3.71.30 \(\int \frac {-8 x^2-6 x^3+e (2 x+6 x^2)+e^{x^2} (6 e x^2-6 x^3)+(-2 x^2+2 e x^2-2 x^3+e^{x^2} (2 e x^2-2 x^3)) \log (x)+(-8 x-6 x^2+e (2+6 x)+(-2 x+2 e x-2 x^2) \log (x)) \log (-3 e+3 x+(-e+x) \log (x))}{3 e x-3 x^2+(e x-x^2) \log (x)} \, dx\)

Optimal. Leaf size=21 \[ e^{x^2}+(x+\log ((-e+x) (3+\log (x))))^2 \]

________________________________________________________________________________________

Rubi [F]  time = 10.11, 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 {-8 x^2-6 x^3+e \left (2 x+6 x^2\right )+e^{x^2} \left (6 e x^2-6 x^3\right )+\left (-2 x^2+2 e x^2-2 x^3+e^{x^2} \left (2 e x^2-2 x^3\right )\right ) \log (x)+\left (-8 x-6 x^2+e (2+6 x)+\left (-2 x+2 e x-2 x^2\right ) \log (x)\right ) \log (-3 e+3 x+(-e+x) \log (x))}{3 e x-3 x^2+\left (e x-x^2\right ) \log (x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-8*x^2 - 6*x^3 + E*(2*x + 6*x^2) + E^x^2*(6*E*x^2 - 6*x^3) + (-2*x^2 + 2*E*x^2 - 2*x^3 + E^x^2*(2*E*x^2 -
2*x^3))*Log[x] + (-8*x - 6*x^2 + E*(2 + 6*x) + (-2*x + 2*E*x - 2*x^2)*Log[x])*Log[-3*E + 3*x + (-E + x)*Log[x
]])/(3*E*x - 3*x^2 + (E*x - x^2)*Log[x]),x]

[Out]

