∫ −8e2x+e4x(4e2x+ex(1−2x)−4x)+ex(−2+4x)+(−2+e4x+eex (−2ex+e5x)) log2(2−e4x)+(−8e2x+e4x(4e2x+ex(1−x))+ex(−2+2x)) log(x)+(−2e2x+e6x) log2(x)+eex (−8e3x+4e7x+(−8e3x+4e7x) log(x)+(−2e3x+e7x) log2(x))+log(2−e4x)(−2−8ex+e4x(1+4ex)+(−4ex+2e5x) log(x)+eex (−8e2x+4e6x+(−4e2x+2e6x) log(x)))_____________________________________________________________________________________________________________________________________________________________________________________________________________________________________ −8e2x+4e6x+(−2+e4x) log2(2−e4x)+(−8e2x+4e6x) log(x)+(−2e2x+e6x) log2(x)+log(2−e4x)(−8ex+4e5x+(−4ex+2e5x) log(x)) dx

3.79.17 $\int \frac {-8 e^{2 x}+e^{4 x} (4 e^{2 x}+e^x (1-2 x)-4 x)+e^x (-2+4 x)+(-2+e^{4 x}+e^{e^x} (-2 e^x+e^{5 x})) \log ^2(2-e^{4 x})+(-8 e^{2 x}+e^{4 x} (4 e^{2 x}+e^x (1-x))+e^x (-2+2 x)) \log (x)+(-2 e^{2 x}+e^{6 x}) \log ^2(x)+e^{e^x} (-8 e^{3 x}+4 e^{7 x}+(-8 e^{3 x}+4 e^{7 x}) \log (x)+(-2 e^{3 x}+e^{7 x}) \log ^2(x))+\log (2-e^{4 x}) (-2-8 e^x+e^{4 x} (1+4 e^x)+(-4 e^x+2 e^{5 x}) \log (x)+e^{e^x} (-8 e^{2 x}+4 e^{6 x}+(-4 e^{2 x}+2 e^{6 x}) \log (x)))}{-8 e^{2 x}+4 e^{6 x}+(-2+e^{4 x}) \log ^2(2-e^{4 x})+(-8 e^{2 x}+4 e^{6 x}) \log (x)+(-2 e^{2 x}+e^{6 x}) \log ^2(x)+\log (2-e^{4 x}) (-8 e^x+4 e^{5 x}+(-4 e^x+2 e^{5 x}) \log (x))} \, dx$

Optimal. Leaf size=30 \[ e^{e^x}+x+\frac {x}{\log \left (2-e^{4 x}\right )+e^x (2+\log (x))} \]

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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*E^(2*x) + E^(4*x)*(4*E^(2*x) + E^x*(1 - 2*x) - 4*x) + E^x*(-2 + 4*x) + (-2 + E^(4*x) + E^E^x*(-2*E^x +

E^(5*x)))*Log[2 - E^(4*x)]^2 + (-8*E^(2*x) + E^(4*x)*(4*E^(2*x) + E^x*(1 - x)) + E^x*(-2 + 2*x))*Log[x] + (-2

*E^(2*x) + E^(6*x))*Log[x]^2 + E^E^x*(-8*E^(3*x) + 4*E^(7*x) + (-8*E^(3*x) + 4*E^(7*x))*Log[x] + (-2*E^(3*x) +

E^(7*x))*Log[x]^2) + Log[2 - E^(4*x)]*(-2 - 8*E^x + E^(4*x)*(1 + 4*E^x) + (-4*E^x + 2*E^(5*x))*Log[x] + E^E^x

*(-8*E^(2*x) + 4*E^(6*x) + (-4*E^(2*x) + 2*E^(6*x))*Log[x])))/(-8*E^(2*x) + 4*E^(6*x) + (-2 + E^(4*x))*Log[2 -

E^(4*x)]^2 + (-8*E^(2*x) + 4*E^(6*x))*Log[x] + (-2*E^(2*x) + E^(6*x))*Log[x]^2 + Log[2 - E^(4*x)]*(-8*E^x + 4

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

[Out]

$Aborted

Rubi steps

Aborted

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Mathematica [A] time = 0.47, size = 30, normalized size = 1.00 \begin {gather*} e^{e^x}+x+\frac {x}{\log \left (2-e^{4 x}\right )+e^x (2+\log (x))} \end {gather*}

Antiderivative was successfully veriﬁed.

