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

Optimal. Leaf size=34 \[ e^{-\frac {-x+\log \left (\left (6+e^3-x\right ) \log (x-\log (4 (1+x)))\right )}{x}} x \]

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Rubi [F]  time = 10.08, 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 {-x+\log \left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )}{x}\right ) \left (6 x^2+e^3 x^2-x^3+\left (-7 x^2-6 x^3+x^4+e^3 \left (-x^2-x^3\right )+\left (7 x+6 x^2-x^3+e^3 \left (x+x^2\right )\right ) \log (4+4 x)\right ) \log (x-\log (4+4 x))+\left (-6 x-5 x^2+x^3+e^3 \left (-x-x^2\right )+\left (6+5 x-x^2+e^3 (1+x)\right ) \log (4+4 x)\right ) \log (x-\log (4+4 x)) \log \left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )\right )}{\left (-6 x^2-5 x^3+x^4+e^3 \left (-x^2-x^3\right )+\left (6 x+5 x^2-x^3+e^3 \left (x+x^2\right )\right ) \log (4+4 x)\right ) \log (x-\log (4+4 x))} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(6*x^2 + E^3*x^2 - x^3 + (-7*x^2 - 6*x^3 + x^4 + E^3*(-x^2 - x^3) + (7*x + 6*x^2 - x^3 + E^3*(x + x^2))*Lo
g[4 + 4*x])*Log[x - Log[4 + 4*x]] + (-6*x - 5*x^2 + x^3 + E^3*(-x - x^2) + (6 + 5*x - x^2 + E^3*(1 + x))*Log[4
+ 4*x])*Log[x - Log[4 + 4*x]]*Log[(6 + E^3 - x)*Log[x - Log[4 + 4*x]]])/(E^((-x + Log[(6 + E^3 - x)*Log[x - L
og[4 + 4*x]]])/x)*(-6*x^2 - 5*x^3 + x^4 + E^3*(-x^2 - x^3) + (6*x + 5*x^2 - x^3 + E^3*(x + x^2))*Log[4 + 4*x])
*Log[x - Log[4 + 4*x]]),x]

[Out]