E^x^2 + 2*(1 - E)*x + 2*E*x + x^2 + 2*(1 - E)*E*Log[E - x] + 2*E^2*Log[E - x] - 8*Defer[Int][x/((E - x)*(3 + L
og[x])), x] + 6*(1 - E)*Defer[Int][x/((E - x)*(3 + Log[x])), x] + 2*E*Defer[Int][(1 + 3*x)/((E - x)*(3 + Log[x
])), x] + 6*Defer[Int][Log[-((E - x)*(3 + Log[x]))]/(3 + Log[x]), x] + 2*Defer[Int][Log[-((E - x)*(3 + Log[x])
)]/((E - x)*(3 + Log[x])), x] - 2*(4 - 3*E)*Defer[Int][Log[-((E - x)*(3 + Log[x]))]/((E - x)*(3 + Log[x])), x]
- 6*E*Defer[Int][Log[-((E - x)*(3 + Log[x]))]/((E - x)*(3 + Log[x])), x] + 2*Defer[Int][Log[-((E - x)*(3 + Lo
g[x]))]/(x*(3 + Log[x])), x] + 2*Defer[Int][(Log[x]*Log[-((E - x)*(3 + Log[x]))])/(3 + Log[x]), x] - 2*(1 - E)
*Defer[Int][(Log[x]*Log[-((E - x)*(3 + Log[x]))])/((E - x)*(3 + Log[x])), x] - 2*E*Defer[Int][(Log[x]*Log[-((E
- x)*(3 + Log[x]))])/((E - x)*(3 + Log[x])), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-8 x^2-6 x^3+e \left (2 x+6 x^2\right )+e^{x^2} \left (6 e x^2-6 x^3\right )+\left (-2 x^2+2 e x^2-2 x^3+e^{x^2} \left (2 e x^2-2 x^3\right )\right ) \log (x)+\left (-8 x-6 x^2+e (2+6 x)+\left (-2 x+2 e x-2 x^2\right ) \log (x)\right ) \log (-3 e+3 x+(-e+x) \log (x))}{(e-x) x (3+\log (x))} \, dx\\ &=\int \left (2 e^{x^2} x-\frac {8 x}{(e-x) (3+\log (x))}-\frac {6 x^2}{(e-x) (3+\log (x))}+\frac {2 e (1+3 x)}{(e-x) (3+\log (x))}-\frac {2 (1-e) x \log (x)}{(e-x) (3+\log (x))}-\frac {2 x^2 \log (x)}{(e-x) (3+\log (x))}+\frac {2 \left (e-4 \left (1-\frac {3 e}{4}\right ) x-3 x^2-(1-e) x \log (x)-x^2 \log (x)\right ) \log (-((e-x) (3+\log (x))))}{(e-x) x (3+\log (x))}\right ) \, dx\\ &=2 \int e^{x^2} x \, dx-2 \int \frac {x^2 \log (x)}{(e-x) (3+\log (x))} \, dx+2 \int \frac {\left (e-4 \left (1-\frac {3 e}{4}\right ) x-3 x^2-(1-e) x \log (x)-x^2 \log (x)\right ) \log (-((e-x) (3+\log (x))))}{(e-x) x (3+\log (x))} \, dx-6 \int \frac {x^2}{(e-x) (3+\log (x))} \, dx-8 \int \frac {x}{(e-x) (3+\log (x))} \, dx-(2 (1-e)) \int \frac {x \log (x)}{(e-x) (3+\log (x))} \, dx+(2 e) \int \frac {1+3 x}{(e-x) (3+\log (x))} \, dx\\ &=e^{x^2}-2 \int \left (\frac {x^2}{e-x}-\frac {3 x^2}{(e-x) (3+\log (x))}\right ) \, dx+2 \int \frac {(e+3 e x-x (4+3 x)-x (1-e+x) \log (x)) \log (-((e-x) (3+\log (x))))}{(e-x) x (3+\log (x))} \, dx-6 \int \frac {x^2}{(e-x) (3+\log (x))} \, dx-8 \int \frac {x}{(e-x) (3+\log (x))} \, dx-(2 (1-e)) \int \left (\frac {x}{e-x}-\frac {3 x}{(e-x) (3+\log (x))}\right ) \, dx+(2 e) \int \frac {1+3 x}{(e-x) (3+\log (x))} \, dx\\ &=e^{x^2}-2 \int \frac {x^2}{e-x} \, dx+2 \int \left (\frac {\left (e-4 \left (1-\frac {3 e}{4}\right ) x-3 x^2-(1-e) x \log (x)-x^2 \log (x)\right ) \log (-((e-x) (3+\log (x))))}{e (e-x) (3+\log (x))}+\frac {\left (e-4 \left (1-\frac {3 e}{4}\right ) x-3 x^2-(1-e) x \log (x)-x^2 \log (x)\right ) \log (-((e-x) (3+\log (x))))}{e x (3+\log (x))}\right ) \, dx-8 \int \frac {x}{(e-x) (3+\log (x))} \, dx-(2 (1-e)) \int \frac {x}{e-x} \, dx+(6 (1-e)) \int \frac {x}{(e-x) (3+\log (x))} \, dx+(2 e) \int \frac {1+3 