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

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

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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 = {} $$\begin{array}{c}\text{\$Aborted}\end{array}$$

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 $$\begin{array}{c}x(2+e^{x+\frac{{\log }^2(-x(2-e^x+x))}{x}}+x)\end{array}$$

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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fricas [A]  time = 0.57, size = 34, normalized size = 1.21 $$\begin{array}{c}{x}^2+x{e}^{\left(\frac{x^2+\log {(-x^2+x{e}^x-2x)}^2}{x}\right)}+2x\end{array}$$

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

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*x+2)*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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maple [C]  time = 0.34, size = 812, normalized size = 29.00

method	result	size
risch	$x^2+x{x}^{\frac{2i\pi }{x}}{(x-{\mathrm{e}}^x+2)}^{\frac{2i\pi }{x}}{x}^{\frac{i\pi \mathrm{csgn}\left(ix\right)}{x}}{(x-{\mathrm{e}}^x+2)}^{\frac{i\pi \mathrm{csgn}\left(ix\right)}{x}}{x}^{-\frac{i\pi \mathrm{csgn}\left(i({\mathrm{e}}^x-2-x)\right)}{x}}{(x-{\mathrm{e}}^x+2)}^{-\frac{i\pi \mathrm{csgn}\left(i({\mathrm{e}}^x-2-x)\right)}{x}}{(x-{\mathrm{e}}^x+2)}^{\frac{2\ln (x)}{x}}{x}^{-\frac{i\pi \mathrm{csgn}\left(ix({\mathrm{e}}^x-2-x)\right)\mathrm{csgn}\left(ix\right)\mathrm{csgn}\left(i({\mathrm{e}}^x-2-x)\right)}{x}}{(x-{\mathrm{e}}^x+2)}^{-\frac{i\pi \mathrm{csgn}\left(ix({\mathrm{e}}^x-2-x)\right)\mathrm{csgn}\left(ix\right)\mathrm{csgn}\left(i({\mathrm{e}}^x-2-x)\right)}{x}}{x}^{-\frac{i\mathrm{csgn}\left(ix({\mathrm{e}}^x-2-x)\right)\pi }{x}}{(x-{\mathrm{e}}^x+2)}^{-\frac{i\mathrm{csgn}\left(ix({\mathrm{e}}^x-2-x)\right)\pi }{x}}{x}^{-\frac{2i\pi }{x}}{(x-{\mathrm{e}}^x+2)}^{-\frac{2i\pi }{x}}{\mathrm{e}}^{\frac{-{\pi }^2\mathrm{csgn}{\left(ix({\mathrm{e}}^x-2-x)\right)}^4\mathrm{csgn}{\left(i({\mathrm{e}}^x-2-x)\right)}^2-2{\pi }^2\mathrm{csgn}{\left(ix({\mathrm{e}}^x-2-x)\right)}^3\mathrm{csgn}{\left(i({\mathrm{e}}^x-2-x)\right)}^2\mathrm{csgn}\left(ix\right)-{\pi }^2\mathrm{csgn}{\left(ix({\mathrm{e}}^x-2-x)\right)}^2\mathrm{csgn}{\left(ix\right)}^2\mathrm{csgn}{\left(i({\mathrm{e}}^x-2-x)\right)}^2-2{\pi }^2\mathrm{csgn}{\left(ix({\mathrm{e}}^x-2-x)\right)}^5\mathrm{csgn}\left(i({\mathrm{e}}^x-2-x)\right)+2{\pi }^2\mathrm{csgn}{\left(ix({\mathrm{e}}^x-2-x)\right)}^3\mathrm{csgn}{\left(ix\right)}^2\mathrm{csgn}\left(i({\mathrm{e}}^x-2-x)\right)-{\pi }^2\mathrm{csgn}{\left(ix({\mathrm{e}}^x-2-x)\right)}^6+2{\pi }^2\mathrm{csgn}{\left(ix({\mathrm{e}}^x-2-x)\right)}^5\mathrm{csgn}\left(ix\right)-{\pi }^2\mathrm{csgn}{\left(ix({\mathrm{e}}^x-2-x)\right)}^4\mathrm{csgn}{\left(ix\right)}^2-4{\pi }^2\mathrm{csgn}{\left(ix({\mathrm{e}}^x-2-x)\right)}^4\mathrm{csgn}\left(i({\mathrm{e}}^x-2-x)\right)-4{\pi }^2\mathrm{csgn}{\left(ix({\mathrm{e}}^x-2-x)\right)}^3\mathrm{csgn}\left(ix\right)\mathrm{csgn}\left(i({\mathrm{e}}^x-2-x)\right)-4{\pi }^2\mathrm{csgn}{\left(ix({\mathrm{e}}^x-2-x)\right)}^5+4{\pi }^2\mathrm{csgn}{\left(ix({\mathrm{e}}^x-2-x)\right)}^4\mathrm{csgn}\left(ix\right)-4{\pi }^2\mathrm{csgn}{\left(ix({\mathrm{e}}^x-2-x)\right)}^4+4{\pi }^2\mathrm{csgn}{\left(ix({\mathrm{e}}^x-2-x)\right)}^2\mathrm{csgn}\left(i({\mathrm{e}}^x-2-x)\right)+4{\pi }^2\mathrm{csgn}\left(ix({\mathrm{e}}^x-2-x)\right)\mathrm{csgn}\left(ix\right)\mathrm{csgn}\left(i({\mathrm{e}}^x-2-x)\right)+4{\pi }^2\mathrm{csgn}{\left(ix({\mathrm{e}}^x-2-x)\right)}^3-4{\pi }^2\mathrm{csgn}{\left(ix({\mathrm{e}}^x-2-x)\right)}^2\mathrm{csgn}\left(ix\right)+8{\pi }^2\mathrm{csgn}{\left(ix({\mathrm{e}}^x-2-x)\right)}^2-4{\pi }^2+4\ln (x{)}^2+4\ln {(x-{\mathrm{e}}^x+2)}^2+4x^2}{4x}}+2x$	$812$