[In]

Integrate[(-8*E^(2*x) + E^(4*x)*(4*E^(2*x) + E^x*(1 - 2*x) - 4*x) + E^x*(-2 + 4*x) + (-2 + E^(4*x) + E^E^x*(-2

*E^x + E^(5*x)))*Log[2 - E^(4*x)]^2 + (-8*E^(2*x) + E^(4*x)*(4*E^(2*x) + E^x*(1 - x)) + E^x*(-2 + 2*x))*Log[x]

+ (-2*E^(2*x) + E^(6*x))*Log[x]^2 + E^E^x*(-8*E^(3*x) + 4*E^(7*x) + (-8*E^(3*x) + 4*E^(7*x))*Log[x] + (-2*E^(

3*x) + E^(7*x))*Log[x]^2) + Log[2 - E^(4*x)]*(-2 - 8*E^x + E^(4*x)*(1 + 4*E^x) + (-4*E^x + 2*E^(5*x))*Log[x] +

E^E^x*(-8*E^(2*x) + 4*E^(6*x) + (-4*E^(2*x) + 2*E^(6*x))*Log[x])))/(-8*E^(2*x) + 4*E^(6*x) + (-2 + E^(4*x))*L

og[2 - E^(4*x)]^2 + (-8*E^(2*x) + 4*E^(6*x))*Log[x] + (-2*E^(2*x) + E^(6*x))*Log[x]^2 + Log[2 - E^(4*x)]*(-8*E

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

[Out]

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

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fricas [B] time = 0.65, size = 64, normalized size = 2.13 \begin {gather*} \frac {x e^{x} \log \relax (x) + 2 \, x e^{x} + {\left (e^{x} \log \relax (x) + 2 \, e^{x}\right )} e^{\left (e^{x}\right )} + {\left (x + e^{\left (e^{x}\right )}\right )} \log \left (-e^{\left (4 \, x\right )} + 2\right ) + x}{e^{x} \log \relax (x) + 2 \, e^{x} + \log \left (-e^{\left (4 \, x\right )} + 2\right )} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate((((exp(x)*exp(4*x)-2*exp(x))*exp(exp(x))+exp(4*x)-2)*log(-exp(4*x)+2)^2+(((2*exp(x)^2*exp(4*x)-4*exp

(x)^2)*log(x)+4*exp(x)^2*exp(4*x)-8*exp(x)^2)*exp(exp(x))+(2*exp(x)*exp(4*x)-4*exp(x))*log(x)+(4*exp(x)+1)*exp

(4*x)-8*exp(x)-2)*log(-exp(4*x)+2)+((exp(x)^3*exp(4*x)-2*exp(x)^3)*log(x)^2+(4*exp(x)^3*exp(4*x)-8*exp(x)^3)*l

og(x)+4*exp(x)^3*exp(4*x)-8*exp(x)^3)*exp(exp(x))+(exp(x)^2*exp(4*x)-2*exp(x)^2)*log(x)^2+((4*exp(x)^2+(-x+1)*

exp(x))*exp(4*x)-8*exp(x)^2+(2*x-2)*exp(x))*log(x)+(4*exp(x)^2+(1-2*x)*exp(x)-4*x)*exp(4*x)-8*exp(x)^2+(4*x-2)

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

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

*x)-8*exp(x)^2),x, algorithm="fricas")

[Out]

(x*e^x*log(x) + 2*x*e^x + (e^x*log(x) + 2*e^x)*e^(e^x) + (x + e^(e^x))*log(-e^(4*x) + 2) + x)/(e^x*log(x) + 2*

e^x + log(-e^(4*x) + 2))

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giac [B] time = 0.78, size = 736, normalized size = 24.53 result too large to display

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate((((exp(x)*exp(4*x)-2*exp(x))*exp(exp(x))+exp(4*x)-2)*log(-exp(4*x)+2)^2+(((2*exp(x)^2*exp(4*x)-4*exp

