(64 + 72*x) + (-24 + E^x*(-24 - 24*x))*Log[x] + (48 + E^x*(48 +
48*x) + (-16 + E^x*(-16 - 16*x))*Log[x])*Log[E^3*x + E^(3 + x)*x]))/(x + E^x*x),x]

[Out]

$Aborted

Rubi steps

Aborted

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Mathematica [B]  time = 1.19, size = 71, normalized size = 2.45 \begin {gather*} 16 e^{\frac {81}{2}+2 \log ^2\left (\left (1+e^x\right ) x\right )} \left (1+e^x\right )^{18} x^{18}-8 e^{\frac {81}{4}+\log ^2\left (\left (1+e^x\right ) x\right )} \left (1+e^x\right )^9 x^9 (-3+\log (x))-6 \log (x)+\log ^2(x) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-6 - 6*E^x + (2 + 2*E^x)*Log[x] + E^((9 + 12*Log[E^3*x + E^(3 + x)*x] + 4*Log[E^3*x + E^(3 + x)*x]^
2)/2)*(96 + E^x*(96 + 96*x) + (64 + E^x*(64 + 64*x))*Log[E^3*x + E^(3 + x)*x]) + E^((9 + 12*Log[E^3*x + E^(3 +
x)*x] + 4*Log[E^3*x + E^(3 + x)*x]^2)/4)*(64 + E^x*(64 + 72*x) + (-24 + E^x*(-24 - 24*x))*Log[x] + (48 + E^x*
(48 + 48*x) + (-16 + E^x*(-16 - 16*x))*Log[x])*Log[E^3*x + E^(3 + x)*x]))/(x + E^x*x),x]

[Out]

16*E^(81/2 + 2*Log[(1 + E^x)*x]^2)*(1 + E^x)^18*x^18 - 8*E^(81/4 + Log[(1 + E^x)*x]^2)*(1 + E^x)^9*x^9*(-3 + L
og[x]) - 6*Log[x] + Log[x]^2

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fricas [B]  time = 0.60, size = 81, normalized size = 2.79 \begin {gather*} -8 \, {\left (\log \relax (x) - 3\right )} e^{\left (\log \left (x e^{3} + x e^{\left (x + 3\right )}\right )^{2} + 3 \, \log \left (x e^{3} + x e^{\left (x + 3\right )}\right ) + \frac {9}{4}\right )} + \log \relax (x)^{2} + 16 \, e^{\left (2 \, \log \left (x e^{3} + x e^{\left (x + 3\right )}\right )^{2} + 6 \, \log \left (x e^{3} + x e^{\left (x + 3\right )}\right ) + \frac {9}{2}\right )} - 6 \, \log \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((((64*x+64)*exp(x)+64)*log(x*exp(3)*exp(x)+x*exp(3))+(96*x+96)*exp(x)+96)*exp(log(x*exp(3)*exp(x)+x
*exp(3))^2+3*log(x*exp(3)*exp(x)+x*exp(3))+9/4)^2+((((-16*x-16)*exp(x)-16)*log(x)+(48*x+48)*exp(x)+48)*log(x*e
xp(3)*exp(x)+x*exp(3))+((-24*x-24)*exp(x)-24)*log(x)+(72*x+64)*exp(x)+64)*exp(log(x*exp(3)*exp(x)+x*exp(3))^2+
3*log(x*exp(3)*exp(x)+x*exp(3))+9/4)+(2*exp(x)+2)*log(x)-6*exp(x)-6)/(exp(x)*x+x),x, algorithm="fricas")

[Out]

-8*(log(x) - 3)*e^(log(x*e^3 + x*e^(x + 3))^2 + 3*log(x*e^3 + x*e^(x + 3)) + 9/4) + log(x)^2 + 16*e^(2*log(x*e
^3 + x*e^(x + 3))^2 + 6*log(x*e^3 + x*e^(x + 3)) + 9/2) - 6*log(x)

