3.41.59 $\int \frac{e^{9x+3x^2+(3x+x^2)\log (-1+e^{e^x}+x)}(-9+6x+7x^2+e^{e^x}(9+6x+e^x(3x+x^2))+(-3+x+2x^2+e^{e^x}(3+2x))\log (-1+e^{e^x}+x))}{-1+e^{e^x}+x}dx$

Optimal. Leaf size=18 $$e^{x(3+x)(3+\log (-1+e^{e^x}+x))}$$

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Rubi [F]  time = 127.75, 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 = {} $$\begin{array}{c}\int \frac{\exp (9x+3x^2+(3x+x^2)\log (-1+e^{e^x}+x))(-9+6x+7x^2+e^{e^x}(9+6x+e^x(3x+x^2))+(-3+x+2x^2+e^{e^x}(3+2x))\log (-1+e^{e^x}+x))}{-1+e^{e^x}+x}dx\end{array}$$

Verification is not applicable to the result.

[In]

Int[(E^(9*x + 3*x^2 + (3*x + x^2)*Log[-1 + E^E^x + x])*(-9 + 6*x + 7*x^2 + E^E^x*(9 + 6*x + E^x*(3*x + x^2)) +
(-3 + x + 2*x^2 + E^E^x*(3 + 2*x))*Log[-1 + E^E^x + x]))/(-1 + E^E^x + x),x]

[Out]

9*Defer[Int][E^(x*(3 + x)*(3 + Log[-1 + E^E^x + x])), x] + 6*Defer[Int][E^(x*(3 + x)*(3 + Log[-1 + E^E^x + x])
)*x, x] + 3*Defer[Int][(E^(x*(3 + x)*(3 + Log[-1 + E^E^x + x]))*x)/(-1 + E^E^x + x), x] + 3*Defer[Int][(E^(E^x
+ x + x*(3 + x)*(3 + Log[-1 + E^E^x + x]))*x)/(-1 + E^E^x + x), x] + Defer[Int][(E^(x*(3 + x)*(3 + Log[-1 + E
^E^x + x]))*x^2)/(-1 + E^E^x + x), x] + Defer[Int][(E^(E^x + x + x*(3 + x)*(3 + Log[-1 + E^E^x + x]))*x^2)/(-1
+ E^E^x + x), x] + 3*Defer[Int][E^(x*(3 + x)*(3 + Log[-1 + E^E^x + x]))*Log[-1 + E^E^x + x], x] + 2*Defer[Int
][E^(x*(3 + x)*(3 + Log[-1 + E^E^x + x]))*x*Log[-1 + E^E^x + x], x]