-(E*(7 + E^3)*Defer[Int][((6 + E^3 - x)*Log[x - Log[4 + 4*x]])^(-1 - x^(-1))/(x - Log[4 + 4*x]), x]) + E*Defer
[Int][(x*((6 + E^3 - x)*Log[x - Log[4 + 4*x]])^(-1 - x^(-1)))/(x - Log[4 + 4*x]), x] + E*(7 + E^3)*Defer[Int][
((6 + E^3 - x)*Log[x - Log[4 + 4*x]])^(-1 - x^(-1))/((1 + x)*(x - Log[4 + 4*x])), x] + E*(7 + E^3)*Defer[Int][
Log[x - Log[4 + 4*x]]*((6 + E^3 - x)*Log[x - Log[4 + 4*x]])^(-1 - x^(-1)), x] - E*Defer[Int][x*Log[x - Log[4 +
4*x]]*((6 + E^3 - x)*Log[x - Log[4 + 4*x]])^(-1 - x^(-1)), x] + E*Defer[Int][Log[(6 + E^3 - x)*Log[x - Log[4
+ 4*x]]]/(x*((6 + E^3 - x)*Log[x - Log[4 + 4*x]])^x^(-1)), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {\exp \left (-\frac {-x+\log \left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )}{x}\right ) \left (\left (6+e^3\right ) x^2-x^3+\left (-7 x^2-6 x^3+x^4+e^3 \left (-x^2-x^3\right )+\left (7 x+6 x^2-x^3+e^3 \left (x+x^2\right )\right ) \log (4+4 x)\right ) \log (x-\log (4+4 x))+\left (-6 x-5 x^2+x^3+e^3 \left (-x-x^2\right )+\left (6+5 x-x^2+e^3 (1+x)\right ) \log (4+4 x)\right ) \log (x-\log (4+4 x)) \log \left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )\right )}{\left (-6 x^2-5 x^3+x^4+e^3 \left (-x^2-x^3\right )+\left (6 x+5 x^2-x^3+e^3 \left (x+x^2\right )\right ) \log (4+4 x)\right ) \log (x-\log (4+4 x))} \, dx\\ &=\int \frac {e \left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )^{-1-\frac {1}{x}} \left (-\left (\left (6+e^3\right ) x^2\right )+x^3-x (1+x) \left (-7-e^3+x\right ) (x-\log (4+4 x)) \log (x-\log (4+4 x))+\left (6+5 x-x^2+e^3 (1+x)\right ) (x-\log (4+4 x)) \log (x-\log (4+4 x)) \log \left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )\right )}{x (1+x) (x-\log (4+4 x))} \, dx\\ &=e \int \frac {\left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )^{-1-\frac {1}{x}} \left (-\left (\left (6+e^3\right ) x^2\right )+x^3-x (1+x) \left (-7-e^3+x\right ) (x-\log (4+4 x)) \log (x-\log (4+4 x))+\left (6+5 x-x^2+e^3 (1+x)\right ) (x-\log (4+4 x)) \log (x-\log (4+4 x)) \log \left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )\right )}{x (1+x) (x-\log (4+4 x))} \, dx\\ &=e \int \left (\frac {\left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )^{-1-\frac {1}{x}} \left (-6 \left (1+\frac {e^3}{6}\right ) x+x^2+7 \left (1+\frac {e^3}{7}\right ) x \log (x-\log (4+4 x))+6 \left (1+\frac {e^3}{6}\right ) x^2 \log (x-\log (4+4 x))-x^3 \log (x-\log (4+4 x))-7 \left (1+\frac {e^3}{7}\right ) \log (4+4 x) \log (x-\log (4+4 x))-6 \left (1+\frac {e^3}{6}\right ) x \log (4+4 x) \log (x-\log (4+4 x))+x^2 \log (4+4 x) \log (x-\log (4+4 x))\right )}{(1+x) (x-\log (4+4 x))}+\frac {\left (6+e^3-x\right ) \log (x-\log (4+4 x)) \left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )^{-1-\frac {1}{x}} \log \left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )}{x}\right ) \, dx\\ &=e \int \frac {\left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )^{-1-\frac {1}{x}} \left (-6 \left (1+\frac {e^3}{6}\right ) x+x^2+7 \left (1+\frac {e^3}{7}\right ) x \log (x-\log (4+4 x))+6 \left (1+\frac {e^3}{6}\right ) x^2 \log (x-\log (4+4 x))-x^3 \log (x-\log (4+4 x))-7 \left (1+\frac {e^3}{7}\right ) \log (4+4 x) \log (x-\log (4+4 x))-6 \left (1+\frac {e^3}{6}\right ) x \log (4+4 x) \log (x-\log (4+4 x))+x^2 \log (4+4 x) \log (x-\log (4+4 x))\right )}{(1+x) (x-\log (4+4 x))} \, dx+e \int \frac {\left (6+e^3-x\right ) \log (x-\log (4+4 x)) \left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )^{-1-\frac {1}{x}} \log \left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )}{x} \, dx\\ &=e \int \frac {\left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )^{-1-\frac {1}{x}} \left (x \left (-6-e^3+x\right )+\left (7+6 x-x^2+e^3 (1+x)\right ) (x-\log (4+4 x)) \log (x-\log (4+4 x))\right )}{(1+x) (x-\log (4+4 x))} \, dx+e \int \frac {\left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )^{-1/x} \log \left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )}{x} \, dx\\ &=e \int \left (\frac {x \left (-6-e^3+x\right ) \left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )^{-1-\frac {1}{x}}}{(1+x) (x-\log (4+4 x))}+\left (7+e^3-x\right ) \log (x-\log (4+4 x)) \left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )^{-1-\frac {1}{x}}\right ) \, dx+e \int \frac {\left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )^{-1/x} \log \left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )}{x} \, dx\\ &=e \int \frac {x \left (-6-e^3+x\right ) \left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )^{-1-\frac {1}{x}}}{(1+x) (x-\log (4+4 x))} \, dx+e \int \left (7+e^3-x\right ) \log (x-\log (4+4 x)) \left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )^{-1-\frac {1}{x}} \, dx+e \int \frac {\left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )^{-1/x} \log \left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )}{x} \, dx\\ &=e \int \left (-\frac {7 \left (1+\frac {e^3}{7}\right ) \left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )^{-1-\frac {1}{x}}}{x-\log (4+4 x)}+\frac {x \left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )^{-1-\frac {1}{x}}}{x-\log (4+4 x)}+\frac {\left (7+e^3\right ) \left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )^{-1-\frac {1}{x}}}{(1+x) (x-\log (4+4 x))}\right ) \, dx+e \int \left (7 \left (1+\frac {e^3}{7}\right ) \log (x-\log (4+4 x)) \left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )^{-1-\frac {1}{x}}-x \log (x-\log (4+4 x)) \left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )^{-1-\frac {1}{x}}\right ) \, dx+e \int \frac {\left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )^{-1/x} \log \left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )}{x} \, dx\\ &=e \int \frac {x \left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )^{-1-\frac {1}{x}}}{x-\log (4+4 x)} \, dx-e \int x \log (x-\log (4+4 x)) \left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )^{-1-\frac {1}{x}} \, dx+e \int \frac {\left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )^{-1/x} \log \left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )}{x} \, dx-\left (e \left (7+e^3\right )\right ) \int \frac {\left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )^{-1-\frac {1}{x}}}{x-\log (4+4 x)} \, dx+\left (e \left (7+e^3\right )\right ) \int \frac {\left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )^{-1-\frac {1}{x}}}{(1+x) (x-\log (4+4 x))} \, dx+\left (e \left (7+e^3\right )\right ) \int \log (x-\log (4+4 x)) \left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )^{-1-\frac {1}{x}} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.30, size = 29, normalized size = 0.85 \begin {gather*} e x \left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )^{-1/x} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(6*x^2 + E^3*x^2 - x^3 + (-7*x^2 - 6*x^3 + x^4 + E^3*(-x^2 - x^3) + (7*x + 6*x^2 - x^3 + E^3*(x + x^
2))*Log[4 + 4*x])*Log[x - Log[4 + 4*x]] + (-6*x - 5*x^2 + x^3 + E^3*(-x - x^2) + (6 + 5*x - x^2 + E^3*(1 + x))
*Log[4 + 4*x])*Log[x - Log[4 + 4*x]]*Log[(6 + E^3 - x)*Log[x - Log[4 + 4*x]]])/(E^((-x + Log[(6 + E^3 - x)*Log
[x - Log[4 + 4*x]]])/x)*(-6*x^2 - 5*x^3 + x^4 + E^3*(-x^2 - x^3) + (6*x + 5*x^2 - x^3 + E^3*(x + x^2))*Log[4 +
4*x])*Log[x - Log[4 + 4*x]]),x]