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {2 \, {\left (16 \, {\left (3 \, {\left (x + 1\right )} e^{x} + 2 \, {\left ({\left (x + 1\right )} e^{x} + 1\right )} \log \left (x e^{3} + x e^{\left (x + 3\right )}\right ) + 3\right )} e^{\left (2 \, \log \left (x e^{3} + x e^{\left (x + 3\right )}\right )^{2} + 6 \, \log \left (x e^{3} + x e^{\left (x + 3\right )}\right ) + \frac {9}{2}\right )} + 4 \, {\left ({\left (9 \, x + 8\right )} e^{x} + 2 \, {\left (3 \, {\left (x + 1\right )} e^{x} - {\left ({\left (x + 1\right )} e^{x} + 1\right )} \log \relax (x) + 3\right )} \log \left (x e^{3} + x e^{\left (x + 3\right )}\right ) - 3 \, {\left ({\left (x + 1\right )} e^{x} + 1\right )} \log \relax (x) + 8\right )} e^{\left (\log \left (x e^{3} + x e^{\left (x + 3\right )}\right )^{2} + 3 \, \log \left (x e^{3} + x e^{\left (x + 3\right )}\right ) + \frac {9}{4}\right )} + {\left (e^{x} + 1\right )} \log \relax (x) - 3 \, e^{x} - 3\right )}}{x e^{x} + x}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((((64*x+64)*exp(x)+64)*log(x*exp(3)*exp(x)+x*exp(3))+(96*x+96)*exp(x)+96)*exp(log(x*exp(3)*exp(x)+x
*exp(3))^2+3*log(x*exp(3)*exp(x)+x*exp(3))+9/4)^2+((((-16*x-16)*exp(x)-16)*log(x)+(48*x+48)*exp(x)+48)*log(x*e
xp(3)*exp(x)+x*exp(3))+((-24*x-24)*exp(x)-24)*log(x)+(72*x+64)*exp(x)+64)*exp(log(x*exp(3)*exp(x)+x*exp(3))^2+
3*log(x*exp(3)*exp(x)+x*exp(3))+9/4)+(2*exp(x)+2)*log(x)-6*exp(x)-6)/(exp(x)*x+x),x, algorithm="giac")

[Out]

integrate(2*(16*(3*(x + 1)*e^x + 2*((x + 1)*e^x + 1)*log(x*e^3 + x*e^(x + 3)) + 3)*e^(2*log(x*e^3 + x*e^(x + 3
))^2 + 6*log(x*e^3 + x*e^(x + 3)) + 9/2) + 4*((9*x + 8)*e^x + 2*(3*(x + 1)*e^x - ((x + 1)*e^x + 1)*log(x) + 3)
*log(x*e^3 + x*e^(x + 3)) - 3*((x + 1)*e^x + 1)*log(x) + 8)*e^(log(x*e^3 + x*e^(x + 3))^2 + 3*log(x*e^3 + x*e^
(x + 3)) + 9/4) + (e^x + 1)*log(x) - 3*e^x - 3)/(x*e^x + x), x)

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maple [C]  time = 0.38, size = 971, normalized size = 33.48

