3.57.49 \(\int \frac {e^{\frac {-7 x+e^{36+e^4+12 x^2+x^4+e^2 (-12-2 x^2)} x}{16+\log (x)}} (-105+e^{36+e^4+12 x^2+x^4+e^2 (-12-2 x^2)} (15+384 x^2-64 e^2 x^2+64 x^4)+(-7+e^{36+e^4+12 x^2+x^4+e^2 (-12-2 x^2)} (1+24 x^2-4 e^2 x^2+4 x^4)) \log (x))}{256+32 \log (x)+\log ^2(x)} \, dx\)

Optimal. Leaf size=26 \[ e^{\frac {\left (-7+e^{\left (-6+e^2-x^2\right )^2}\right ) x}{16+\log (x)}} \]

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Rubi [F]  time = 68.24, 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*} \int \frac {\exp \left (\frac {-7 x+e^{36+e^4+12 x^2+x^4+e^2 \left (-12-2 x^2\right )} x}{16+\log (x)}\right ) \left (-105+e^{36+e^4+12 x^2+x^4+e^2 \left (-12-2 x^2\right )} \left (15+384 x^2-64 e^2 x^2+64 x^4\right )+\left (-7+e^{36+e^4+12 x^2+x^4+e^2 \left (-12-2 x^2\right )} \left (1+24 x^2-4 e^2 x^2+4 x^4\right )\right ) \log (x)\right )}{256+32 \log (x)+\log ^2(x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^((-7*x + E^(36 + E^4 + 12*x^2 + x^4 + E^2*(-12 - 2*x^2))*x)/(16 + Log[x]))*(-105 + E^(36 + E^4 + 12*x^2
+ x^4 + E^2*(-12 - 2*x^2))*(15 + 384*x^2 - 64*E^2*x^2 + 64*x^4) + (-7 + E^(36 + E^4 + 12*x^2 + x^4 + E^2*(-12
- 2*x^2))*(1 + 24*x^2 - 4*E^2*x^2 + 4*x^4))*Log[x]))/(256 + 32*Log[x] + Log[x]^2),x]

[Out]