[Out]

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

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fricas [A]  time = 1.04, size = 32, normalized size = 0.94 \begin {gather*} x e^{\left (\frac {x - \log \left (-{\left (x - e^{3} - 6\right )} \log \left (x - \log \left (4 \, x + 4\right )\right )\right )}{x}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((((x+1)*exp(3)-x^2+5*x+6)*log(4*x+4)+(-x^2-x)*exp(3)+x^3-5*x^2-6*x)*log(-log(4*x+4)+x)*log((exp(3)-
x+6)*log(-log(4*x+4)+x))+(((x^2+x)*exp(3)-x^3+6*x^2+7*x)*log(4*x+4)+(-x^3-x^2)*exp(3)+x^4-6*x^3-7*x^2)*log(-lo
g(4*x+4)+x)+x^2*exp(3)-x^3+6*x^2)/(((x^2+x)*exp(3)-x^3+5*x^2+6*x)*log(4*x+4)+(-x^3-x^2)*exp(3)+x^4-5*x^3-6*x^2
)/log(-log(4*x+4)+x)/exp((log((exp(3)-x+6)*log(-log(4*x+4)+x))-x)/x),x, algorithm="fricas")

[Out]

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

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int -\frac {{\left (x^{3} - x^{2} e^{3} - {\left (x^{3} - 5 \, x^{2} - {\left (x^{2} + x\right )} e^{3} - {\left (x^{2} - {\left (x + 1\right )} e^{3} - 5 \, x - 6\right )} \log \left (4 \, x + 4\right ) - 6 \, x\right )} \log \left (-{\left (x - e^{3} - 6\right )} \log \left (x - \log \left (4 \, x + 4\right )\right )\right ) \log \left (x - \log \left (4 \, x + 4\right )\right ) - 6 \, x^{2} - {\left (x^{4} - 6 \, x^{3} - 7 \, x^{2} - {\left (x^{3} + x^{2}\right )} e^{3} - {\left (x^{3} - 6 \, x^{2} - {\left (x^{2} + x\right )} e^{3} - 7 \, x\right )} \log \left (4 \, x + 4\right )\right )} \log \left (x - \log \left (4 \, x + 4\right )\right )\right )} e^{\left (\frac {x - \log \left (-{\left (x - e^{3} - 6\right )} \log \left (x - \log \left (4 \, x + 4\right )\right )\right )}{x}\right )}}{{\left (x^{4} - 5 \, x^{3} - 6 \, x^{2} - {\left (x^{3} + x^{2}\right )} e^{3} - {\left (x^{3} - 5 \, x^{2} - {\left (x^{2} + x\right )} e^{3} - 6 \, x\right )} \log \left (4 \, x + 4\right )\right )} \log \left (x - \log \left (4 \, x + 4\right )\right )}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((((x+1)*exp(3)-x^2+5*x+6)*log(4*x+4)+(-x^2-x)*exp(3)+x^3-5*x^2-6*x)*log(-log(4*x+4)+x)*log((exp(3)-
x+6)*log(-log(4*x+4)+x))+(((x^2+x)*exp(3)-x^3+6*x^2+7*x)*log(4*x+4)+(-x^3-x^2)*exp(3)+x^4-6*x^3-7*x^2)*log(-lo
g(4*x+4)+x)+x^2*exp(3)-x^3+6*x^2)/(((x^2+x)*exp(3)-x^3+5*x^2+6*x)*log(4*x+4)+(-x^3-x^2)*exp(3)+x^4-5*x^3-6*x^2
)/log(-log(4*x+4)+x)/exp((log((exp(3)-x+6)*log(-log(4*x+4)+x))-x)/x),x, algorithm="giac")