method	result	size
risch	\(\ln \relax (x )^{2}-6 \ln \relax (x )+16 \left ({\mathrm e}^{x}+1\right )^{2 i \pi \,\mathrm {csgn}\left (i \left ({\mathrm e}^{x}+1\right )\right )} \left ({\mathrm e}^{x}+1\right )^{4 \ln \relax (x )} \left ({\mathrm e}^{x}+1\right )^{-2 i \pi \,\mathrm {csgn}\left (i x \left ({\mathrm e}^{x}+1\right )\right ) \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i \left ({\mathrm e}^{x}+1\right )\right )} x^{-2 i \pi \,\mathrm {csgn}\left (i x \left ({\mathrm e}^{x}+1\right )\right ) \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i \left ({\mathrm e}^{x}+1\right )\right )} \left ({\mathrm e}^{x}+1\right )^{-2 i \pi \,\mathrm {csgn}\left (i x \left ({\mathrm e}^{x}+1\right )\right )} x^{-2 i \pi \,\mathrm {csgn}\left (i x \left ({\mathrm e}^{x}+1\right )\right )} \left ({\mathrm e}^{x}+1\right )^{2 i \pi \,\mathrm {csgn}\left (i x \right )} x^{2 i \pi \,\mathrm {csgn}\left (i \left ({\mathrm e}^{x}+1\right )\right )} x^{2 i \pi \,\mathrm {csgn}\left (i x \right )} \left ({\mathrm e}^{x}+1\right )^{6} x^{6} {\mathrm e}^{2 \ln \relax (x )^{2}+\frac {9}{2}+2 \ln \left ({\mathrm e}^{x}+1\right )^{2}} {\mathrm e}^{\pi ^{2} \mathrm {csgn}\left (i x \left ({\mathrm e}^{x}+1\right )\right )^{3} \mathrm {csgn}\left (i \left ({\mathrm e}^{x}+1\right )\right )^{2} \mathrm {csgn}\left (i x \right )} {\mathrm e}^{-\frac {\pi ^{2} \mathrm {csgn}\left (i x \left ({\mathrm e}^{x}+1\right )\right )^{2} \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i \left ({\mathrm e}^{x}+1\right )\right )^{2}}{2}} {\mathrm e}^{-2 \pi ^{2} \mathrm {csgn}\left (i x \left ({\mathrm e}^{x}+1\right )\right )^{4} \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i \left ({\mathrm e}^{x}+1\right )\right )} {\mathrm e}^{\pi ^{2} \mathrm {csgn}\left (i x \left ({\mathrm e}^{x}+1\right )\right )^{3} \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i \left ({\mathrm e}^{x}+1\right )\right )} {\mathrm e}^{\pi ^{2} \mathrm {csgn}\left (i x \left ({\mathrm e}^{x}+1\right )\right )^{5} \mathrm {csgn}\left (i x \right )} {\mathrm e}^{\pi ^{2} \mathrm {csgn}\left (i x \left ({\mathrm e}^{x}+1\right )\right )^{5} \mathrm {csgn}\left (i \left ({\mathrm e}^{x}+1\right )\right )} {\mathrm e}^{-\frac {\pi ^{2} \mathrm {csgn}\left (i x \left ({\mathrm e}^{x}+1\right )\right )^{4} \mathrm {csgn}\left (i x \right )^{2}}{2}} {\mathrm e}^{-\frac {\pi ^{2} \mathrm {csgn}\left (i x \left ({\mathrm e}^{x}+1\right )\right )^{4} \mathrm {csgn}\left (i \left ({\mathrm e}^{x}+1\right )\right )^{2}}{2}} {\mathrm e}^{-\frac {\pi ^{2} \mathrm {csgn}\left (i x \left ({\mathrm e}^{x}+1\right )\right )^{6}}{2}}+\left (-8 \ln \relax (x )+24\right ) x^{3} \left ({\mathrm e}^{x}+1\right )^{3} x^{i \pi \,\mathrm {csgn}\left (i x \right )} x^{i \pi \,\mathrm {csgn}\left (i \left ({\mathrm e}^{x}+1\right )\right )} \left ({\mathrm e}^{x}+1\right )^{i \pi \,\mathrm {csgn}\left (i x \right )} x^{-i \pi \,\mathrm {csgn}\left (i x \left ({\mathrm e}^{x}+1\right )\right )} \left ({\mathrm e}^{x}+1\right )^{-i \pi \,\mathrm {csgn}\left (i x \left ({\mathrm e}^{x}+1\right )\right )} x^{-i \pi \,\mathrm {csgn}\left (i x \left ({\mathrm e}^{x}+1\right )\right ) \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i \left ({\mathrm e}^{x}+1\right )\right )} \left ({\mathrm e}^{x}+1\right )^{-i \pi \,\mathrm {csgn}\left (i x \left ({\mathrm e}^{x}+1\right )\right ) \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i \left ({\mathrm e}^{x}+1\right )\right )} \left ({\mathrm e}^{x}+1\right )^{2 \ln \relax (x )} \left ({\mathrm e}^{x}+1\right )^{i \pi \,\mathrm {csgn}\left (i \left ({\mathrm e}^{x}+1\right )\right )} {\mathrm e}^{\ln \relax (x )^{2}+\frac {9}{4}+\ln \left ({\mathrm e}^{x}+1\right )^{2}} {\mathrm e}^{\frac {\pi ^{2} \mathrm {csgn}\left (i x \left ({\mathrm e}^{x}+1\right )\right )^{3} \mathrm {csgn}\left (i \left ({\mathrm e}^{x}+1\right )\right )^{2} \mathrm {csgn}\left (i x \right )}{2}} {\mathrm e}^{\frac {3 i \pi \mathrm {csgn}\left (i x \left ({\mathrm e}^{x}+1\right )\right )^{2} \mathrm {csgn}\left (i x \right )}{2}} {\mathrm e}^{\frac {3 i \pi \mathrm {csgn}\left (i x \left ({\mathrm e}^{x}+1\right )\right )^{2} \mathrm {csgn}\left (i \left ({\mathrm e}^{x}+1\right )\right )}{2}} {\mathrm e}^{-\frac {\pi ^{2} \mathrm {csgn}\left (i x \left ({\mathrm e}^{x}+1\right )\right )^{2} \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i \left ({\mathrm e}^{x}+1\right )\right )^{2}}{4}} {\mathrm e}^{-\pi ^{2} \mathrm {csgn}\left (i x \left ({\mathrm e}^{x}+1\right )\right )^{4} \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i \left ({\mathrm e}^{x}+1\right )\right )} {\mathrm e}^{\frac {\pi ^{2} \mathrm {csgn}\left (i x \left ({\mathrm e}^{x}+1\right )\right )^{3} \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i \left ({\mathrm e}^{x}+1\right )\right )}{2}} {\mathrm e}^{\frac {\pi ^{2} \mathrm {csgn}\left (i x \left ({\mathrm e}^{x}+1\right )\right )^{5} \mathrm {csgn}\left (i x \right )}{2}} {\mathrm e}^{\frac {\pi ^{2} \mathrm {csgn}\left (i x \left ({\mathrm e}^{x}+1\right )\right )^{5} \mathrm {csgn}\left (i \left ({\mathrm e}^{x}+1\right )\right )}{2}} {\mathrm e}^{-\frac {\pi ^{2} \mathrm {csgn}\left (i x \left ({\mathrm e}^{x}+1\right )\right )^{4} \mathrm {csgn}\left (i x \right )^{2}}{4}} {\mathrm e}^{-\frac {\pi ^{2} \mathrm {csgn}\left (i x \left ({\mathrm e}^{x}+1\right )\right )^{4} \mathrm {csgn}\left (i \left ({\mathrm e}^{x}+1\right )\right )^{2}}{4}} {\mathrm e}^{-\frac {3 i \pi \,\mathrm {csgn}\left (i x \left ({\mathrm e}^{x}+1\right )\right ) \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i \left ({\mathrm e}^{x}+1\right )\right )}{2}} {\mathrm e}^{-\frac {\pi ^{2} \mathrm {csgn}\left (i x \left ({\mathrm e}^{x}+1\right )\right )^{6}}{4}} {\mathrm e}^{-\frac {3 i \pi \mathrm {csgn}\left (i x \left ({\mathrm e}^{x}+1\right )\right )^{3}}{2}}\)	\(971\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((((64*x+64)*exp(x)+64)*ln(x*exp(3)*exp(x)+x*exp(3))+(96*x+96)*exp(x)+96)*exp(ln(x*exp(3)*exp(x)+x*exp(3))
^2+3*ln(x*exp(3)*exp(x)+x*exp(3))+9/4)^2+((((-16*x-16)*exp(x)-16)*ln(x)+(48*x+48)*exp(x)+48)*ln(x*exp(3)*exp(x
)+x*exp(3))+((-24*x-24)*exp(x)-24)*ln(x)+(72*x+64)*exp(x)+64)*exp(ln(x*exp(3)*exp(x)+x*exp(3))^2+3*ln(x*exp(3)
*exp(x)+x*exp(3))+9/4)+(2*exp(x)+2)*ln(x)-6*exp(x)-6)/(exp(x)*x+x),x,method=_RETURNVERBOSE)

