∫ ex2+2e3x4+e10−4xx4+e6x6+e2−2x(2e3x3+2e6x5) _____________________________________________________________________ e4−4x+2e2−2xx+x2 (4e12−6xx3+4e3x4+4e6x6+e4−4x(12e6x4+e3(6x2+4x3))+e2−2x(2x+4x2+12e6x5+e3(10x3+4x4))) __________________________________________________________________________________________________________________________________________________________________________________________________ −4e6−6x−12e4−4xx−12e2−2xx2−4x3+ex2+2e3x4+e10−4xx4+e6x6+e2−2x(2e3x3+2e6x5) _____________________________________________________________________ e4−4x+2e2−2xx+x2 (e6−6x+3e4−4xx+3e2−2xx2+x3) dx

3.15.61 $\int \frac {e^{\frac {x^2+2 e^3 x^4+e^{10-4 x} x^4+e^6 x^6+e^{2-2 x} (2 e^3 x^3+2 e^6 x^5)}{e^{4-4 x}+2 e^{2-2 x} x+x^2}} (4 e^{12-6 x} x^3+4 e^3 x^4+4 e^6 x^6+e^{4-4 x} (12 e^6 x^4+e^3 (6 x^2+4 x^3))+e^{2-2 x} (2 x+4 x^2+12 e^6 x^5+e^3 (10 x^3+4 x^4)))}{-4 e^{6-6 x}-12 e^{4-4 x} x-12 e^{2-2 x} x^2-4 x^3+e^{\frac {x^2+2 e^3 x^4+e^{10-4 x} x^4+e^6 x^6+e^{2-2 x} (2 e^3 x^3+2 e^6 x^5)}{e^{4-4 x}+2 e^{2-2 x} x+x^2}} (e^{6-6 x}+3 e^{4-4 x} x+3 e^{2-2 x} x^2+x^3)} \, dx$

Optimal. Leaf size=34 \[ \log \left (\frac {3}{2} \left (-4+e^{\left (e^3 x^2+\frac {x}{e^{2 (1-x)}+x}\right )^2}\right )\right ) \]

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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[(E^((x^2 + 2*E^3*x^4 + E^(10 - 4*x)*x^4 + E^6*x^6 + E^(2 - 2*x)*(2*E^3*x^3 + 2*E^6*x^5))/(E^(4 - 4*x) + 2*

E^(2 - 2*x)*x + x^2))*(4*E^(12 - 6*x)*x^3 + 4*E^3*x^4 + 4*E^6*x^6 + E^(4 - 4*x)*(12*E^6*x^4 + E^3*(6*x^2 + 4*x

^3)) + E^(2 - 2*x)*(2*x + 4*x^2 + 12*E^6*x^5 + E^3*(10*x^3 + 4*x^4))))/(-4*E^(6 - 6*x) - 12*E^(4 - 4*x)*x - 12

*E^(2 - 2*x)*x^2 - 4*x^3 + E^((x^2 + 2*E^3*x^4 + E^(10 - 4*x)*x^4 + E^6*x^6 + E^(2 - 2*x)*(2*E^3*x^3 + 2*E^6*x

^5))/(E^(4 - 4*x) + 2*E^(2 - 2*x)*x + x^2))*(E^(6 - 6*x) + 3*E^(4 - 4*x)*x + 3*E^(2 - 2*x)*x^2 + x^3)),x]

[Out]

$Aborted

Rubi steps

Aborted

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Mathematica [A] time = 0.69, size = 67, normalized size = 1.97 \begin {gather*} \log \left (4-e^{1+2 e^3 x^2+e^6 x^4+\frac {e^4}{\left (e^2+e^{2 x} x\right )^2}-\frac {2 \left (e^2+e^5 x^2\right )}{e^2+e^{2 x} x}}\right ) \end {gather*}

Antiderivative was successfully veriﬁed.