(x)^2)*log(x)+4*exp(x)^2*exp(4*x)-8*exp(x)^2)*exp(exp(x))+(2*exp(x)*exp(4*x)-4*exp(x))*log(x)+(4*exp(x)+1)*exp

(4*x)-8*exp(x)-2)*log(-exp(4*x)+2)+((exp(x)^3*exp(4*x)-2*exp(x)^3)*log(x)^2+(4*exp(x)^3*exp(4*x)-8*exp(x)^3)*l

og(x)+4*exp(x)^3*exp(4*x)-8*exp(x)^3)*exp(exp(x))+(exp(x)^2*exp(4*x)-2*exp(x)^2)*log(x)^2+((4*exp(x)^2+(-x+1)*

exp(x))*exp(4*x)-8*exp(x)^2+(2*x-2)*exp(x))*log(x)+(4*exp(x)^2+(1-2*x)*exp(x)-4*x)*exp(4*x)-8*exp(x)^2+(4*x-2)

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

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

*x)-8*exp(x)^2),x, algorithm="giac")

[Out]

(x^2*e^(6*x)*log(x)^2 - 2*x^2*e^(2*x)*log(x)^2 + x^2*e^(5*x)*log(x)*log(-e^(4*x) + 2) - 2*x^2*e^x*log(x)*log(-

e^(4*x) + 2) + 4*x^2*e^(6*x)*log(x) + 5*x^2*e^(5*x)*log(x) - 8*x^2*e^(2*x)*log(x) - 2*x^2*e^x*log(x) + x*e^(6*

x + e^x)*log(x)^2 - 2*x*e^(2*x + e^x)*log(x)^2 + 2*x^2*e^(5*x)*log(-e^(4*x) + 2) + 4*x^2*e^(4*x)*log(-e^(4*x)

+ 2) - 4*x^2*e^x*log(-e^(4*x) + 2) + x*e^(5*x + e^x)*log(x)*log(-e^(4*x) + 2) - 2*x*e^(x + e^x)*log(x)*log(-e^

(4*x) + 2) + 4*x^2*e^(6*x) + 10*x^2*e^(5*x) + 4*x^2*e^(4*x) - 8*x^2*e^(2*x) - 4*x^2*e^x + x*e^(6*x)*log(x) - 2

*x*e^(2*x)*log(x) + 4*x*e^(6*x + e^x)*log(x) + 4*x*e^(5*x + e^x)*log(x) - 8*x*e^(2*x + e^x)*log(x) + x*e^(5*x)

*log(-e^(4*x) + 2) + 2*x*e^(5*x + e^x)*log(-e^(4*x) + 2) + 4*x*e^(4*x + e^x)*log(-e^(4*x) + 2) - 4*x*e^(x + e^

x)*log(-e^(4*x) + 2) - 2*x*e^x*log(-e^(4*x) + 2) + 2*x*e^(6*x) + x*e^(5*x) - 4*x*e^(2*x) + 4*x*e^(6*x + e^x) +

8*x*e^(5*x + e^x) - 8*x*e^(2*x + e^x) - 2*x*e^x + e^(6*x + e^x)*log(x) - 2*e^(2*x + e^x)*log(x) + e^(5*x + e^

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

2 - 2*x*e^(2*x)*log(x)^2 + x*e^(5*x)*log(x)*log(-e^(4*x) + 2) - 2*x*e^x*log(x)*log(-e^(4*x) + 2) + 4*x*e^(6*x)

*log(x) + 4*x*e^(5*x)*log(x) - 8*x*e^(2*x)*log(x) + 2*x*e^(5*x)*log(-e^(4*x) + 2) + 4*x*e^(4*x)*log(-e^(4*x) +

2) - 4*x*e^x*log(-e^(4*x) + 2) + 4*x*e^(6*x) + 8*x*e^(5*x) - 8*x*e^(2*x) + e^(6*x)*log(x) - 2*e^(2*x)*log(x)

+ e^(5*x)*log(-e^(4*x) + 2) - 2*e^x*log(-e^(4*x) + 2) + 2*e^(6*x) - 4*e^(2*x))