x}{(e-x) (3+\log (x))} \, dx\\ &=e^{x^2}-2 \int \left (-e+\frac {e^2}{e-x}-x\right ) \, dx-8 \int \frac {x}{(e-x) (3+\log (x))} \, dx-(2 (1-e)) \int \left (-1+\frac {e}{e-x}\right ) \, dx+(6 (1-e)) \int \frac {x}{(e-x) (3+\log (x))} \, dx+\frac {2 \int \frac {\left (e-4 \left (1-\frac {3 e}{4}\right ) x-3 x^2-(1-e) x \log (x)-x^2 \log (x)\right ) \log (-((e-x) (3+\log (x))))}{(e-x) (3+\log (x))} \, dx}{e}+\frac {2 \int \frac {\left (e-4 \left (1-\frac {3 e}{4}\right ) x-3 x^2-(1-e) x \log (x)-x^2 \log (x)\right ) \log (-((e-x) (3+\log (x))))}{x (3+\log (x))} \, dx}{e}+(2 e) \int \frac {1+3 x}{(e-x) (3+\log (x))} \, dx\\ &=e^{x^2}+2 (1-e) x+2 e x+x^2+2 (1-e) e \log (e-x)+2 e^2 \log (e-x)-8 \int \frac {x}{(e-x) (3+\log (x))} \, dx+(6 (1-e)) \int \frac {x}{(e-x) (3+\log (x))} \, dx+\frac {2 \int \frac {(e+3 e x-x (4+3 x)-x (1-e+x) \log (x)) \log (-((e-x) (3+\log (x))))}{(e-x) (3+\log (x))} \, dx}{e}+\frac {2 \int \frac {(e+3 e x-x (4+3 x)-x (1-e+x) \log (x)) \log (-((e-x) (3+\log (x))))}{x (3+\log (x))} \, dx}{e}+(2 e) \int \frac {1+3 x}{(e-x) (3+\log (x))} \, dx\\ &=e^{x^2}+2 (1-e) x+2 e x+x^2+2 (1-e) e \log (e-x)+2 e^2 \log (e-x)-8 \int \frac {x}{(e-x) (3+\log (x))} \, dx+(6 (1-e)) \int \frac {x}{(e-x) (3+\log (x))} \, dx+\frac {2 \int \left (-\frac {4 \left (1-\frac {3 e}{4}\right ) \log (-((e-x) (3+\log (x))))}{3+\log (x)}+\frac {e \log (-((e-x) (3+\log (x))))}{x (3+\log (x))}-\frac {3 x \log (-((e-x) (3+\log (x))))}{3+\log (x)}-\frac {(1-e) \log (x) \log (-((e-x) (3+\log (x))))}{3+\log (x)}-\frac {x \log (x) \log (-((e-x) (3+\log (x))))}{3+\log (x)}\right ) \, dx}{e}+\frac {2 \int \left (\frac {e \log (-((e-x) (3+\log (x))))}{(e-x) (3+\log (x))}-\frac {4 \left (1-\frac {3 e}{4}\right ) x \log (-((e-x) (3+\log (x))))}{(e-x) (3+\log (x))}-\frac {3 x^2 \log (-((e-x) (3+\log (x))))}{(e-x) (3+\log (x))}-\frac {(1-e) x \log (x) \log (-((e-x) (3+\log (x))))}{(e-x) (3+\log (x))}-\frac {x^2 \log (x) \log (-((e-x) (3+\log (x))))}{(e-x) (3+\log (x))}\right ) \, dx}{e}+(2 e) \int \frac {1+3 x}{(e-x) (3+\log (x))} \, dx\\ &=e^{x^2}+2 (1-e) x+2 e x+x^2+2 (1-e) e \log (e-x)+2 e^2 \log (e-x)+2 \int \frac {\log (-((e-x) (3+\log (x))))}{(e-x) (3+\log (x))} \, dx+2 \int \frac {\log (-((e-x) (3+\log (x))))}{x (3+\log (x))} \, dx-8 \int \frac {x}{(e-x) (3+\log (x))} \, dx+(6 (1-e)) \int \frac {x}{(e-x) (3+\log (x))} \, dx-\frac {2 \int \frac {x \log (x) \log (-((e-x) (3+\log (x))))}{3+\log (x)} \, dx}{e}-\frac {2 \int \frac {x^2 \log (x) \log (-((e-x) (3+\log (x))))}{(e-x) (3+\log (x))} \, dx}{e}-\frac {6 \int \frac {x \log (-((e-x) (3+\log (x))))}{3+\log (x)} \, dx}{e}-\frac {6 \int \frac {x^2 \log (-((e-x) (3+\log (x))))}{(e-x) (3+\log (x))} \, dx}{e}-\frac {(2 (4-3 e)) \int \frac {\log (-((e-x) (3+\log (x))))}{3+\log (x)} \, dx}{e}-\frac {(2 (4-3 e)) \int \frac {x \log (-((e-x) (3+\log (x))))}{(e-x) (3+\log (x))} \, dx}{e}+\frac {(2 (-1+e)) \int \frac {\log (x) \log (-((e-x) (3+\log (x))))}{3+\log (x)} \, dx}{e}+\frac {(2 (-1+e)) \int \frac {x \log (x) \log (-((e-x) (3+\log (x))))}{(e-x) (3+\log (x))} \, dx}{e}+(2 e) \int \frac {1+3 x}{(e-x) (3+\log (x))} \, dx\\ &=e^{x^2}+2 (1-e) x+2 e x+x^2+2 (1-e) e \log (e-x)+2 e^2 \log (e-x)+2 \int \frac {\log (-((e-x) (3+\log (x))))}{(e-x) (3+\log (x))} \, dx+2 \int \frac {\log (-((e-x) (3+\log (x))))}{x (3+\log (x))} \, dx-8 \int \frac {x}{(e-x) (3+\log (x))} \, dx+(6 (1-e)) \int \frac {x}{(e-x) (3+\log (x))} \, dx-\frac {2 \int \frac {x \log (x) \log (-((e-x) (3+\log (x))))}{3+\log (x)} \, dx}{e}-\frac {2 \int \left (-\frac {e \log (x) \log (-((e-x) (3+\log (x))))}{3+\log (x)}+\frac {e^2 \log (x) \log (-((e-x) (3+\log (x))))}{(e-x) (3+\log (x))}-\frac {x \log (x) \log (-((e-x) (3+\log (x))))}{3+\log (x)}\right ) \, dx}{e}-\frac {6 \int \frac {x \log (-((e-x) (3+\log (x))))}{3+\log (x)} \, dx}{e}-\frac {6 \int \left (-\frac {e \log (-((e-x) (3+\log (x))))}{3+\log (x)}+\frac {e^2 \log (-((e-x) (3+\log (x))))}{(e-x) (3+\log (x))}-\frac {x \log (-((e-x) (3+\log (x))))}{3+\log (x)}\right ) \, dx}{e}-\frac {(2 (4-3 e)) \int \frac {\log (-((e-x) (3+\log (x))))}{3+\log (x)} \, dx}{e}-\frac {(2 (4-3 e)) \int \left (-\frac {\log (-((e-x) (3+\log (x))))}{3+\log (x)}+\frac {e \log (-((e-x) (3+\log (x))))}{(e-x) (3+\log (x))}\right ) \, dx}{e}+\frac {(2 (-1+e)) \int \frac {\log (x) \log (-((e-x) (3+\log (x))))}{3+\log (x)} \, dx}{e}+\frac {(2 (-1+e)) \int \left (-\frac {\log (x) \log (-((e-x) (3+\log (x))))}{3+\log (x)}+\frac {e \log (x) \log (-((e-x) (3+\log (x))))}{(e-x) (3+\log (x))}\right ) \, dx}{e}+(2 e) \int \frac {1+3 x}{(e-x) (3+\log (x))} \, dx\\ &=e^{x^2}+2 (1-e) x+2 e x+x^2+2 (1-e) e \log (e-x)+2 e^2 \log (e-x)+2 \int \frac {\log (-((e-x) (3+\log (x))))}{(e-x) (3+\log (x))} \, dx+2 \int \frac {\log (-((e-x) (3+\log (x))))}{x (3+\log (x))} \, dx+2 \int \frac {\log (x) \log (-((e-x) (3+\log (x))))}{3+\log (x)} \, dx+6 \int \frac {\log (-((e-x) (3+\log (x))))}{3+\log (x)} \, dx-8 \int \frac {x}{(e-x) (3+\log (x))} \, dx-(2 (4-3 e)) \int \frac {\log (-((e-x) (3+\log (x))))}{(e-x) (3+\log (x))} \, dx-(2 (1-e)) \int \frac {\log (x) \log (-((e-x) (3+\log (x))))}{(e-x) (3+\log (x))} \, dx+(6 (1-e)) \int \frac {x}{(e-x) (3+\log (x))} \, dx+(2 e) \int \frac {1+3 x}{(e-x) (3+\log (x))} \, dx-(2 e) \int \frac {\log (x) \log (-((e-x) (3+\log (x))))}{(e-x) (3+\log (x))} \, dx-(6 e) \int \frac {\log (-((e-x) (3+\log (x))))}{(e-x) (3+\log (x))} \, dx\\ \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [A]  time = 0.18, size = 38, normalized size = 1.81 \begin {gather*} e^{x^2}+x^2+2 x \log (-((e-x) (3+\log (x))))+\log ^2(-((e-x) (3+\log (x)))) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-8*x^2 - 6*x^3 + E*(2*x + 6*x^2) + E^x^2*(6*E*x^2 - 6*x^3) + (-2*x^2 + 2*E*x^2 - 2*x^3 + E^x^2*(2*E
*x^2 - 2*x^3))*Log[x] + (-8*x - 6*x^2 + E*(2 + 6*x) + (-2*x + 2*E*x - 2*x^2)*Log[x])*Log[-3*E + 3*x + (-E + x)
*Log[x]])/(3*E*x - 3*x^2 + (E*x - x^2)*Log[x]),x]