Rubi steps

$$\begin{array}{c}\begin{array}{rl}\text{integral}& =\int \frac{e^{x(3+x)(3+\log (-1+e^{e^x}+x))}(9-6x-7x^2-e^{e^x}(9+6x+e^x(3x+x^2))-(-3+x+2x^2+e^{e^x}(3+2x))\log (-1+e^{e^x}+x))}{1-e^{e^x}-x}dx\\ & =\int (\frac{e^{e^x+x+x(3+x)(3+\log (-1+e^{e^x}+x))}x(3+x)}{-1+e^{e^x}+x}+\frac{e^{x(3+x)(3+\log (-1+e^{e^x}+x))}(-9+9e^{e^x}+6x+6e^{e^x}x+7x^2-3\log (-1+e^{e^x}+x)+3e^{e^x}\log (-1+e^{e^x}+x)+x\log (-1+e^{e^x}+x)+2e^{e^x}x\log (-1+e^{e^x}+x)+2x^2\log (-1+e^{e^x}+x))}{-1+e^{e^x}+x})dx\\ & =\int \frac{e^{e^x+x+x(3+x)(3+\log (-1+e^{e^x}+x))}x(3+x)}{-1+e^{e^x}+x}dx+\int \frac{e^{x(3+x)(3+\log (-1+e^{e^x}+x))}(-9+9e^{e^x}+6x+6e^{e^x}x+7x^2-3\log (-1+e^{e^x}+x)+3e^{e^x}\log (-1+e^{e^x}+x)+x\log (-1+e^{e^x}+x)+2e^{e^x}x\log (-1+e^{e^x}+x)+2x^2\log (-1+e^{e^x}+x))}{-1+e^{e^x}+x}dx\\ & =\int (\frac{3e^{e^x+x+x(3+x)(3+\log (-1+e^{e^x}+x))}x}{-1+e^{e^x}+x}+\frac{e^{e^x+x+x(3+x)(3+\log (-1+e^{e^x}+x))}{x}^2}{-1+e^{e^x}+x})dx+\int \frac{e^{x(3+x)(3+\log (-1+e^{e^x}+x))}(9-6x-7x^2-e^{e^x}(9+6x)-(-1+e^{e^x}+x)(3+2x)\log (-1+e^{e^x}+x))}{1-e^{e^x}-x}dx\\ & =3\int \frac{e^{e^x+x+x(3+x)(3+\log (-1+e^{e^x}+x))}x}{-1+e^{e^x}+x}dx+\int \frac{e^{e^x+x+x(3+x)(3+\log (-1+e^{e^x}+x))}{x}^2}{-1+e^{e^x}+x}dx+\int (\frac{e^{x(3+x)(3+\log (-1+e^{e^x}+x))}x(3+x)}{-1+e^{e^x}+x}+e^{x(3+x)(3+\log (-1+e^{e^x}+x))}(3+2x)(3+\log (-1+e^{e^x}+x)))dx\\ & =3\int \frac{e^{e^x+x+x(3+x)(3+\log (-1+e^{e^x}+x))}x}{-1+e^{e^x}+x}dx+\int \frac{e^{e^x+x+x(3+x)(3+\log (-1+e^{e^x}+x))}{x}^2}{-1+e^{e^x}+x}dx+\int \frac{e^{x(3+x)(3+\log (-1+e^{e^x}+x))}x(3+x)}{-1+e^{e^x}+x}dx+\int e^{x(3+x)(3+\log (-1+e^{e^x}+x))}(3+2x)(3+\log (-1+e^{e^x}+x))dx\\ & =3\int \frac{e^{e^x+x+x(3+x)(3+\log (-1+e^{e^x}+x))}x}{-1+e^{e^x}+x}dx+\int \frac{e^{e^x+x+x(3+x)(3+\log (-1+e^{e^x}+x))}{x}^2}{-1+e^{e^x}+x}dx+\int (\frac{3e^{x(3+x)(3+\log (-1+e^{e^x}+x))}x}{-1+e^{e^x}+x}+\frac{e^{x(3+x)(3+\log (-1+e^{e^x}+x))}{x}^2}{-1+e^{e^x}+x})dx+\int (3e^{x(3+x)(3+\log (-1+e^{e^x}+x))}(3+2x)+e^{x(3+x)(3+\log (-1+e^{e^x}+x))}(3+2x)\log (-1+e^{e^x}+x))dx\\ & =3\int \frac{e^{x(3+x)(3+\log (-1+e^{e^x}+x))}x}{-1+e^{e^x}+x}dx+3\int \frac{e^{e^x+x+x(3+x)(3+\log (-1+e^{e^x}+x))}x}{-1+e^{e^x}+x}dx+3\int e^{x(3+x)(3+\log (-1+e^{e^x}+x))}(3+2x)dx+\int \frac{e^{x(3+x)(3+\log (-1+e^{e^x}+x))}{x}^2}{-1+e^{e^x}+x}dx+\int \frac{e^{e^x+x+x(3+x)(3+\log (-1+e^{e^x}+x))}{x}^2}{-1+e^{e^x}+x}dx+\int e^{x(3+x)(3+\log (-1+e^{e^x}+x))}(3+2x)\log (-1+e^{e^x}+x)dx\\ & =3\int \frac{e^{x(3+x)(3+\log (-1+e^{e^x}+x))}x}{-1+e^{e^x}+x}dx+3\int \frac{e^{e^x+x+x(3+x)(3+\log (-1+e^{e^x}+x))}x}{-1+e^{e^x}+x}dx+3\int (3e^{x(3+x)(3+\log (-1+e^{e^x}+x))}+2e^{x(3+x)(3+\log (-1+e^{e^x}+x))}x)dx+\int \frac{e^{x(3+x)(3+\log (-1+e^{e^x}+x))}{x}^2}{-1+e^{e^x}+x}dx+\int \frac{e^{e^x+x+x(3+x)(3+\log (-1+e^{e^x}+x))}{x}^2}{-1+e^{e^x}+x}dx+\int (3e^{x(3+x)(3+\log (-1+e^{e^x}+x))}\log (-1+e^{e^x}+x)+2e^{x(3+x)(3+\log (-1+e^{e^x}+x))}x\log (-1+e^{e^x}+x))dx\\ & =2\int e^{x(3+x)(3+\log (-1+e^{e^x}+x))}x\log (-1+e^{e^x}+x)dx+3\int \frac{e^{x(3+x)(3+\log (-1+e^{e^x}+x))}x}{-1+e^{e^x}+x}dx+3\int \frac{e^{e^x+x+x(3+x)(3+\log (-1+e^{e^x}+x))}x}{-1+e^{e^x}+x}dx+3\int e^{x(3+x)(3+\log (-1+e^{e^x}+x))}\log (-1+e^{e^x}+x)dx+6\int e^{x(3+x)(3+\log (-1+e^{e^x}+x))}xdx+9\int e^{x(3+x)(3+\log (-1+e^{e^x}+x))}dx+\int \frac{e^{x(3+x)(3+\log (-1+e^{e^x}+x))}{x}^2}{-1+e^{e^x}+x}dx+\int \frac{e^{e^x+x+x(3+x)(3+\log (-1+e^{e^x}+x))}{x}^2}{-1+e^{e^x}+x}dx\end{array}\end{array}$$

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Mathematica [A]  time = 0.16, size = 23, normalized size = 1.28 $$\begin{array}{c}{e}^{3x(3+x)}{(-1+e^{e^x}+x)}^{x(3+x)}\end{array}$$

Antiderivative was successfully verified.