[Out]

integrate(-(x^3 - x^2*e^3 - (x^3 - 5*x^2 - (x^2 + x)*e^3 - (x^2 - (x + 1)*e^3 - 5*x - 6)*log(4*x + 4) - 6*x)*l
og(-(x - e^3 - 6)*log(x - log(4*x + 4)))*log(x - log(4*x + 4)) - 6*x^2 - (x^4 - 6*x^3 - 7*x^2 - (x^3 + x^2)*e^
3 - (x^3 - 6*x^2 - (x^2 + x)*e^3 - 7*x)*log(4*x + 4))*log(x - log(4*x + 4)))*e^((x - log(-(x - e^3 - 6)*log(x
- log(4*x + 4))))/x)/((x^4 - 5*x^3 - 6*x^2 - (x^3 + x^2)*e^3 - (x^3 - 5*x^2 - (x^2 + x)*e^3 - 6*x)*log(4*x + 4
))*log(x - log(4*x + 4))), x)

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maple [C]  time = 0.30, size = 199, normalized size = 5.85

method	result	size
risch	\(x \,{\mathrm e}^{\frac {i \pi \mathrm {csgn}\left (i \ln \left (-\ln \left (4 x +4\right )+x \right ) \left ({\mathrm e}^{3}-x +6\right )\right )^{3}-i \pi \mathrm {csgn}\left (i \ln \left (-\ln \left (4 x +4\right )+x \right ) \left ({\mathrm e}^{3}-x +6\right )\right )^{2} \mathrm {csgn}\left (i \ln \left (-\ln \left (4 x +4\right )+x \right )\right )-i \pi \mathrm {csgn}\left (i \ln \left (-\ln \left (4 x +4\right )+x \right ) \left ({\mathrm e}^{3}-x +6\right )\right )^{2} \mathrm {csgn}\left (i \left ({\mathrm e}^{3}-x +6\right )\right )+i \pi \,\mathrm {csgn}\left (i \ln \left (-\ln \left (4 x +4\right )+x \right ) \left ({\mathrm e}^{3}-x +6\right )\right ) \mathrm {csgn}\left (i \ln \left (-\ln \left (4 x +4\right )+x \right )\right ) \mathrm {csgn}\left (i \left ({\mathrm e}^{3}-x +6\right )\right )-2 \ln \left (\ln \left (-\ln \left (4 x +4\right )+x \right )\right )-2 \ln \left ({\mathrm e}^{3}-x +6\right )+2 x}{2 x}}\)	\(199\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((((x+1)*exp(3)-x^2+5*x+6)*ln(4*x+4)+(-x^2-x)*exp(3)+x^3-5*x^2-6*x)*ln(-ln(4*x+4)+x)*ln((exp(3)-x+6)*ln(-l
n(4*x+4)+x))+(((x^2+x)*exp(3)-x^3+6*x^2+7*x)*ln(4*x+4)+(-x^3-x^2)*exp(3)+x^4-6*x^3-7*x^2)*ln(-ln(4*x+4)+x)+x^2
*exp(3)-x^3+6*x^2)/(((x^2+x)*exp(3)-x^3+5*x^2+6*x)*ln(4*x+4)+(-x^3-x^2)*exp(3)+x^4-5*x^3-6*x^2)/ln(-ln(4*x+4)+
x)/exp((ln((exp(3)-x+6)*ln(-ln(4*x+4)+x))-x)/x),x,method=_RETURNVERBOSE)