[Out]

E^x^2 + x^2 + 2*x*Log[-((E - x)*(3 + Log[x]))] + Log[-((E - x)*(3 + Log[x]))]^2

________________________________________________________________________________________

fricas [B]  time = 0.62, size = 49, normalized size = 2.33 \begin {gather*} x^{2} + 2 \, x \log \left ({\left (x - e\right )} \log \relax (x) + 3 \, x - 3 \, e\right ) + \log \left ({\left (x - e\right )} \log \relax (x) + 3 \, x - 3 \, e\right )^{2} + e^{\left (x^{2}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((2*x*exp(1)-2*x^2-2*x)*log(x)+(6*x+2)*exp(1)-6*x^2-8*x)*log((x-exp(1))*log(x)-3*exp(1)+3*x)+((2*x^
2*exp(1)-2*x^3)*exp(x^2)+2*x^2*exp(1)-2*x^3-2*x^2)*log(x)+(6*x^2*exp(1)-6*x^3)*exp(x^2)+(6*x^2+2*x)*exp(1)-6*x
^3-8*x^2)/((x*exp(1)-x^2)*log(x)+3*x*exp(1)-3*x^2),x, algorithm="fricas")

[Out]

x^2 + 2*x*log((x - e)*log(x) + 3*x - 3*e) + log((x - e)*log(x) + 3*x - 3*e)^2 + e^(x^2)

________________________________________________________________________________________

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((2*x*exp(1)-2*x^2-2*x)*log(x)+(6*x+2)*exp(1)-6*x^2-8*x)*log((x-exp(1))*log(x)-3*exp(1)+3*x)+((2*x^
2*exp(1)-2*x^3)*exp(x^2)+2*x^2*exp(1)-2*x^3-2*x^2)*log(x)+(6*x^2*exp(1)-6*x^3)*exp(x^2)+(6*x^2+2*x)*exp(1)-6*x
^3-8*x^2)/((x*exp(1)-x^2)*log(x)+3*x*exp(1)-3*x^2),x, algorithm="giac")

[Out]