[Out]

ln(x)^2-6*ln(x)+16*((exp(x)+1)^(I*Pi*csgn(I*(exp(x)+1))))^2*((exp(x)+1)^(2*ln(x)))^2*((exp(x)+1)^(-I*Pi*csgn(I
*x*(exp(x)+1))*csgn(I*x)*csgn(I*(exp(x)+1))))^2*(x^(-I*Pi*csgn(I*x*(exp(x)+1))*csgn(I*x)*csgn(I*(exp(x)+1))))^
2*((exp(x)+1)^(-I*Pi*csgn(I*x*(exp(x)+1))))^2*(x^(-I*Pi*csgn(I*x*(exp(x)+1))))^2*((exp(x)+1)^(I*Pi*csgn(I*x)))
^2*(x^(I*Pi*csgn(I*(exp(x)+1))))^2*(x^(I*Pi*csgn(I*x)))^2*(exp(x)+1)^6*x^6*exp(2*ln(x)^2+9/2+2*ln(exp(x)+1)^2)
*exp(Pi^2*csgn(I*x*(exp(x)+1))^3*csgn(I*(exp(x)+1))^2*csgn(I*x))*exp(-1/2*Pi^2*csgn(I*x*(exp(x)+1))^2*csgn(I*x
)^2*csgn(I*(exp(x)+1))^2)*exp(-2*Pi^2*csgn(I*x*(exp(x)+1))^4*csgn(I*x)*csgn(I*(exp(x)+1)))*exp(Pi^2*csgn(I*x*(
exp(x)+1))^3*csgn(I*x)^2*csgn(I*(exp(x)+1)))*exp(Pi^2*csgn(I*x*(exp(x)+1))^5*csgn(I*x))*exp(Pi^2*csgn(I*x*(exp
(x)+1))^5*csgn(I*(exp(x)+1)))*exp(-1/2*Pi^2*csgn(I*x*(exp(x)+1))^4*csgn(I*x)^2)*exp(-1/2*Pi^2*csgn(I*x*(exp(x)
+1))^4*csgn(I*(exp(x)+1))^2)*exp(-1/2*Pi^2*csgn(I*x*(exp(x)+1))^6)+(-8*ln(x)+24)*x^3*(exp(x)+1)^3*x^(I*Pi*csgn
(I*x))*x^(I*Pi*csgn(I*(exp(x)+1)))*(exp(x)+1)^(I*Pi*csgn(I*x))*x^(-I*Pi*csgn(I*x*(exp(x)+1)))*(exp(x)+1)^(-I*P
i*csgn(I*x*(exp(x)+1)))*x^(-I*Pi*csgn(I*x*(exp(x)+1))*csgn(I*x)*csgn(I*(exp(x)+1)))*(exp(x)+1)^(-I*Pi*csgn(I*x
*(exp(x)+1))*csgn(I*x)*csgn(I*(exp(x)+1)))*(exp(x)+1)^(2*ln(x))*(exp(x)+1)^(I*Pi*csgn(I*(exp(x)+1)))*exp(ln(x)
^2+9/4+ln(exp(x)+1)^2)*exp(1/2*Pi^2*csgn(I*x*(exp(x)+1))^3*csgn(I*(exp(x)+1))^2*csgn(I*x))*exp(3/2*I*Pi*csgn(I
*x*(exp(x)+1))^2*csgn(I*x))*exp(3/2*I*Pi*csgn(I*x*(exp(x)+1))^2*csgn(I*(exp(x)+1)))*exp(-1/4*Pi^2*csgn(I*x*(ex
p(x)+1))^2*csgn(I*x)^2*csgn(I*(exp(x)+1))^2)*exp(-Pi^2*csgn(I*x*(exp(x)+1))^4*csgn(I*x)*csgn(I*(exp(x)+1)))*ex
p(1/2*Pi^2*csgn(I*x*(exp(x)+1))^3*csgn(I*x)^2*csgn(I*(exp(x)+1)))*exp(1/2*Pi^2*csgn(I*x*(exp(x)+1))^5*csgn(I*x
))*exp(1/2*Pi^2*csgn(I*x*(exp(x)+1))^5*csgn(I*(exp(x)+1)))*exp(-1/4*Pi^2*csgn(I*x*(exp(x)+1))^4*csgn(I*x)^2)*e
xp(-1/4*Pi^2*csgn(I*x*(exp(x)+1))^4*csgn(I*(exp(x)+1))^2)*exp(-3/2*I*Pi*csgn(I*x*(exp(x)+1))*csgn(I*x)*csgn(I*
(exp(x)+1)))*exp(-1/4*Pi^2*csgn(I*x*(exp(x)+1))^6)*exp(-3/2*I*Pi*csgn(I*x*(exp(x)+1))^3)