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^(2*I/x*Pi)*(x-exp(x)+2)^(2*I/x*Pi)*x^(I/x*Pi*csgn(I*x))*(x-exp(x)+2)^(I/x*Pi*csgn(I*x))*x^(-I/x*Pi*csg
n(I*(exp(x)-2-x)))*(x-exp(x)+2)^(-I/x*Pi*csgn(I*(exp(x)-2-x)))*(x-exp(x)+2)^(2*ln(x)/x)*x^(-I/x*Pi*csgn(I*x*(e
xp(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*csgn(I*x*(exp(x)-2-x))*Pi/x)*(x-exp(x)+2)^(-I*csgn(I*x*(exp(x)-2-x))*Pi/x)*x^(-2*I/x*Pi)*(x-e
xp(x)+2)^(-2*I/x*Pi)*exp(1/4*(-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))^3*csgn(I*(exp(x)-2-x))^2*csgn(I*x)-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))^5*csgn(I*(exp(x)-2-x))+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))^6+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
*x)^2-4*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))^3*csgn(I*x)*csgn(I*(e
xp(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*csgn(I*x)-4*Pi^2*csgn(I*x*(exp(x)-
2-x))^4+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))*csgn(I*x)*csgn(I*(e
xp(x)-2-x))+4*Pi^2*csgn(I*x*(exp(x)-2-x))^3-4*Pi^2*csgn(I*x*(exp(x)-2-x))^2*csgn(I*x)+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 = 0.44, size = 49, normalized size = 1.75 $$\begin{array}{c}{x}^2+x{e}^{(x+\frac{\log (x{)}^2}{x}+\frac{2\log (x)\log (-x+e^x-2)}{x}+\frac{\log {(-x+e^x-2)}^2}{x})}+2x\end{array}$$

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*x+2)*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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mupad [B]  time = 4.30, size = 32, normalized size = 1.14 $$\begin{array}{c}2x+x^2+x{\mathrm{e}}^{\frac{{\ln (x{\mathrm{e}}^x-2x-x^2)}^2}{x}}{\mathrm{e}}^x\end{array}$$

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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sympy [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 $$\begin{array}{c}\text{Timed out}\end{array}$$

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*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)

[Out]

Timed out

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