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

________________________________________________________________________________________

maple [C]  time = 0.32, size = 544, normalized size = 25.90

method	result	size
risch	\(\ln \left (3+\ln \relax (x )\right )^{2}+{\mathrm e}^{x^{2}}+x^{2}-2 i \pi x \mathrm {csgn}\left (i \left (3+\ln \relax (x )\right ) \left ({\mathrm e}-x \right )\right )^{2}-2 i \pi \ln \left (3+\ln \relax (x )\right ) \mathrm {csgn}\left (i \left (3+\ln \relax (x )\right ) \left ({\mathrm e}-x \right )\right )^{2}-2 i \pi \ln \left (x -{\mathrm e}\right ) \mathrm {csgn}\left (i \left (3+\ln \relax (x )\right ) \left ({\mathrm e}-x \right )\right )^{2}+2 i \pi \ln \left (x -{\mathrm e}\right )+2 i \pi \ln \left (3+\ln \relax (x )\right )+2 i \pi x +2 x \ln \left (3+\ln \relax (x )\right )+\ln \left ({\mathrm e}-x \right )^{2}+i \pi x \mathrm {csgn}\left (i \left (3+\ln \relax (x )\right ) \left ({\mathrm e}-x \right )\right )^{3}+i \pi \ln \left (3+\ln \relax (x )\right ) \mathrm {csgn}\left (i \left (3+\ln \relax (x )\right ) \left ({\mathrm e}-x \right )\right )^{3}+i \pi x \,\mathrm {csgn}\left (i \left ({\mathrm e}-x \right )\right ) \mathrm {csgn}\left (i \left (3+\ln \relax (x )\right ) \left ({\mathrm e}-x \right )\right )^{2}+i \pi \ln \left (3+\ln \relax (x )\right ) \mathrm {csgn}\left (i \left (3+\ln \relax (x )\right )\right ) \mathrm {csgn}\left (i \left (3+\ln \relax (x )\right ) \left ({\mathrm e}-x \right )\right )^{2}+i \pi \ln \left (3+\ln \relax (x )\right ) \mathrm {csgn}\left (i \left ({\mathrm e}-x \right )\right ) \mathrm {csgn}\left (i \left (3+\ln \relax (x )\right ) \left ({\mathrm e}-x \right )\right )^{2}+\left (2 x +2 \ln \left (3+\ln \relax (x )\right )\right ) \ln \left ({\mathrm e}-x \right )+i \pi \ln \left (x -{\mathrm e}\right ) \mathrm {csgn}\left (i \left (3+\ln \relax (x )\right )\right ) \mathrm {csgn}\left (i \left (3+\ln \relax (x )\right ) \left ({\mathrm e}-x \right )\right )^{2}+i \pi \ln \left (x -{\mathrm e}\right ) \mathrm {csgn}\left (i \left ({\mathrm e}-x \right )\right ) \mathrm {csgn}\left (i \left (3+\ln \relax (x )\right ) \left ({\mathrm e}-x \right )\right )^{2}+i \pi x \,\mathrm {csgn}\left (i \left (3+\ln \relax (x )\right )\right ) \mathrm {csgn}\left (i \left (3+\ln \relax (x )\right ) \left ({\mathrm e}-x \right )\right )^{2}+i \pi \ln \left (x -{\mathrm e}\right ) \mathrm {csgn}\left (i \left (3+\ln \relax (x )\right ) \left ({\mathrm e}-x \right )\right )^{3}-i \pi x \,\mathrm {csgn}\left (i \left (3+\ln \relax (x )\right )\right ) \mathrm {csgn}\left (i \left ({\mathrm e}-x \right )\right ) \mathrm {csgn}\left (i \left (3+\ln \relax (x )\right ) \left ({\mathrm e}-x \right )\right )-i \pi \ln \left (x -{\mathrm e}\right ) \mathrm {csgn}\left (i \left (3+\ln \relax (x )\right )\right ) \mathrm {csgn}\left (i \left ({\mathrm e}-x \right )\right ) \mathrm {csgn}\left (i \left (3+\ln \relax (x )\right ) \left ({\mathrm e}-x \right )\right )-i \pi \ln \left (3+\ln \relax (x )\right ) \mathrm {csgn}\left (i \left (3+\ln \relax (x )\right )\right ) \mathrm {csgn}\left (i \left ({\mathrm e}-x \right )\right ) \mathrm {csgn}\left (i \left (3+\ln \relax (x )\right ) \left ({\mathrm e}-x \right )\right )\)	\(544\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((2*x*exp(1)-2*x^2-2*x)*ln(x)+(6*x+2)*exp(1)-6*x^2-8*x)*ln((x-exp(1))*ln(x)-3*exp(1)+3*x)+((2*x^2*exp(1)-
2*x^3)*exp(x^2)+2*x^2*exp(1)-2*x^3-2*x^2)*ln(x)+(6*x^2*exp(1)-6*x^3)*exp(x^2)+(6*x^2+2*x)*exp(1)-6*x^3-8*x^2)/
((x*exp(1)-x^2)*ln(x)+3*x*exp(1)-3*x^2),x,method=_RETURNVERBOSE)

[Out]

ln(3+ln(x))^2+exp(x^2)+x^2-2*I*Pi*x*csgn(I*(3+ln(x))*(exp(1)-x))^2-2*I*Pi*ln(3+ln(x))*csgn(I*(3+ln(x))*(exp(1)
-x))^2-2*I*Pi*ln(x-exp(1))*csgn(I*(3+ln(x))*(exp(1)-x))^2+2*I*Pi*ln(x-exp(1))+2*I*Pi*ln(3+ln(x))+2*I*Pi*x+2*x*
ln(3+ln(x))+ln(exp(1)-x)^2+I*Pi*x*csgn(I*(3+ln(x))*(exp(1)-x))^3+I*Pi*ln(3+ln(x))*csgn(I*(3+ln(x))*(exp(1)-x))
^3+I*Pi*x*csgn(I*(exp(1)-x))*csgn(I*(3+ln(x))*(exp(1)-x))^2+I*Pi*ln(3+ln(x))*csgn(I*(3+ln(x)))*csgn(I*(3+ln(x)
)*(exp(1)-x))^2+I*Pi*ln(3+ln(x))*csgn(I*(exp(1)-x))*csgn(I*(3+ln(x))*(exp(1)-x))^2+(2*x+2*ln(3+ln(x)))*ln(exp(
1)-x)+I*Pi*ln(x-exp(1))*csgn(I*(3+ln(x)))*csgn(I*(3+ln(x))*(exp(1)-x))^2+I*Pi*ln(x-exp(1))*csgn(I*(exp(1)-x))*
csgn(I*(3+ln(x))*(exp(1)-x))^2+I*Pi*x*csgn(I*(3+ln(x)))*csgn(I*(3+ln(x))*(exp(1)-x))^2+I*Pi*ln(x-exp(1))*csgn(
I*(3+ln(x))*(exp(1)-x))^3-I*Pi*x*csgn(I*(3+ln(x)))*csgn(I*(exp(1)-x))*csgn(I*(3+ln(x))*(exp(1)-x))-I*Pi*ln(x-e
xp(1))*csgn(I*(3+ln(x)))*csgn(I*(exp(1)-x))*csgn(I*(3+ln(x))*(exp(1)-x))-I*Pi*ln(3+ln(x))*csgn(I*(3+ln(x)))*cs
gn(I*(exp(1)-x))*csgn(I*(3+ln(x))*(exp(1)-x))