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maxima [B]  time = 0.55, size = 474, normalized size = 16.34 \begin {gather*} 16 \, {\left (x^{18} e^{\frac {81}{2}} + x^{18} e^{\left (18 \, x + \frac {81}{2}\right )} + 18 \, x^{18} e^{\left (17 \, x + \frac {81}{2}\right )} + 153 \, x^{18} e^{\left (16 \, x + \frac {81}{2}\right )} + 816 \, x^{18} e^{\left (15 \, x + \frac {81}{2}\right )} + 3060 \, x^{18} e^{\left (14 \, x + \frac {81}{2}\right )} + 8568 \, x^{18} e^{\left (13 \, x + \frac {81}{2}\right )} + 18564 \, x^{18} e^{\left (12 \, x + \frac {81}{2}\right )} + 31824 \, x^{18} e^{\left (11 \, x + \frac {81}{2}\right )} + 43758 \, x^{18} e^{\left (10 \, x + \frac {81}{2}\right )} + 48620 \, x^{18} e^{\left (9 \, x + \frac {81}{2}\right )} + 43758 \, x^{18} e^{\left (8 \, x + \frac {81}{2}\right )} + 31824 \, x^{18} e^{\left (7 \, x + \frac {81}{2}\right )} + 18564 \, x^{18} e^{\left (6 \, x + \frac {81}{2}\right )} + 8568 \, x^{18} e^{\left (5 \, x + \frac {81}{2}\right )} + 3060 \, x^{18} e^{\left (4 \, x + \frac {81}{2}\right )} + 816 \, x^{18} e^{\left (3 \, x + \frac {81}{2}\right )} + 153 \, x^{18} e^{\left (2 \, x + \frac {81}{2}\right )} + 18 \, x^{18} e^{\left (x + \frac {81}{2}\right )}\right )} e^{\left (2 \, \log \relax (x)^{2} + 4 \, \log \relax (x) \log \left (e^{x} + 1\right ) + 2 \, \log \left (e^{x} + 1\right )^{2}\right )} - 8 \, {\left (x^{9} e^{\frac {81}{4}} \log \relax (x) - 3 \, x^{9} e^{\frac {81}{4}} + {\left (x^{9} e^{\frac {81}{4}} \log \relax (x) - 3 \, x^{9} e^{\frac {81}{4}}\right )} e^{\left (9 \, x\right )} + 9 \, {\left (x^{9} e^{\frac {81}{4}} \log \relax (x) - 3 \, x^{9} e^{\frac {81}{4}}\right )} e^{\left (8 \, x\right )} + 36 \, {\left (x^{9} e^{\frac {81}{4}} \log \relax (x) - 3 \, x^{9} e^{\frac {81}{4}}\right )} e^{\left (7 \, x\right )} + 84 \, {\left (x^{9} e^{\frac {81}{4}} \log \relax (x) - 3 \, x^{9} e^{\frac {81}{4}}\right )} e^{\left (6 \, x\right )} + 126 \, {\left (x^{9} e^{\frac {81}{4}} \log \relax (x) - 3 \, x^{9} e^{\frac {81}{4}}\right )} e^{\left (5 \, x\right )} + 126 \, {\left (x^{9} e^{\frac {81}{4}} \log \relax (x) - 3 \, x^{9} e^{\frac {81}{4}}\right )} e^{\left (4 \, x\right )} + 84 \, {\left (x^{9} e^{\frac {81}{4}} \log \relax (x) - 3 \, x^{9} e^{\frac {81}{4}}\right )} e^{\left (3 \, x\right )} + 36 \, {\left (x^{9} e^{\frac {81}{4}} \log \relax (x) - 3 \, x^{9} e^{\frac {81}{4}}\right )} e^{\left (2 \, x\right )} + 9 \, {\left (x^{9} e^{\frac {81}{4}} \log \relax (x) - 3 \, x^{9} e^{\frac {81}{4}}\right )} e^{x}\right )} e^{\left (\log \relax (x)^{2} + 2 \, \log \relax (x) \log \left (e^{x} + 1\right ) + \log \left (e^{x} + 1\right )^{2}\right )} + \log \relax (x)^{2} - 6 \, \log \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((((64*x+64)*exp(x)+64)*log(x*exp(3)*exp(x)+x*exp(3))+(96*x+96)*exp(x)+96)*exp(log(x*exp(3)*exp(x)+x
*exp(3))^2+3*log(x*exp(3)*exp(x)+x*exp(3))+9/4)^2+((((-16*x-16)*exp(x)-16)*log(x)+(48*x+48)*exp(x)+48)*log(x*e
xp(3)*exp(x)+x*exp(3))+((-24*x-24)*exp(x)-24)*log(x)+(72*x+64)*exp(x)+64)*exp(log(x*exp(3)*exp(x)+x*exp(3))^2+
3*log(x*exp(3)*exp(x)+x*exp(3))+9/4)+(2*exp(x)+2)*log(x)-6*exp(x)-6)/(exp(x)*x+x),x, algorithm="maxima")