[Out]

x*exp(1/2*(I*Pi*csgn(I*ln(-ln(4*x+4)+x)*(exp(3)-x+6))^3-I*Pi*csgn(I*ln(-ln(4*x+4)+x)*(exp(3)-x+6))^2*csgn(I*ln
(-ln(4*x+4)+x))-I*Pi*csgn(I*ln(-ln(4*x+4)+x)*(exp(3)-x+6))^2*csgn(I*(exp(3)-x+6))+I*Pi*csgn(I*ln(-ln(4*x+4)+x)
*(exp(3)-x+6))*csgn(I*ln(-ln(4*x+4)+x))*csgn(I*(exp(3)-x+6))-2*ln(ln(-ln(4*x+4)+x))-2*ln(exp(3)-x+6)+2*x)/x)

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maxima [A]  time = 0.70, size = 37, normalized size = 1.09 \begin {gather*} x e^{\left (-\frac {\log \left (-x + e^{3} + 6\right )}{x} - \frac {\log \left (\log \left (x - 2 \, \log \relax (2) - \log \left (x + 1\right )\right )\right )}{x} + 1\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((((x+1)*exp(3)-x^2+5*x+6)*log(4*x+4)+(-x^2-x)*exp(3)+x^3-5*x^2-6*x)*log(-log(4*x+4)+x)*log((exp(3)-
x+6)*log(-log(4*x+4)+x))+(((x^2+x)*exp(3)-x^3+6*x^2+7*x)*log(4*x+4)+(-x^3-x^2)*exp(3)+x^4-6*x^3-7*x^2)*log(-lo
g(4*x+4)+x)+x^2*exp(3)-x^3+6*x^2)/(((x^2+x)*exp(3)-x^3+5*x^2+6*x)*log(4*x+4)+(-x^3-x^2)*exp(3)+x^4-5*x^3-6*x^2
)/log(-log(4*x+4)+x)/exp((log((exp(3)-x+6)*log(-log(4*x+4)+x))-x)/x),x, algorithm="maxima")

[Out]

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

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mupad [B]  time = 5.73, size = 52, normalized size = 1.53 \begin {gather*} \frac {x\,\mathrm {e}}{{\left (6\,\ln \left (x-\ln \left (4\,x+4\right )\right )+\ln \left (x-\ln \left (4\,x+4\right )\right )\,{\mathrm {e}}^3-x\,\ln \left (x-\ln \left (4\,x+4\right )\right )\right )}^{1/x}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp((x - log(log(x - log(4*x + 4))*(exp(3) - x + 6)))/x)*(log(x - log(4*x + 4))*(exp(3)*(x^2 + x^3) - log
(4*x + 4)*(7*x + exp(3)*(x + x^2) + 6*x^2 - x^3) + 7*x^2 + 6*x^3 - x^4) - x^2*exp(3) - 6*x^2 + x^3 + log(x - l
og(4*x + 4))*log(log(x - log(4*x + 4))*(exp(3) - x + 6))*(6*x - log(4*x + 4)*(5*x + exp(3)*(x + 1) - x^2 + 6)
+ exp(3)*(x + x^2) + 5*x^2 - x^3)))/(log(x - log(4*x + 4))*(exp(3)*(x^2 + x^3) - log(4*x + 4)*(6*x + exp(3)*(x
+ x^2) + 5*x^2 - x^3) + 6*x^2 + 5*x^3 - x^4)),x)

[Out]

(x*exp(1))/(6*log(x - log(4*x + 4)) + log(x - log(4*x + 4))*exp(3) - x*log(x - log(4*x + 4)))^(1/x)

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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(((((x+1)*exp(3)-x**2+5*x+6)*ln(4*x+4)+(-x**2-x)*exp(3)+x**3-5*x**2-6*x)*ln(-ln(4*x+4)+x)*ln((exp(3)-
x+6)*ln(-ln(4*x+4)+x))+(((x**2+x)*exp(3)-x**3+6*x**2+7*x)*ln(4*x+4)+(-x**3-x**2)*exp(3)+x**4-6*x**3-7*x**2)*ln
(-ln(4*x+4)+x)+x**2*exp(3)-x**3+6*x**2)/(((x**2+x)*exp(3)-x**3+5*x**2+6*x)*ln(4*x+4)+(-x**3-x**2)*exp(3)+x**4-
5*x**3-6*x**2)/ln(-ln(4*x+4)+x)/exp((ln((exp(3)-x+6)*ln(-ln(4*x+4)+x))-x)/x),x)

[Out]

Timed out

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