[In]

Integrate[(E^((x^2 + 2*E^3*x^4 + E^(10 - 4*x)*x^4 + E^6*x^6 + E^(2 - 2*x)*(2*E^3*x^3 + 2*E^6*x^5))/(E^(4 - 4*x

) + 2*E^(2 - 2*x)*x + x^2))*(4*E^(12 - 6*x)*x^3 + 4*E^3*x^4 + 4*E^6*x^6 + E^(4 - 4*x)*(12*E^6*x^4 + E^3*(6*x^2

+ 4*x^3)) + E^(2 - 2*x)*(2*x + 4*x^2 + 12*E^6*x^5 + E^3*(10*x^3 + 4*x^4))))/(-4*E^(6 - 6*x) - 12*E^(4 - 4*x)*

x - 12*E^(2 - 2*x)*x^2 - 4*x^3 + E^((x^2 + 2*E^3*x^4 + E^(10 - 4*x)*x^4 + E^6*x^6 + E^(2 - 2*x)*(2*E^3*x^3 + 2

*E^6*x^5))/(E^(4 - 4*x) + 2*E^(2 - 2*x)*x + x^2))*(E^(6 - 6*x) + 3*E^(4 - 4*x)*x + 3*E^(2 - 2*x)*x^2 + x^3)),x

]

[Out]

Log[4 - E^(1 + 2*E^3*x^2 + E^6*x^4 + E^4/(E^2 + E^(2*x)*x)^2 - (2*(E^2 + E^5*x^2))/(E^2 + E^(2*x)*x))]

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fricas [B] time = 0.78, size = 80, normalized size = 2.35 \begin {gather*} \log \left (e^{\left (\frac {x^{6} e^{10} + 2 \, x^{4} e^{7} + x^{4} e^{\left (-4 \, x + 14\right )} + x^{2} e^{4} + 2 \, {\left (x^{5} e^{8} + x^{3} e^{5}\right )} e^{\left (-2 \, x + 4\right )}}{x^{2} e^{4} + 2 \, x e^{\left (-2 \, x + 6\right )} + e^{\left (-4 \, x + 8\right )}}\right )} - 4\right ) \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate((4*x^3*exp(3)^2*exp(-2*x+2)^3+(12*x^4*exp(3)^2+(4*x^3+6*x^2)*exp(3))*exp(-2*x+2)^2+(12*x^5*exp(3)^2+

(4*x^4+10*x^3)*exp(3)+4*x^2+2*x)*exp(-2*x+2)+4*x^6*exp(3)^2+4*x^4*exp(3))*exp((x^4*exp(3)^2*exp(-2*x+2)^2+(2*x

^5*exp(3)^2+2*x^3*exp(3))*exp(-2*x+2)+x^6*exp(3)^2+2*x^4*exp(3)+x^2)/(exp(-2*x+2)^2+2*x*exp(-2*x+2)+x^2))/((ex

p(-2*x+2)^3+3*x*exp(-2*x+2)^2+3*x^2*exp(-2*x+2)+x^3)*exp((x^4*exp(3)^2*exp(-2*x+2)^2+(2*x^5*exp(3)^2+2*x^3*exp

(3))*exp(-2*x+2)+x^6*exp(3)^2+2*x^4*exp(3)+x^2)/(exp(-2*x+2)^2+2*x*exp(-2*x+2)+x^2))-4*exp(-2*x+2)^3-12*x*exp(

-2*x+2)^2-12*x^2*exp(-2*x+2)-4*x^3),x, algorithm="fricas")

[Out]

log(e^((x^6*e^10 + 2*x^4*e^7 + x^4*e^(-4*x + 14) + x^2*e^4 + 2*(x^5*e^8 + x^3*e^5)*e^(-2*x + 4))/(x^2*e^4 + 2*

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

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giac [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((4*x^3*exp(3)^2*exp(-2*x+2)^3+(12*x^4*exp(3)^2+(4*x^3+6*x^2)*exp(3))*exp(-2*x+2)^2+(12*x^5*exp(3)^2+

(4*x^4+10*x^3)*exp(3)+4*x^2+2*x)*exp(-2*x+2)+4*x^6*exp(3)^2+4*x^4*exp(3))*exp((x^4*exp(3)^2*exp(-2*x+2)^2+(2*x

^5*exp(3)^2+2*x^3*exp(3))*exp(-2*x+2)+x^6*exp(3)^2+2*x^4*exp(3)+x^2)/(exp(-2*x+2)^2+2*x*exp(-2*x+2)+x^2))/((ex

p(-2*x+2)^3+3*x*exp(-2*x+2)^2+3*x^2*exp(-2*x+2)+x^3)*exp((x^4*exp(3)^2*exp(-2*x+2)^2+(2*x^5*exp(3)^2+2*x^3*exp

