3.73.32 $\int \frac{-6+6x-24x^2+e^{e^{-5x^2+x^2\log (x)}}(-4x^3+e^{-5x^2+x^2\log (x)}(-9x^3+9x^4+(2x^3-2x^4)\log (x)))+(-6+12x+e^{e^{-5x^2+x^2\log (x)}}(-x+2x^2))\log (\frac{6+e^{e^{-5x^2+x^2\log (x)}}x}{x})}{6x^2-12x^3+6x^4+e^{e^{-5x^2+x^2\log (x)}}(x^3-2x^4+x^5)}dx$

Optimal. Leaf size=33 $$\frac{-4x+\log (e^{e^{x^2(-5+\log (x))}}+\frac{6}{x})}{x-x^2}$$

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Rubi [F]  time = 15.07, 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 = {} $$\begin{array}{c}\int \frac{-6+6x-24x^2+e^{e^{-5x^2+x^2\log (x)}}(-4x^3+e^{-5x^2+x^2\log (x)}(-9x^3+9x^4+(2x^3-2x^4)\log (x)))+(-6+12x+e^{e^{-5x^2+x^2\log (x)}}(-x+2x^2))\log \left(\frac{6+e^{e^{-5x^2+x^2\log (x)}}x}{x}\right)}{6x^2-12x^3+6x^4+e^{e^{-5x^2+x^2\log (x)}}(x^3-2x^4+x^5)}dx\end{array}$$

Verification is not applicable to the result.

[In]

Int[(-6 + 6*x - 24*x^2 + E^E^(-5*x^2 + x^2*Log[x])*(-4*x^3 + E^(-5*x^2 + x^2*Log[x])*(-9*x^3 + 9*x^4 + (2*x^3
- 2*x^4)*Log[x])) + (-6 + 12*x + E^E^(-5*x^2 + x^2*Log[x])*(-x + 2*x^2))*Log[(6 + E^E^(-5*x^2 + x^2*Log[x])*x)
/x])/(6*x^2 - 12*x^3 + 6*x^4 + E^E^(-5*x^2 + x^2*Log[x])*(x^3 - 2*x^4 + x^5)),x]

[Out]

Log[E^(x^x^2/E^(5*x^2)) + 6/x]/((1 - x)*x) - 24*Defer[Int][1/((-1 + x)^2*(6 + E^(x^x^2/E^(5*x^2))*x)), x] - 4*
Defer[Int][E^(x^x^2/E^(5*x^2))/((-1 + x)^2*(6 + E^(x^x^2/E^(5*x^2))*x)), x] - 4*Defer[Int][E^(x^x^2/E^(5*x^2))
/((-1 + x)*(6 + E^(x^x^2/E^(5*x^2))*x)), x]