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maple [A] time = 0.09, size = 29, normalized size = 0.97


method	result	size

risch	$x +{\mathrm e}^{{\mathrm e}^{x}}+\frac {x}{{\mathrm e}^{x} \ln \relax (x )+2 \,{\mathrm e}^{x}+\ln \left (-{\mathrm e}^{4 x}+2\right )}$	$29$

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int((((exp(x)*exp(4*x)-2*exp(x))*exp(exp(x))+exp(4*x)-2)*ln(-exp(4*x)+2)^2+(((2*exp(x)^2*exp(4*x)-4*exp(x)^2)*

ln(x)+4*exp(x)^2*exp(4*x)-8*exp(x)^2)*exp(exp(x))+(2*exp(x)*exp(4*x)-4*exp(x))*ln(x)+(4*exp(x)+1)*exp(4*x)-8*e

xp(x)-2)*ln(-exp(4*x)+2)+((exp(x)^3*exp(4*x)-2*exp(x)^3)*ln(x)^2+(4*exp(x)^3*exp(4*x)-8*exp(x)^3)*ln(x)+4*exp(

x)^3*exp(4*x)-8*exp(x)^3)*exp(exp(x))+(exp(x)^2*exp(4*x)-2*exp(x)^2)*ln(x)^2+((4*exp(x)^2+(1-x)*exp(x))*exp(4*

x)-8*exp(x)^2+(2*x-2)*exp(x))*ln(x)+(4*exp(x)^2+(1-2*x)*exp(x)-4*x)*exp(4*x)-8*exp(x)^2+(4*x-2)*exp(x))/((exp(

4*x)-2)*ln(-exp(4*x)+2)^2+((2*exp(x)*exp(4*x)-4*exp(x))*ln(x)+4*exp(x)*exp(4*x)-8*exp(x))*ln(-exp(4*x)+2)+(exp

(x)^2*exp(4*x)-2*exp(x)^2)*ln(x)^2+(4*exp(x)^2*exp(4*x)-8*exp(x)^2)*ln(x)+4*exp(x)^2*exp(4*x)-8*exp(x)^2),x,me

thod=_RETURNVERBOSE)

[Out]

x+exp(exp(x))+x/(exp(x)*ln(x)+2*exp(x)+ln(-exp(4*x)+2))

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maxima [B] time = 0.69, size = 58, normalized size = 1.93 \begin {gather*} \frac {{\left (\log \relax (x) + 2\right )} e^{\left (x + e^{x}\right )} + {\left (x \log \relax (x) + 2 \, x\right )} e^{x} + {\left (x + e^{\left (e^{x}\right )}\right )} \log \left (-e^{\left (4 \, x\right )} + 2\right ) + x}{{\left (\log \relax (x) + 2\right )} e^{x} + \log \left (-e^{\left (4 \, x\right )} + 2\right )} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate((((exp(x)*exp(4*x)-2*exp(x))*exp(exp(x))+exp(4*x)-2)*log(-exp(4*x)+2)^2+(((2*exp(x)^2*exp(4*x)-4*exp

(x)^2)*log(x)+4*exp(x)^2*exp(4*x)-8*exp(x)^2)*exp(exp(x))+(2*exp(x)*exp(4*x)-4*exp(x))*log(x)+(4*exp(x)+1)*exp

(4*x)-8*exp(x)-2)*log(-exp(4*x)+2)+((exp(x)^3*exp(4*x)-2*exp(x)^3)*log(x)^2+(4*exp(x)^3*exp(4*x)-8*exp(x)^3)*l

og(x)+4*exp(x)^3*exp(4*x)-8*exp(x)^3)*exp(exp(x))+(exp(x)^2*exp(4*x)-2*exp(x)^2)*log(x)^2+((4*exp(x)^2+(-x+1)*

exp(x))*exp(4*x)-8*exp(x)^2+(2*x-2)*exp(x))*log(x)+(4*exp(x)^2+(1-2*x)*exp(x)-4*x)*exp(4*x)-8*exp(x)^2+(4*x-2)

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

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

*x)-8*exp(x)^2),x, algorithm="maxima")

[Out]