(3))*exp(-2*x+2)+x^6*exp(3)^2+2*x^4*exp(3)+x^2)/(exp(-2*x+2)^2+2*x*exp(-2*x+2)+x^2))-4*exp(-2*x+2)^3-12*x*exp(

-2*x+2)^2-12*x^2*exp(-2*x+2)-4*x^3),x, algorithm="giac")

[Out]

Timed out

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maple [B] time = 0.55, size = 186, normalized size = 5.47


method	result	size

risch	$x^{4} {\mathrm e}^{6}+\frac {x^{2} \left (2 x^{2} {\mathrm e}^{3}+2 x \,{\mathrm e}^{-2 x +5}+1\right )}{\left (x +{\mathrm e}^{-2 x +2}\right )^{2}}-\frac {x^{4} {\mathrm e}^{10-4 x}+\left (2 x^{5} {\mathrm e}^{6}+2 x^{3} {\mathrm e}^{3}\right ) {\mathrm e}^{-2 x +2}+x^{6} {\mathrm e}^{6}+2 x^{4} {\mathrm e}^{3}+x^{2}}{{\mathrm e}^{-4 x +4}+2 x \,{\mathrm e}^{-2 x +2}+x^{2}}+\ln \left ({\mathrm e}^{\frac {x^{2} \left (2 x^{3} {\mathrm e}^{-2 x +8}+x^{4} {\mathrm e}^{6}+2 x \,{\mathrm e}^{-2 x +5}+2 x^{2} {\mathrm e}^{3}+{\mathrm e}^{10-4 x} x^{2}+1\right )}{{\mathrm e}^{-4 x +4}+2 x \,{\mathrm e}^{-2 x +2}+x^{2}}}-4\right )$	$186$

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int((4*x^3*exp(3)^2*exp(-2*x+2)^3+(12*x^4*exp(3)^2+(4*x^3+6*x^2)*exp(3))*exp(-2*x+2)^2+(12*x^5*exp(3)^2+(4*x^4

+10*x^3)*exp(3)+4*x^2+2*x)*exp(-2*x+2)+4*x^6*exp(3)^2+4*x^4*exp(3))*exp((x^4*exp(3)^2*exp(-2*x+2)^2+(2*x^5*exp

(3)^2+2*x^3*exp(3))*exp(-2*x+2)+x^6*exp(3)^2+2*x^4*exp(3)+x^2)/(exp(-2*x+2)^2+2*x*exp(-2*x+2)+x^2))/((exp(-2*x

+2)^3+3*x*exp(-2*x+2)^2+3*x^2*exp(-2*x+2)+x^3)*exp((x^4*exp(3)^2*exp(-2*x+2)^2+(2*x^5*exp(3)^2+2*x^3*exp(3))*e

xp(-2*x+2)+x^6*exp(3)^2+2*x^4*exp(3)+x^2)/(exp(-2*x+2)^2+2*x*exp(-2*x+2)+x^2))-4*exp(-2*x+2)^3-12*x*exp(-2*x+2

)^2-12*x^2*exp(-2*x+2)-4*x^3),x,method=_RETURNVERBOSE)

[Out]

x^4*exp(6)+x^2*(2*x^2*exp(3)+2*x*exp(-2*x+5)+1)/(x+exp(-2*x+2))^2-(x^4*exp(10-4*x)+(2*x^5*exp(6)+2*x^3*exp(3))

*exp(-2*x+2)+x^6*exp(6)+2*x^4*exp(3)+x^2)/(exp(-4*x+4)+2*x*exp(-2*x+2)+x^2)+ln(exp(x^2*(2*x^3*exp(-2*x+8)+x^4*

exp(6)+2*x*exp(-2*x+5)+2*x^2*exp(3)+exp(10-4*x)*x^2+1)/(exp(-4*x+4)+2*x*exp(-2*x+2)+x^2))-4)