[Out]

16*(x^18*e^(81/2) + x^18*e^(18*x + 81/2) + 18*x^18*e^(17*x + 81/2) + 153*x^18*e^(16*x + 81/2) + 816*x^18*e^(15
*x + 81/2) + 3060*x^18*e^(14*x + 81/2) + 8568*x^18*e^(13*x + 81/2) + 18564*x^18*e^(12*x + 81/2) + 31824*x^18*e
^(11*x + 81/2) + 43758*x^18*e^(10*x + 81/2) + 48620*x^18*e^(9*x + 81/2) + 43758*x^18*e^(8*x + 81/2) + 31824*x^
18*e^(7*x + 81/2) + 18564*x^18*e^(6*x + 81/2) + 8568*x^18*e^(5*x + 81/2) + 3060*x^18*e^(4*x + 81/2) + 816*x^18
*e^(3*x + 81/2) + 153*x^18*e^(2*x + 81/2) + 18*x^18*e^(x + 81/2))*e^(2*log(x)^2 + 4*log(x)*log(e^x + 1) + 2*lo
g(e^x + 1)^2) - 8*(x^9*e^(81/4)*log(x) - 3*x^9*e^(81/4) + (x^9*e^(81/4)*log(x) - 3*x^9*e^(81/4))*e^(9*x) + 9*(
x^9*e^(81/4)*log(x) - 3*x^9*e^(81/4))*e^(8*x) + 36*(x^9*e^(81/4)*log(x) - 3*x^9*e^(81/4))*e^(7*x) + 84*(x^9*e^
(81/4)*log(x) - 3*x^9*e^(81/4))*e^(6*x) + 126*(x^9*e^(81/4)*log(x) - 3*x^9*e^(81/4))*e^(5*x) + 126*(x^9*e^(81/
4)*log(x) - 3*x^9*e^(81/4))*e^(4*x) + 84*(x^9*e^(81/4)*log(x) - 3*x^9*e^(81/4))*e^(3*x) + 36*(x^9*e^(81/4)*log
(x) - 3*x^9*e^(81/4))*e^(2*x) + 9*(x^9*e^(81/4)*log(x) - 3*x^9*e^(81/4))*e^x)*e^(log(x)^2 + 2*log(x)*log(e^x +
1) + log(e^x + 1)^2) + log(x)^2 - 6*log(x)