7*Defer[Int][E^(((-7 + E^(6 - E^2 + x^2)^2)*x)/(16 + Log[x]))/(16 + Log[x])^2, x] - Defer[Int][E^((-6 + E^2)^2
+ 2*(6 - E^2)*x^2 + x^4 + ((-7 + E^(6 - E^2 + x^2)^2)*x)/(16 + Log[x]))/(16 + Log[x])^2, x] - 7*Defer[Int][E^
(((-7 + E^(6 - E^2 + x^2)^2)*x)/(16 + Log[x]))/(16 + Log[x]), x] + Defer[Int][E^((-6 + E^2)^2 + 2*(6 - E^2)*x^
2 + x^4 + ((-7 + E^(6 - E^2 + x^2)^2)*x)/(16 + Log[x]))/(16 + Log[x]), x] + 4*(6 - E^2)*Defer[Int][(E^((-6 + E
^2)^2 + 2*(6 - E^2)*x^2 + x^4 + ((-7 + E^(6 - E^2 + x^2)^2)*x)/(16 + Log[x]))*x^2)/(16 + Log[x]), x] + 4*Defer
[Int][(E^((-6 + E^2)^2 + 2*(6 - E^2)*x^2 + x^4 + ((-7 + E^(6 - E^2 + x^2)^2)*x)/(16 + Log[x]))*x^4)/(16 + Log[
x]), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {\exp \left (\frac {-7 x+e^{36+e^4+12 x^2+x^4+e^2 \left (-12-2 x^2\right )} x}{16+\log (x)}\right ) \left (-105+e^{36+e^4+12 x^2+x^4+e^2 \left (-12-2 x^2\right )} \left (15+384 x^2-64 e^2 x^2+64 x^4\right )+\left (-7+e^{36+e^4+12 x^2+x^4+e^2 \left (-12-2 x^2\right )} \left (1+24 x^2-4 e^2 x^2+4 x^4\right )\right ) \log (x)\right )}{(16+\log (x))^2} \, dx\\ &=\int \frac {e^{\frac {\left (-7+e^{\left (6-e^2+x^2\right )^2}\right ) x}{16+\log (x)}} \left (-105+e^{\left (6-e^2+x^2\right )^2} \left (15-64 \left (-6+e^2\right ) x^2+64 x^4\right )+\left (-7+e^{\left (6-e^2+x^2\right )^2} \left (1-4 \left (-6+e^2\right ) x^2+4 x^4\right )\right ) \log (x)\right )}{(16+\log (x))^2} \, dx\\ &=\int \left (-\frac {7 e^{\frac {\left (-7+e^{\left (6-e^2+x^2\right )^2}\right ) x}{16+\log (x)}} (15+\log (x))}{(16+\log (x))^2}+\frac {\exp \left (\left (-6+e^2\right )^2+2 \left (6-e^2\right ) x^2+x^4+\frac {\left (-7+e^{\left (6-e^2+x^2\right )^2}\right ) x}{16+\log (x)}\right ) \left (15+384 \left (1-\frac {e^2}{6}\right ) x^2+64 x^4+\log (x)+24 \left (1-\frac {e^2}{6}\right ) x^2 \log (x)+4 x^4 \log (x)\right )}{(16+\log (x))^2}\right ) \, dx\\ &=-\left (7 \int \frac {e^{\frac {\left (-7+e^{\left (6-e^2+x^2\right )^2}\right ) x}{16+\log (x)}} (15+\log (x))}{(16+\log (x))^2} \, dx\right )+\int \frac {\exp \left (\left (-6+e^2\right )^2+2 \left (6-e^2\right ) x^2+x^4+\frac {\left (-7+e^{\left (6-e^2+x^2\right )^2}\right ) x}{16+\log (x)}\right ) \left (15+384 \left (1-\frac {e^2}{6}\right ) x^2+64 x^4+\log (x)+24 \left (1-\frac {e^2}{6}\right ) x^2 \log (x)+4 x^4 \log (x)\right )}{(16+\log (x))^2} \, dx\\ &=-\left (7 \int \left (-\frac {e^{\frac {\left (-7+e^{\left (6-e^2+x^2\right )^2}\right ) x}{16+\log (x)}}}{(16+\log (x))^2}+\frac {e^{\frac {\left (-7+e^{\left (6-e^2+x^2\right )^2}\right ) x}{16+\log (x)}}}{16+\log (x)}\right ) \, dx\right )+\int \left (-\frac {\exp \left (\left (-6+e^2\right )^2+2 \left (6-e^2\right ) x^2+x^4+\frac {\left (-7+e^{\left (6-e^2+x^2\right )^2}\right ) x}{16+\log (x)}\right )}{(16+\log (x))^2}+\frac {\exp \left (\left (-6+e^2\right )^2+2 \left (6-e^2\right ) x^2+x^4+\frac {\left (-7+e^{\left (6-e^2+x^2\right )^2}\right ) x}{16+\log (x)}\right ) \left (1+4 \left (6-e^2\right ) x^2+4 x^4\right )}{16+\log (x)}\right ) \, dx\\ &=7 \int \frac {e^{\frac {\left (-7+e^{\left (6-e^2+x^2\right )^2}\right ) x}{16+\log (x)}}}{(16+\log (x))^2} \, dx-7 \int \frac {e^{\frac {\left (-7+e^{\left (6-e^2+x^2\right )^2}\right ) x}{16+\log (x)}}}{16+\log (x)} \, dx-\int \frac {\exp \left (\left (-6+e^2\right )^2+2 \left (6-e^2\right ) x^2+x^4+\frac {\left (-7+e^{\left (6-e^2+x^2\right )^2}\right ) x}{16+\log (x)}\right )}{(16+\log (x))^2} \, dx+\int \frac {\exp \left (\left (-6+e^2\right )^2+2 \left (6-e^2\right ) x^2+x^4+\frac {\left (-7+e^{\left (6-e^2+x^2\right )^2}\right ) x}{16+\log (x)}\right ) \left (1+4 \left (6-e^2\right ) x^2+4 x^4\right )}{16+\log (x)} \, dx\\ &=7 \int \frac {e^{\frac {\left (-7+e^{\left (6-e^2+x^2\right )^2}\right ) x}{16+\log (x)}}}{(16+\log (x))^2} \, dx-7 \int \frac {e^{\frac {\left (-7+e^{\left (6-e^2+x^2\right )^2}\right ) x}{16+\log (x)}}}{16+\log (x)} \, dx-\int \frac {\exp \left (\left (-6+e^2\right )^2+2 \left (6-e^2\right ) x^2+x^4+\frac {\left (-7+e^{\left (6-e^2+x^2\right )^2}\right ) x}{16+\log (x)}\right )}{(16+\log (x))^2} \, dx+\int \left (\frac {\exp \left (\left (-6+e^2\right )^2+2 \left (6-e^2\right ) x^2+x^4+\frac {\left (-7+e^{\left (6-e^2+x^2\right )^2}\right ) x}{16+\log (x)}\right )}{16+\log (x)}-\frac {4 \exp \left (\left (-6+e^2\right )^2+2 \left (6-e^2\right ) x^2+x^4+\frac {\left (-7+e^{\left (6-e^2+x^2\right )^2}\right ) x}{16+\log (x)}\right ) \left (-6+e^2\right ) x^2}{16+\log (x)}+\frac {4 \exp \left (\left (-6+e^2\right )^2+2 \left (6-e^2\right ) x^2+x^4+\frac {\left (-7+e^{\left (6-e^2+x^2\right )^2}\right ) x}{16+\log (x)}\right ) x^4}{16+\log (x)}\right ) \, dx\\ &=4 \int \frac {\exp \left (\left (-6+e^2\right )^2+2 \left (6-e^2\right ) x^2+x^4+\frac {\left (-7+e^{\left (6-e^2+x^2\right )^2}\right ) x}{16+\log (x)}\right ) x^4}{16+\log (x)} \, dx+7 \int \frac {e^{\frac {\left (-7+e^{\left (6-e^2+x^2\right )^2}\right ) x}{16+\log (x)}}}{(16+\log (x))^2} \, dx-7 \int \frac {e^{\frac {\left (-7+e^{\left (6-e^2+x^2\right )^2}\right ) x}{16+\log (x)}}}{16+\log (x)} \, dx+\left (4 \left (6-e^2\right )\right ) \int \frac {\exp \left (\left (-6+e^2\right )^2+2 \left (6-e^2\right ) x^2+x^4+\frac {\left (-7+e^{\left (6-e^2+x^2\right )^2}\right ) x}{16+\log (x)}\right ) x^2}{16+\log (x)} \, dx-\int \frac {\exp \left (\left (-6+e^2\right )^2+2 \left (6-e^2\right ) x^2+x^4+\frac {\left (-7+e^{\left (6-e^2+x^2\right )^2}\right ) x}{16+\log (x)}\right )}{(16+\log (x))^2} \, dx+\int \frac {\exp \left (\left (-6+e^2\right )^2+2 \left (6-e^2\right ) x^2+x^4+\frac {\left (-7+e^{\left (6-e^2+x^2\right )^2}\right ) x}{16+\log (x)}\right )}{16+\log (x)} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [F]  time = 15.48, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {e^{\frac {-7 x+e^{36+e^4+12 x^2+x^4+e^2 \left (-12-2 x^2\right )} x}{16+\log (x)}} \left (-105+e^{36+e^4+12 x^2+x^4+e^2 \left (-12-2 x^2\right )} \left (15+384 x^2-64 e^2 x^2+64 x^4\right )+\left (-7+e^{36+e^4+12 x^2+x^4+e^2 \left (-12-2 x^2\right )} \left (1+24 x^2-4 e^2 x^2+4 x^4\right )\right ) \log (x)\right )}{256+32 \log (x)+\log ^2(x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[(E^((-7*x + E^(36 + E^4 + 12*x^2 + x^4 + E^2*(-12 - 2*x^2))*x)/(16 + Log[x]))*(-105 + E^(36 + E^4 +
12*x^2 + x^4 + E^2*(-12 - 2*x^2))*(15 + 384*x^2 - 64*E^2*x^2 + 64*x^4) + (-7 + E^(36 + E^4 + 12*x^2 + x^4 + E^
2*(-12 - 2*x^2))*(1 + 24*x^2 - 4*E^2*x^2 + 4*x^4))*Log[x]))/(256 + 32*Log[x] + Log[x]^2),x]