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maxima [B] time = 2.52, size = 167, normalized size = 4.91 \begin {gather*} \frac {x^{4} e^{8} + {\left (x^{5} e^{6} + 2 \, x^{3} e^{3}\right )} e^{\left (2 \, x\right )} - 2 \, e^{2}}{x e^{\left (2 \, x\right )} + e^{2}} + \log \left ({\left (e^{\left (x^{4} e^{6} + 2 \, x^{2} e^{3} + \frac {e^{4}}{x^{2} e^{\left (4 \, x\right )} + 2 \, x e^{\left (2 \, x + 2\right )} + e^{4}} + 2 \, e^{\left (-4 \, x + 7\right )} + 1\right )} - 4 \, e^{\left (2 \, x e^{\left (-2 \, x + 5\right )} + \frac {2 \, e^{9}}{x e^{\left (6 \, x\right )} + e^{\left (4 \, x + 2\right )}} + \frac {2 \, e^{2}}{x e^{\left (2 \, x\right )} + e^{2}}\right )}\right )} e^{\left (-x^{4} e^{6} - 2 \, x^{2} e^{3} - 2 \, e^{\left (-4 \, x + 7\right )} - 1\right )}\right ) \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate((4*x^3*exp(3)^2*exp(-2*x+2)^3+(12*x^4*exp(3)^2+(4*x^3+6*x^2)*exp(3))*exp(-2*x+2)^2+(12*x^5*exp(3)^2+

(4*x^4+10*x^3)*exp(3)+4*x^2+2*x)*exp(-2*x+2)+4*x^6*exp(3)^2+4*x^4*exp(3))*exp((x^4*exp(3)^2*exp(-2*x+2)^2+(2*x

^5*exp(3)^2+2*x^3*exp(3))*exp(-2*x+2)+x^6*exp(3)^2+2*x^4*exp(3)+x^2)/(exp(-2*x+2)^2+2*x*exp(-2*x+2)+x^2))/((ex

p(-2*x+2)^3+3*x*exp(-2*x+2)^2+3*x^2*exp(-2*x+2)+x^3)*exp((x^4*exp(3)^2*exp(-2*x+2)^2+(2*x^5*exp(3)^2+2*x^3*exp

(3))*exp(-2*x+2)+x^6*exp(3)^2+2*x^4*exp(3)+x^2)/(exp(-2*x+2)^2+2*x*exp(-2*x+2)+x^2))-4*exp(-2*x+2)^3-12*x*exp(

-2*x+2)^2-12*x^2*exp(-2*x+2)-4*x^3),x, algorithm="maxima")

[Out]

(x^4*e^8 + (x^5*e^6 + 2*x^3*e^3)*e^(2*x) - 2*e^2)/(x*e^(2*x) + e^2) + log((e^(x^4*e^6 + 2*x^2*e^3 + e^4/(x^2*e

^(4*x) + 2*x*e^(2*x + 2) + e^4) + 2*e^(-4*x + 7) + 1) - 4*e^(2*x*e^(-2*x + 5) + 2*e^9/(x*e^(6*x) + e^(4*x + 2)

) + 2*e^2/(x*e^(2*x) + e^2)))*e^(-x^4*e^6 - 2*x^2*e^3 - 2*e^(-4*x + 7) - 1))

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mupad [B] time = 1.98, size = 191, normalized size = 5.62 \begin {gather*} \ln \left ({\mathrm {e}}^{\frac {2\,x^4\,{\mathrm {e}}^3}{{\mathrm {e}}^{-4\,x}\,{\mathrm {e}}^4+x^2+2\,x\,{\mathrm {e}}^{-2\,x}\,{\mathrm {e}}^2}}\,{\mathrm {e}}^{\frac {x^6\,{\mathrm {e}}^6}{{\mathrm {e}}^{-4\,x}\,{\mathrm {e}}^4+x^2+2\,x\,{\mathrm {e}}^{-2\,x}\,{\mathrm {e}}^2}}\,{\mathrm {e}}^{\frac {2\,x^3\,{\mathrm {e}}^{-2\,x}\,{\mathrm {e}}^5}{{\mathrm {e}}^{-4\,x}\,{\mathrm {e}}^4+x^2+2\,x\,{\mathrm {e}}^{-2\,x}\,{\mathrm {e}}^2}}\,{\mathrm {e}}^{\frac {2\,x^5\,{\mathrm {e}}^{-2\,x}\,{\mathrm {e}}^8}{{\mathrm {e}}^{-4\,x}\,{\mathrm {e}}^4+x^2+2\,x\,{\mathrm {e}}^{-2\,x}\,{\mathrm {e}}^2}}\,{\mathrm {e}}^{\frac {x^4\,{\mathrm {e}}^{-4\,x}\,{\mathrm {e}}^{10}}{{\mathrm {e}}^{-4\,x}\,{\mathrm {e}}^4+x^2+2\,x\,{\mathrm {e}}^{-2\,x}\,{\mathrm {e}}^2}}\,{\mathrm {e}}^{\frac {x^2}{{\mathrm {e}}^{-4\,x}\,{\mathrm {e}}^4+x^2+2\,x\,{\mathrm {e}}^{-2\,x}\,{\mathrm {e}}^2}}-4\right ) \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp((exp(2 - 2*x)*(2*x^3*exp(3) + 2*x^5*exp(6)) + 2*x^4*exp(3) + x^6*exp(6) + x^2 + x^4*exp(6)*exp(4 - 4