((log(x) + 2)*e^(x + e^x) + (x*log(x) + 2*x)*e^x + (x + e^(e^x))*log(-e^(4*x) + 2) + x)/((log(x) + 2)*e^x + lo

g(-e^(4*x) + 2))

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mupad [F] time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int \frac {8\,{\mathrm {e}}^{2\,x}+\ln \left (2-{\mathrm {e}}^{4\,x}\right )\,\left (8\,{\mathrm {e}}^x+{\mathrm {e}}^{{\mathrm {e}}^x}\,\left (8\,{\mathrm {e}}^{2\,x}-4\,{\mathrm {e}}^{6\,x}+\ln \relax (x)\,\left (4\,{\mathrm {e}}^{2\,x}-2\,{\mathrm {e}}^{6\,x}\right )\right )-{\mathrm {e}}^{4\,x}\,\left (4\,{\mathrm {e}}^x+1\right )-\ln \relax (x)\,\left (2\,{\mathrm {e}}^{5\,x}-4\,{\mathrm {e}}^x\right )+2\right )+{\ln \relax (x)}^2\,\left (2\,{\mathrm {e}}^{2\,x}-{\mathrm {e}}^{6\,x}\right )-{\ln \left (2-{\mathrm {e}}^{4\,x}\right )}^2\,\left ({\mathrm {e}}^{4\,x}+{\mathrm {e}}^{{\mathrm {e}}^x}\,\left ({\mathrm {e}}^{5\,x}-2\,{\mathrm {e}}^x\right )-2\right )+{\mathrm {e}}^{{\mathrm {e}}^x}\,\left (\left (2\,{\mathrm {e}}^{3\,x}-{\mathrm {e}}^{7\,x}\right )\,{\ln \relax (x)}^2+\left (8\,{\mathrm {e}}^{3\,x}-4\,{\mathrm {e}}^{7\,x}\right )\,\ln \relax (x)+8\,{\mathrm {e}}^{3\,x}-4\,{\mathrm {e}}^{7\,x}\right )-\ln \relax (x)\,\left ({\mathrm {e}}^x\,\left (2\,x-2\right )-8\,{\mathrm {e}}^{2\,x}+{\mathrm {e}}^{4\,x}\,\left (4\,{\mathrm {e}}^{2\,x}-{\mathrm {e}}^x\,\left (x-1\right )\right )\right )-{\mathrm {e}}^x\,\left (4\,x-2\right )+{\mathrm {e}}^{4\,x}\,\left (4\,x-4\,{\mathrm {e}}^{2\,x}+{\mathrm {e}}^x\,\left (2\,x-1\right )\right )}{8\,{\mathrm {e}}^{2\,x}-4\,{\mathrm {e}}^{6\,x}+{\ln \relax (x)}^2\,\left (2\,{\mathrm {e}}^{2\,x}-{\mathrm {e}}^{6\,x}\right )-\ln \left (2-{\mathrm {e}}^{4\,x}\right )\,\left (4\,{\mathrm {e}}^{5\,x}-8\,{\mathrm {e}}^x+\ln \relax (x)\,\left (2\,{\mathrm {e}}^{5\,x}-4\,{\mathrm {e}}^x\right )\right )-{\ln \left (2-{\mathrm {e}}^{4\,x}\right )}^2\,\left ({\mathrm {e}}^{4\,x}-2\right )+\ln \relax (x)\,\left (8\,{\mathrm {e}}^{2\,x}-4\,{\mathrm {e}}^{6\,x}\right )} \,d x \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

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

exp(6*x))) - exp(4*x)*(4*exp(x) + 1) - log(x)*(2*exp(5*x) - 4*exp(x)) + 2) + log(x)^2*(2*exp(2*x) - exp(6*x))

- log(2 - exp(4*x))^2*(exp(4*x) + exp(exp(x))*(exp(5*x) - 2*exp(x)) - 2) + exp(exp(x))*(8*exp(3*x) - 4*exp(7*x

