∫ −4x−6x2−2x3+ex(2x+2x2)+ex2+log2(−2x+exx−x2) ________________________________x (−2x−3x2−x3+ex(x+x2)+(−4−4x+ex(2+2x)) log(−2x+exx−x2)+(2−ex+x) log2(−2x+exx−x2))___________________________________________________________________________________________________________

3.69.21 $\int \frac {-4 x-6 x^2-2 x^3+e^x (2 x+2 x^2)+e^{\frac {x^2+\log ^2(-2 x+e^x x-x^2)}{x}} (-2 x-3 x^2-x^3+e^x (x+x^2)+(-4-4 x+e^x (2+2 x)) \log (-2 x+e^x x-x^2)+(2-e^x+x) \log ^2(-2 x+e^x x-x^2))}{-2 x+e^x x-x^2} \, dx$ [6821]

Optimal. Leaf size=28 \[ -1+x \left (2+e^{x+\frac {\log ^2\left (\left (-2+e^x-x\right ) x\right )}{x}}+x\right ) \]

[Out]

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

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Rubi [F]
time = 180.01, 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[(-4*x - 6*x^2 - 2*x^3 + E^x*(2*x + 2*x^2) + E^((x^2 + Log[-2*x + E^x*x - x^2]^2)/x)*(-2*x - 3*x^2 - x^3 +

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

/(-2*x + E^x*x - x^2),x]

[Out]

$Aborted

Rubi steps

Aborted

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Mathematica [A]
time = 0.15, size = 27, normalized size = 0.96 \begin {gather*} x \left (2+e^{x+\frac {\log ^2\left (-x \left (2-e^x+x\right )\right )}{x}}+x\right ) \end {gather*}

Antiderivative was successfully veriﬁed.

[In]

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

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

2]^2))/(-2*x + E^x*x - x^2),x]

[Out]

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

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Maple [C] Result contains higher order function than in optimal. Order 9 vs. order 3.
time = 0.50, size = 812, normalized size = 29.00


method	result	size

risch	$\text {Expression too large to display}$	$812$

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

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

-2*x)*exp((ln(exp(x)*x-x^2-2*x)^2+x^2)/x)+(2*x^2+2*x)*exp(x)-2*x^3-6*x^2-4*x)/(exp(x)*x-x^2-2*x),x,method=_RET

URNVERBOSE)

[Out]

x^2+x*x^(-I/x*Pi*csgn(I*x*(exp(x)-2-x)))*(x-exp(x)+2)^(-I/x*Pi*csgn(I*x*(exp(x)-2-x)))*x^(-2*I*Pi/x)*(x-exp(x)

+2)^(-2*I*Pi/x)*(x-exp(x)+2)^(2*ln(x)/x)*x^(2*I*Pi/x)*(x-exp(x)+2)^(2*I*Pi/x)*x^(-I/x*Pi*csgn(I*x*(exp(x)-2-x)

)*csgn(I*x)*csgn(I*(exp(x)-2-x)))*(x-exp(x)+2)^(-I/x*Pi*csgn(I*x*(exp(x)-2-x))*csgn(I*x)*csgn(I*(exp(x)-2-x)))

*x^(I/x*Pi*csgn(I*x))*(x-exp(x)+2)^(I/x*Pi*csgn(I*x))*x^(-I/x*Pi*csgn(I*(exp(x)-2-x)))*(x-exp(x)+2)^(-I/x*Pi*c

sgn(I*(exp(x)-2-x)))*exp(1/4*(-Pi^2*csgn(I*x*(exp(x)-2-x))^2*csgn(I*x)^2*csgn(I*(exp(x)-2-x))^2+2*Pi^2*csgn(I*

x*(exp(x)-2-x))^3*csgn(I*x)^2*csgn(I*(exp(x)-2-x))-Pi^2*csgn(I*x*(exp(x)-2-x))^4*csgn(I*x)^2-2*Pi^2*csgn(I*x*(

exp(x)-2-x))^3*csgn(I*(exp(x)-2-x))^2*csgn(I*x)+2*Pi^2*csgn(I*x*(exp(x)-2-x))^5*csgn(I*x)-Pi^2*csgn(I*x*(exp(x

)-2-x))^4*csgn(I*(exp(x)-2-x))^2-2*Pi^2*csgn(I*x*(exp(x)-2-x))^5*csgn(I*(exp(x)-2-x))-Pi^2*csgn(I*x*(exp(x)-2-

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

-4*Pi^2*csgn(I*x*(exp(x)-2-x))^4*csgn(I*(exp(x)-2-x))-4*Pi^2*csgn(I*x*(exp(x)-2-x))^5-4*Pi^2*csgn(I*x*(exp(x)-

2-x))^4+4*Pi^2*csgn(I*x*(exp(x)-2-x))*csgn(I*x)*csgn(I*(exp(x)-2-x))-4*Pi^2*csgn(I*x*(exp(x)-2-x))^2*csgn(I*x)

+4*Pi^2*csgn(I*x*(exp(x)-2-x))^2*csgn(I*(exp(x)-2-x))+4*Pi^2*csgn(I*x*(exp(x)-2-x))^3+8*Pi^2*csgn(I*x*(exp(x)-

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

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Maxima [A]
time = 0.34, size = 49, normalized size = 1.75 \begin {gather*} x^{2} + x e^{\left (x + \frac {\log \left (x\right )^{2}}{x} + \frac {2 \, \log \left (x\right ) \log \left (-x + e^{x} - 2\right )}{x} + \frac {\log \left (-x + e^{x} - 2\right )^{2}}{x}\right )} + 2 \, x \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

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

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

lgorithm="maxima")

[Out]

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

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Fricas [A]
time = 0.39, size = 34, normalized size = 1.21 \begin {gather*} x^{2} + x e^{\left (\frac {x^{2} + \log \left (-x^{2} + x e^{x} - 2 \, x\right )^{2}}{x}\right )} + 2 \, x \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

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

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

lgorithm="fricas")

[Out]

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

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

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

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

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

-2*x),x)

[Out]

Exception raised: SystemError >> excessive stack use: stack is 3005 deep

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Giac [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

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

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

lgorithm="giac")

[Out]

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

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

)/(x^2 - x*e^x + 2*x), x)

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Mupad [B]
time = 4.30, size = 32, normalized size = 1.14 \begin {gather*} 2\,x+x^2+x\,{\mathrm {e}}^{\frac {{\ln \left (x\,{\mathrm {e}}^x-2\,x-x^2\right )}^2}{x}}\,{\mathrm {e}}^x \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

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

g(x*exp(x) - 2*x - x^2)*(4*x - exp(x)*(2*x + 2) + 4) + 3*x^2 + x^3 - exp(x)*(x + x^2)) - exp(x)*(2*x + 2*x^2)

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

[Out]

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

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3.69.21 \(\int \frac {-4 x-6 x^2-2 x^3+e^x (2 x+2 x^2)+e^{\frac {x^2+\log ^2(-2 x+e^x x-x^2)}{x}} (-2 x-3 x^2-x^3+e^x (x+x^2)+(-4-4 x+e^x (2+2 x)) \log (-2 x+e^x x-x^2)+(2-e^x+x) \log ^2(-2 x+e^x x-x^2))}{-2 x+e^x x-x^2} \, dx\) [6821]