*x))/(exp(4 - 4*x) + 2*x*exp(2 - 2*x) + x^2))*(exp(4 - 4*x)*(exp(3)*(6*x^2 + 4*x^3) + 12*x^4*exp(6)) + exp(2 -

2*x)*(2*x + exp(3)*(10*x^3 + 4*x^4) + 12*x^5*exp(6) + 4*x^2) + 4*x^4*exp(3) + 4*x^6*exp(6) + 4*x^3*exp(6)*exp

(6 - 6*x)))/(4*exp(6 - 6*x) - exp((exp(2 - 2*x)*(2*x^3*exp(3) + 2*x^5*exp(6)) + 2*x^4*exp(3) + x^6*exp(6) + x^

2 + x^4*exp(6)*exp(4 - 4*x))/(exp(4 - 4*x) + 2*x*exp(2 - 2*x) + x^2))*(exp(6 - 6*x) + 3*x*exp(4 - 4*x) + 3*x^2

*exp(2 - 2*x) + x^3) + 12*x*exp(4 - 4*x) + 12*x^2*exp(2 - 2*x) + 4*x^3),x)

[Out]

log(exp((2*x^4*exp(3))/(exp(-4*x)*exp(4) + x^2 + 2*x*exp(-2*x)*exp(2)))*exp((x^6*exp(6))/(exp(-4*x)*exp(4) + x

^2 + 2*x*exp(-2*x)*exp(2)))*exp((2*x^3*exp(-2*x)*exp(5))/(exp(-4*x)*exp(4) + x^2 + 2*x*exp(-2*x)*exp(2)))*exp(

(2*x^5*exp(-2*x)*exp(8))/(exp(-4*x)*exp(4) + x^2 + 2*x*exp(-2*x)*exp(2)))*exp((x^4*exp(-4*x)*exp(10))/(exp(-4*

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

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sympy [B] time = 1.85, size = 80, normalized size = 2.35 \begin {gather*} \log {\left (e^{\frac {x^{6} e^{6} + x^{4} e^{6} e^{4 - 4 x} + 2 x^{4} e^{3} + x^{2} + \left (2 x^{5} e^{6} + 2 x^{3} e^{3}\right ) e^{2 - 2 x}}{x^{2} + 2 x e^{2 - 2 x} + e^{4 - 4 x}}} - 4 \right )} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate((4*x**3*exp(3)**2*exp(-2*x+2)**3+(12*x**4*exp(3)**2+(4*x**3+6*x**2)*exp(3))*exp(-2*x+2)**2+(12*x**5*

exp(3)**2+(4*x**4+10*x**3)*exp(3)+4*x**2+2*x)*exp(-2*x+2)+4*x**6*exp(3)**2+4*x**4*exp(3))*exp((x**4*exp(3)**2*

exp(-2*x+2)**2+(2*x**5*exp(3)**2+2*x**3*exp(3))*exp(-2*x+2)+x**6*exp(3)**2+2*x**4*exp(3)+x**2)/(exp(-2*x+2)**2

+2*x*exp(-2*x+2)+x**2))/((exp(-2*x+2)**3+3*x*exp(-2*x+2)**2+3*x**2*exp(-2*x+2)+x**3)*exp((x**4*exp(3)**2*exp(-

2*x+2)**2+(2*x**5*exp(3)**2+2*x**3*exp(3))*exp(-2*x+2)+x**6*exp(3)**2+2*x**4*exp(3)+x**2)/(exp(-2*x+2)**2+2*x*

exp(-2*x+2)+x**2))-4*exp(-2*x+2)**3-12*x*exp(-2*x+2)**2-12*x**2*exp(-2*x+2)-4*x**3),x)

[Out]

log(exp((x**6*exp(6) + x**4*exp(6)*exp(4 - 4*x) + 2*x**4*exp(3) + x**2 + (2*x**5*exp(6) + 2*x**3*exp(3))*exp(2

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

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