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mupad [B]  time = 3.97, size = 295, normalized size = 10.17 \begin {gather*} {\ln \relax (x)}^2-6\,\ln \relax (x)+96\,x^6\,{\mathrm {e}}^{2\,{\ln \left (x\,{\mathrm {e}}^3+x\,{\mathrm {e}}^3\,{\mathrm {e}}^x\right )}^2+x+\frac {45}{2}}-\left (8\,\ln \relax (x)-24\right )\,\left (3\,x^3\,{\mathrm {e}}^{{\ln \left (x\,{\mathrm {e}}^3+x\,{\mathrm {e}}^3\,{\mathrm {e}}^x\right )}^2+2\,x+\frac {45}{4}}+x^3\,{\mathrm {e}}^{{\ln \left (x\,{\mathrm {e}}^3+x\,{\mathrm {e}}^3\,{\mathrm {e}}^x\right )}^2+3\,x+\frac {45}{4}}+x^3\,{\mathrm {e}}^{{\ln \left (x\,{\mathrm {e}}^3+x\,{\mathrm {e}}^3\,{\mathrm {e}}^x\right )}^2+\frac {45}{4}}+3\,x^3\,{\mathrm {e}}^{{\ln \left (x\,{\mathrm {e}}^3+x\,{\mathrm {e}}^3\,{\mathrm {e}}^x\right )}^2+x+\frac {45}{4}}\right )+240\,x^6\,{\mathrm {e}}^{2\,{\ln \left (x\,{\mathrm {e}}^3+x\,{\mathrm {e}}^3\,{\mathrm {e}}^x\right )}^2+2\,x+\frac {45}{2}}+320\,x^6\,{\mathrm {e}}^{2\,{\ln \left (x\,{\mathrm {e}}^3+x\,{\mathrm {e}}^3\,{\mathrm {e}}^x\right )}^2+3\,x+\frac {45}{2}}+240\,x^6\,{\mathrm {e}}^{2\,{\ln \left (x\,{\mathrm {e}}^3+x\,{\mathrm {e}}^3\,{\mathrm {e}}^x\right )}^2+4\,x+\frac {45}{2}}+96\,x^6\,{\mathrm {e}}^{2\,{\ln \left (x\,{\mathrm {e}}^3+x\,{\mathrm {e}}^3\,{\mathrm {e}}^x\right )}^2+5\,x+\frac {45}{2}}+16\,x^6\,{\mathrm {e}}^{2\,{\ln \left (x\,{\mathrm {e}}^3+x\,{\mathrm {e}}^3\,{\mathrm {e}}^x\right )}^2+6\,x+\frac {45}{2}}+16\,x^6\,{\mathrm {e}}^{2\,{\ln \left (x\,{\mathrm {e}}^3+x\,{\mathrm {e}}^3\,{\mathrm {e}}^x\right )}^2+\frac {45}{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(3*log(x*exp(3) + x*exp(3)*exp(x)) + log(x*exp(3) + x*exp(3)*exp(x))^2 + 9/4)*(log(x*exp(3) + x*exp(3)
*exp(x))*(exp(x)*(48*x + 48) - log(x)*(exp(x)*(16*x + 16) + 16) + 48) - log(x)*(exp(x)*(24*x + 24) + 24) + exp
(x)*(72*x + 64) + 64) - 6*exp(x) + exp(6*log(x*exp(3) + x*exp(3)*exp(x)) + 2*log(x*exp(3) + x*exp(3)*exp(x))^2
+ 9/2)*(log(x*exp(3) + x*exp(3)*exp(x))*(exp(x)*(64*x + 64) + 64) + exp(x)*(96*x + 96) + 96) + log(x)*(2*exp(
x) + 2) - 6)/(x + x*exp(x)),x)

[Out]

log(x)^2 - 6*log(x) + 96*x^6*exp(x + 2*log(x*exp(3) + x*exp(3)*exp(x))^2 + 45/2) - (8*log(x) - 24)*(3*x^3*exp(
2*x + log(x*exp(3) + x*exp(3)*exp(x))^2 + 45/4) + x^3*exp(3*x + log(x*exp(3) + x*exp(3)*exp(x))^2 + 45/4) + x^
3*exp(log(x*exp(3) + x*exp(3)*exp(x))^2 + 45/4) + 3*x^3*exp(x + log(x*exp(3) + x*exp(3)*exp(x))^2 + 45/4)) + 2
40*x^6*exp(2*x + 2*log(x*exp(3) + x*exp(3)*exp(x))^2 + 45/2) + 320*x^6*exp(3*x + 2*log(x*exp(3) + x*exp(3)*exp
(x))^2 + 45/2) + 240*x^6*exp(4*x + 2*log(x*exp(3) + x*exp(3)*exp(x))^2 + 45/2) + 96*x^6*exp(5*x + 2*log(x*exp(
3) + x*exp(3)*exp(x))^2 + 45/2) + 16*x^6*exp(6*x + 2*log(x*exp(3) + x*exp(3)*exp(x))^2 + 45/2) + 16*x^6*exp(2*
log(x*exp(3) + x*exp(3)*exp(x))^2 + 45/2)

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sympy [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((((64*x+64)*exp(x)+64)*ln(x*exp(3)*exp(x)+x*exp(3))+(96*x+96)*exp(x)+96)*exp(ln(x*exp(3)*exp(x)+x*e
xp(3))**2+3*ln(x*exp(3)*exp(x)+x*exp(3))+9/4)**2+((((-16*x-16)*exp(x)-16)*ln(x)+(48*x+48)*exp(x)+48)*ln(x*exp(
3)*exp(x)+x*exp(3))+((-24*x-24)*exp(x)-24)*ln(x)+(72*x+64)*exp(x)+64)*exp(ln(x*exp(3)*exp(x)+x*exp(3))**2+3*ln
(x*exp(3)*exp(x)+x*exp(3))+9/4)+(2*exp(x)+2)*ln(x)-6*exp(x)-6)/(exp(x)*x+x),x)

[Out]

Timed out

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