[Out]

Integrate[(E^((-7*x + E^(36 + E^4 + 12*x^2 + x^4 + E^2*(-12 - 2*x^2))*x)/(16 + Log[x]))*(-105 + E^(36 + E^4 +
12*x^2 + x^4 + E^2*(-12 - 2*x^2))*(15 + 384*x^2 - 64*E^2*x^2 + 64*x^4) + (-7 + E^(36 + E^4 + 12*x^2 + x^4 + E^
2*(-12 - 2*x^2))*(1 + 24*x^2 - 4*E^2*x^2 + 4*x^4))*Log[x]))/(256 + 32*Log[x] + Log[x]^2), x]

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fricas [A]  time = 0.68, size = 36, normalized size = 1.38 \begin {gather*} e^{\left (\frac {x e^{\left (x^{4} + 12 \, x^{2} - 2 \, {\left (x^{2} + 6\right )} e^{2} + e^{4} + 36\right )} - 7 \, x}{\log \relax (x) + 16}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-4*x^2*exp(2)+4*x^4+24*x^2+1)*exp(exp(2)^2+(-2*x^2-12)*exp(2)+x^4+12*x^2+36)-7)*log(x)+(-64*x^2*e
xp(2)+64*x^4+384*x^2+15)*exp(exp(2)^2+(-2*x^2-12)*exp(2)+x^4+12*x^2+36)-105)*exp((x*exp(exp(2)^2+(-2*x^2-12)*e
xp(2)+x^4+12*x^2+36)-7*x)/(16+log(x)))/(log(x)^2+32*log(x)+256),x, algorithm="fricas")

[Out]

e^((x*e^(x^4 + 12*x^2 - 2*(x^2 + 6)*e^2 + e^4 + 36) - 7*x)/(log(x) + 16))

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giac [A]  time = 0.78, size = 43, normalized size = 1.65 \begin {gather*} e^{\left (\frac {x e^{\left (x^{4} - 2 \, x^{2} e^{2} + 12 \, x^{2} + e^{4} - 12 \, e^{2} + 36\right )}}{\log \relax (x) + 16} - \frac {7 \, x}{\log \relax (x) + 16}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-4*x^2*exp(2)+4*x^4+24*x^2+1)*exp(exp(2)^2+(-2*x^2-12)*exp(2)+x^4+12*x^2+36)-7)*log(x)+(-64*x^2*e
xp(2)+64*x^4+384*x^2+15)*exp(exp(2)^2+(-2*x^2-12)*exp(2)+x^4+12*x^2+36)-105)*exp((x*exp(exp(2)^2+(-2*x^2-12)*e
xp(2)+x^4+12*x^2+36)-7*x)/(16+log(x)))/(log(x)^2+32*log(x)+256),x, algorithm="giac")

[Out]

e^(x*e^(x^4 - 2*x^2*e^2 + 12*x^2 + e^4 - 12*e^2 + 36)/(log(x) + 16) - 7*x/(log(x) + 16))

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maple [A]  time = 0.06, size = 36, normalized size = 1.38

method	result	size
risch	\({\mathrm e}^{\frac {x \left ({\mathrm e}^{x^{4}-2 x^{2} {\mathrm e}^{2}+12 x^{2}-12 \,{\mathrm e}^{2}+{\mathrm e}^{4}+36}-7\right )}{16+\ln \relax (x )}}\)	\(36\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((-4*x^2*exp(2)+4*x^4+24*x^2+1)*exp(exp(2)^2+(-2*x^2-12)*exp(2)+x^4+12*x^2+36)-7)*ln(x)+(-64*x^2*exp(2)+6
4*x^4+384*x^2+15)*exp(exp(2)^2+(-2*x^2-12)*exp(2)+x^4+12*x^2+36)-105)*exp((x*exp(exp(2)^2+(-2*x^2-12)*exp(2)+x
^4+12*x^2+36)-7*x)/(16+ln(x)))/(ln(x)^2+32*ln(x)+256),x,method=_RETURNVERBOSE)