[In]

Integrate[(E^(9*x + 3*x^2 + (3*x + x^2)*Log[-1 + E^E^x + x])*(-9 + 6*x + 7*x^2 + E^E^x*(9 + 6*x + E^x*(3*x + x
^2)) + (-3 + x + 2*x^2 + E^E^x*(3 + 2*x))*Log[-1 + E^E^x + x]))/(-1 + E^E^x + x),x]

[Out]

E^(3*x*(3 + x))*(-1 + E^E^x + x)^(x*(3 + x))

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fricas [A]  time = 0.72, size = 25, normalized size = 1.39 $$\begin{array}{c}{e}^{(3x^2+(x^2+3x)\log (x+e^{\left(e^x\right)}-1)+9x)}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((2*x+3)*exp(exp(x))+2*x^2+x-3)*log(exp(exp(x))+x-1)+((x^2+3*x)*exp(x)+6*x+9)*exp(exp(x))+7*x^2+6*x
-9)*exp((x^2+3*x)*log(exp(exp(x))+x-1)+3*x^2+9*x)/(exp(exp(x))+x-1),x, algorithm="fricas")

[Out]

e^(3*x^2 + (x^2 + 3*x)*log(x + e^(e^x) - 1) + 9*x)

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giac [B]  time = 2.39, size = 31, normalized size = 1.72 $$\begin{array}{c}{e}^{(x^2\log (x+e^{\left(e^x\right)}-1)+3x^2+3x\log (x+e^{\left(e^x\right)}-1)+9x)}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((2*x+3)*exp(exp(x))+2*x^2+x-3)*log(exp(exp(x))+x-1)+((x^2+3*x)*exp(x)+6*x+9)*exp(exp(x))+7*x^2+6*x
-9)*exp((x^2+3*x)*log(exp(exp(x))+x-1)+3*x^2+9*x)/(exp(exp(x))+x-1),x, algorithm="giac")

[Out]

e^(x^2*log(x + e^(e^x) - 1) + 3*x^2 + 3*x*log(x + e^(e^x) - 1) + 9*x)

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maple [A]  time = 0.06, size = 21, normalized size = 1.17

method	result	size
risch	${({\mathrm{e}}^{{\mathrm{e}}^x}+x-1)}^{(3+x)x}{\mathrm{e}}^{3(3+x)x}$	$21$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((2*x+3)*exp(exp(x))+2*x^2+x-3)*ln(exp(exp(x))+x-1)+((x^2+3*x)*exp(x)+6*x+9)*exp(exp(x))+7*x^2+6*x-9)*exp
((x^2+3*x)*ln(exp(exp(x))+x-1)+3*x^2+9*x)/(exp(exp(x))+x-1),x,method=_RETURNVERBOSE)

[Out]

(exp(exp(x))+x-1)^((3+x)*x)*exp(3*(3+x)*x)

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maxima [B]  time = 0.55, size = 31, normalized size = 1.72 $$\begin{array}{c}{e}^{(x^2\log (x+e^{\left(e^x\right)}-1)+3x^2+3x\log (x+e^{\left(e^x\right)}-1)+9x)}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((2*x+3)*exp(exp(x))+2*x^2+x-3)*log(exp(exp(x))+x-1)+((x^2+3*x)*exp(x)+6*x+9)*exp(exp(x))+7*x^2+6*x
-9)*exp((x^2+3*x)*log(exp(exp(x))+x-1)+3*x^2+9*x)/(exp(exp(x))+x-1),x, algorithm="maxima")

[Out]

e^(x^2*log(x + e^(e^x) - 1) + 3*x^2 + 3*x*log(x + e^(e^x) - 1) + 9*x)

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mupad [B]  time = 0.22, size = 25, normalized size = 1.39 $$\begin{array}{c}{\mathrm{e}}^{3x^2+9x}{(x+{\mathrm{e}}^{{\mathrm{e}}^x}-1)}^{x^2+3x}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(9*x + 3*x^2 + log(x + exp(exp(x)) - 1)*(3*x + x^2))*(6*x + exp(exp(x))*(6*x + exp(x)*(3*x + x^2) + 9)
+ log(x + exp(exp(x)) - 1)*(x + 2*x^2 + exp(exp(x))*(2*x + 3) - 3) + 7*x^2 - 9))/(x + exp(exp(x)) - 1),x)

[Out]

exp(9*x + 3*x^2)*(x + exp(exp(x)) - 1)^(3*x + x^2)

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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((((2*x+3)*exp(exp(x))+2*x**2+x-3)*ln(exp(exp(x))+x-1)+((x**2+3*x)*exp(x)+6*x+9)*exp(exp(x))+7*x**2+6
*x-9)*exp((x**2+3*x)*ln(exp(exp(x))+x-1)+3*x**2+9*x)/(exp(exp(x))+x-1),x)

[Out]

Timed out

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