________________________________________________________________________________________

maxima [B]  time = 0.42, size = 48, normalized size = 2.29 \begin {gather*} x^{2} + 2 \, {\left (x + \log \left (\log \relax (x) + 3\right )\right )} \log \left (x - e\right ) + \log \left (x - e\right )^{2} + 2 \, x \log \left (\log \relax (x) + 3\right ) + \log \left (\log \relax (x) + 3\right )^{2} + e^{\left (x^{2}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((2*x*exp(1)-2*x^2-2*x)*log(x)+(6*x+2)*exp(1)-6*x^2-8*x)*log((x-exp(1))*log(x)-3*exp(1)+3*x)+((2*x^
2*exp(1)-2*x^3)*exp(x^2)+2*x^2*exp(1)-2*x^3-2*x^2)*log(x)+(6*x^2*exp(1)-6*x^3)*exp(x^2)+(6*x^2+2*x)*exp(1)-6*x
^3-8*x^2)/((x*exp(1)-x^2)*log(x)+3*x*exp(1)-3*x^2),x, algorithm="maxima")

[Out]

x^2 + 2*(x + log(log(x) + 3))*log(x - e) + log(x - e)^2 + 2*x*log(log(x) + 3) + log(log(x) + 3)^2 + e^(x^2)

________________________________________________________________________________________

mupad [B]  time = 4.70, size = 72, normalized size = 3.43 \begin {gather*} {\mathrm {e}}^{x^2}+{\ln \left (3\,x-3\,\mathrm {e}+\ln \relax (x)\,\left (x-\mathrm {e}\right )\right )}^2+x^2-\frac {\ln \left (3\,x-3\,\mathrm {e}+\ln \relax (x)\,\left (x-\mathrm {e}\right )\right )\,\left (2\,x^2\,\mathrm {e}-2\,x^3\right )}{x\,\left (x-\mathrm {e}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(1)*(2*x + 6*x^2) + log(x)*(2*x^2*exp(1) + exp(x^2)*(2*x^2*exp(1) - 2*x^3) - 2*x^2 - 2*x^3) + exp(x^2)
*(6*x^2*exp(1) - 6*x^3) - 8*x^2 - 6*x^3 - log(3*x - 3*exp(1) + log(x)*(x - exp(1)))*(8*x + 6*x^2 + log(x)*(2*x
- 2*x*exp(1) + 2*x^2) - exp(1)*(6*x + 2)))/(log(x)*(x*exp(1) - x^2) + 3*x*exp(1) - 3*x^2),x)

[Out]

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

________________________________________________________________________________________

sympy [B]  time = 0.98, size = 49, normalized size = 2.33 \begin {gather*} x^{2} + 2 x \log {\left (3 x + \left (x - e\right ) \log {\relax (x )} - 3 e \right )} + e^{x^{2}} + \log {\left (3 x + \left (x - e\right ) \log {\relax (x )} - 3 e \right )}^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((2*x*exp(1)-2*x**2-2*x)*ln(x)+(6*x+2)*exp(1)-6*x**2-8*x)*ln((x-exp(1))*ln(x)-3*exp(1)+3*x)+((2*x**
2*exp(1)-2*x**3)*exp(x**2)+2*x**2*exp(1)-2*x**3-2*x**2)*ln(x)+(6*x**2*exp(1)-6*x**3)*exp(x**2)+(6*x**2+2*x)*ex
p(1)-6*x**3-8*x**2)/((x*exp(1)-x**2)*ln(x)+3*x*exp(1)-3*x**2),x)

[Out]

x**2 + 2*x*log(3*x + (x - E)*log(x) - 3*E) + exp(x**2) + log(3*x + (x - E)*log(x) - 3*E)**2

________________________________________________________________________________________