[Out]

exp(x*(exp(x^4-2*x^2*exp(2)+12*x^2-12*exp(2)+exp(4)+36)-7)/(16+ln(x)))

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maxima [F(-2)]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: RuntimeError} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-4*x^2*exp(2)+4*x^4+24*x^2+1)*exp(exp(2)^2+(-2*x^2-12)*exp(2)+x^4+12*x^2+36)-7)*log(x)+(-64*x^2*e
xp(2)+64*x^4+384*x^2+15)*exp(exp(2)^2+(-2*x^2-12)*exp(2)+x^4+12*x^2+36)-105)*exp((x*exp(exp(2)^2+(-2*x^2-12)*e
xp(2)+x^4+12*x^2+36)-7*x)/(16+log(x)))/(log(x)^2+32*log(x)+256),x, algorithm="maxima")

[Out]

Exception raised: RuntimeError >> ECL says: In function CAR, the value of the first argument is  0which is not
of the expected type LIST

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mupad [B]  time = 3.95, size = 48, normalized size = 1.85 \begin {gather*} {\mathrm {e}}^{\frac {x\,{\mathrm {e}}^{-2\,x^2\,{\mathrm {e}}^2}\,{\mathrm {e}}^{-12\,{\mathrm {e}}^2}\,{\mathrm {e}}^{x^4}\,{\mathrm {e}}^{36}\,{\mathrm {e}}^{12\,x^2}\,{\mathrm {e}}^{{\mathrm {e}}^4}}{\ln \relax (x)+16}}\,{\mathrm {e}}^{-\frac {7\,x}{\ln \relax (x)+16}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(-(7*x - x*exp(exp(4) - exp(2)*(2*x^2 + 12) + 12*x^2 + x^4 + 36))/(log(x) + 16))*(log(x)*(exp(exp(4) -
exp(2)*(2*x^2 + 12) + 12*x^2 + x^4 + 36)*(24*x^2 - 4*x^2*exp(2) + 4*x^4 + 1) - 7) + exp(exp(4) - exp(2)*(2*x^
2 + 12) + 12*x^2 + x^4 + 36)*(384*x^2 - 64*x^2*exp(2) + 64*x^4 + 15) - 105))/(32*log(x) + log(x)^2 + 256),x)

[Out]

exp((x*exp(-2*x^2*exp(2))*exp(-12*exp(2))*exp(x^4)*exp(36)*exp(12*x^2)*exp(exp(4)))/(log(x) + 16))*exp(-(7*x)/
(log(x) + 16))

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sympy [A]  time = 2.16, size = 37, normalized size = 1.42 \begin {gather*} e^{\frac {x e^{x^{4} + 12 x^{2} + \left (- 2 x^{2} - 12\right ) e^{2} + 36 + e^{4}} - 7 x}{\log {\relax (x )} + 16}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-4*x**2*exp(2)+4*x**4+24*x**2+1)*exp(exp(2)**2+(-2*x**2-12)*exp(2)+x**4+12*x**2+36)-7)*ln(x)+(-64
*x**2*exp(2)+64*x**4+384*x**2+15)*exp(exp(2)**2+(-2*x**2-12)*exp(2)+x**4+12*x**2+36)-105)*exp((x*exp(exp(2)**2
+(-2*x**2-12)*exp(2)+x**4+12*x**2+36)-7*x)/(16+ln(x)))/(ln(x)**2+32*ln(x)+256),x)

[Out]

exp((x*exp(x**4 + 12*x**2 + (-2*x**2 - 12)*exp(2) + 36 + exp(4)) - 7*x)/(log(x) + 16))

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