) + log(x)^2*(2*exp(3*x) - exp(7*x)) + log(x)*(8*exp(3*x) - 4*exp(7*x))) - log(x)*(exp(x)*(2*x - 2) - 8*exp(2*

x) + exp(4*x)*(4*exp(2*x) - exp(x)*(x - 1))) - exp(x)*(4*x - 2) + exp(4*x)*(4*x - 4*exp(2*x) + exp(x)*(2*x - 1

)))/(8*exp(2*x) - 4*exp(6*x) + log(x)^2*(2*exp(2*x) - exp(6*x)) - log(2 - exp(4*x))*(4*exp(5*x) - 8*exp(x) + l

og(x)*(2*exp(5*x) - 4*exp(x))) - log(2 - exp(4*x))^2*(exp(4*x) - 2) + log(x)*(8*exp(2*x) - 4*exp(6*x))),x)

[Out]

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

exp(6*x))) - exp(4*x)*(4*exp(x) + 1) - log(x)*(2*exp(5*x) - 4*exp(x)) + 2) + log(x)^2*(2*exp(2*x) - exp(6*x))

- log(2 - exp(4*x))^2*(exp(4*x) + exp(exp(x))*(exp(5*x) - 2*exp(x)) - 2) + exp(exp(x))*(8*exp(3*x) - 4*exp(7*x

) + log(x)^2*(2*exp(3*x) - exp(7*x)) + log(x)*(8*exp(3*x) - 4*exp(7*x))) - log(x)*(exp(x)*(2*x - 2) - 8*exp(2*

x) + exp(4*x)*(4*exp(2*x) - exp(x)*(x - 1))) - exp(x)*(4*x - 2) + exp(4*x)*(4*x - 4*exp(2*x) + exp(x)*(2*x - 1

)))/(8*exp(2*x) - 4*exp(6*x) + log(x)^2*(2*exp(2*x) - exp(6*x)) - log(2 - exp(4*x))*(4*exp(5*x) - 8*exp(x) + l

og(x)*(2*exp(5*x) - 4*exp(x))) - log(2 - exp(4*x))^2*(exp(4*x) - 2) + log(x)*(8*exp(2*x) - 4*exp(6*x))), x)

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sympy [A] time = 0.94, size = 27, normalized size = 0.90 \begin {gather*} x + \frac {x}{e^{x} \log {\relax (x )} + 2 e^{x} + \log {\left (2 - e^{4 x} \right )}} + e^{e^{x}} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate((((exp(x)*exp(4*x)-2*exp(x))*exp(exp(x))+exp(4*x)-2)*ln(-exp(4*x)+2)**2+(((2*exp(x)**2*exp(4*x)-4*ex

p(x)**2)*ln(x)+4*exp(x)**2*exp(4*x)-8*exp(x)**2)*exp(exp(x))+(2*exp(x)*exp(4*x)-4*exp(x))*ln(x)+(4*exp(x)+1)*e

xp(4*x)-8*exp(x)-2)*ln(-exp(4*x)+2)+((exp(x)**3*exp(4*x)-2*exp(x)**3)*ln(x)**2+(4*exp(x)**3*exp(4*x)-8*exp(x)*

*3)*ln(x)+4*exp(x)**3*exp(4*x)-8*exp(x)**3)*exp(exp(x))+(exp(x)**2*exp(4*x)-2*exp(x)**2)*ln(x)**2+((4*exp(x)**

2+(-x+1)*exp(x))*exp(4*x)-8*exp(x)**2+(2*x-2)*exp(x))*ln(x)+(4*exp(x)**2+(1-2*x)*exp(x)-4*x)*exp(4*x)-8*exp(x)

**2+(4*x-2)*exp(x))/((exp(4*x)-2)*ln(-exp(4*x)+2)**2+((2*exp(x)*exp(4*x)-4*exp(x))*ln(x)+4*exp(x)*exp(4*x)-8*e

xp(x))*ln(-exp(4*x)+2)+(exp(x)**2*exp(4*x)-2*exp(x)**2)*ln(x)**2+(4*exp(x)**2*exp(4*x)-8*exp(x)**2)*ln(x)+4*ex

p(x)**2*exp(4*x)-8*exp(x)**2),x)

[Out]

x + x/(exp(x)*log(x) + 2*exp(x) + log(2 - exp(4*x))) + exp(exp(x))

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