Rubi steps

$$\begin{array}{c}\begin{array}{rl}\text{integral}& =\int \frac{-6+6x-24x^2+e^{e^{-5x^2+x^2\log (x)}}(-4x^3+e^{-5x^2+x^2\log (x)}(-9x^3+9x^4+(2x^3-2x^4)\log (x)))+(-6+12x+e^{e^{-5x^2+x^2\log (x)}}(-x+2x^2))\log \left(\frac{6+e^{e^{-5x^2+x^2\log (x)}}x}{x}\right)}{(1-x{)}^2{x}^2(6+e^{e^{-5x^2}{x}^{x^2}}x)}dx\\ & =\int (-\frac{24}{(-1+x{)}^2(6+e^{e^{-5x^2}{x}^{x^2}}x)}-\frac{6}{(-1+x{)}^2{x}^2(6+e^{e^{-5x^2}{x}^{x^2}}x)}+\frac{6}{(-1+x{)}^{2}x(6+e^{e^{-5x^2}{x}^{x^2}}x)}-\frac{4e^{e^{-5x^2}{x}^{x^2}}x}{(-1+x{)}^2(6+e^{e^{-5x^2}{x}^{x^2}}x)}+\frac{(-1+2x)\log (e^{e^{-5x^2}{x}^{x^2}}+\frac{6}{x})}{(-1+x{)}^2{x}^2}-\frac{e^{-5x^2+e^{-5x^2}{x}^{x^2}}{x}^{1+x^2}(-9+2\log (x))}{(-1+x)(6+e^{e^{-5x^2}{x}^{x^2}}x)})dx\\ & =-(4\int \frac{e^{e^{-5x^2}{x}^{x^2}}x}{(-1+x{)}^2(6+e^{e^{-5x^2}{x}^{x^2}}x)}dx)-6\int \frac{1}{(-1+x{)}^2{x}^2(6+e^{e^{-5x^2}{x}^{x^2}}x)}dx+6\int \frac{1}{(-1+x{)}^{2}x(6+e^{e^{-5x^2}{x}^{x^2}}x)}dx-24\int \frac{1}{(-1+x{)}^2(6+e^{e^{-5x^2}{x}^{x^2}}x)}dx+\int \frac{(-1+2x)\log (e^{e^{-5x^2}{x}^{x^2}}+\frac{6}{x})}{(-1+x{)}^2{x}^2}dx-\int \frac{e^{-5x^2+e^{-5x^2}{x}^{x^2}}{x}^{1+x^2}(-9+2\log (x))}{(-1+x)(6+e^{e^{-5x^2}{x}^{x^2}}x)}dx\\ & =\frac{\log (e^{e^{-5x^2}{x}^{x^2}}+\frac{6}{x})}{(1-x)x}-4\int (\frac{e^{e^{-5x^2}{x}^{x^2}}}{(-1+x{)}^2(6+e^{e^{-5x^2}{x}^{x^2}}x)}+\frac{e^{e^{-5x^2}{x}^{x^2}}}{(-1+x)(6+e^{e^{-5x^2}{x}^{x^2}}x)})dx+6\int (\frac{1}{(-1+x{)}^2(6+e^{e^{-5x^2}{x}^{x^2}}x)}-\frac{1}{(-1+x)(6+e^{e^{-5x^2}{x}^{x^2}}x)}+\frac{1}{x(6+e^{e^{-5x^2}{x}^{x^2}}x)})dx-6\int (\frac{1}{(-1+x{)}^2(6+e^{e^{-5x^2}{x}^{x^2}}x)}-\frac{2}{(-1+x)(6+e^{e^{-5x^2}{x}^{x^2}}x)}+\frac{1}{x^2(6+e^{e^{-5x^2}{x}^{x^2}}x)}+\frac{2}{x(6+e^{e^{-5x^2}{x}^{x^2}}x)})dx-24\int \frac{1}{(-1+x{)}^2(6+e^{e^{-5x^2}{x}^{x^2}}x)}dx-\int \frac{e^{-5x^2}(-6e^{5x^2}-9e^{e^{-5x^2}{x}^{x^2}}{x}^{3+x^2}+2e^{e^{-5x^2}{x}^{x^2}}{x}^{3+x^2}\log (x))}{(1-x)x^2(6+e^{e^{-5x^2}{x}^{x^2}}x)}dx-\int (-\frac{9e^{-5x^2+e^{-5x^2}{x}^{x^2}}{x}^{1+x^2}}{(-1+x)(6+e^{e^{-5x^2}{x}^{x^2}}x)}+\frac{2e^{-5x^2+e^{-5x^2}{x}^{x^2}}{x}^{1+x^2}\log (x)}{(-1+x)(6+e^{e^{-5x^2}{x}^{x^2}}x)})dx\\ & =\frac{\log (e^{e^{-5x^2}{x}^{x^2}}+\frac{6}{x})}{(1-x)x}-2\int \frac{e^{-5x^2+e^{-5x^2}{x}^{x^2}}{x}^{1+x^2}\log (x)}{(-1+x)(6+e^{e^{-5x^2}{x}^{x^2}}x)}dx-4\int \frac{e^{e^{-5x^2}{x}^{x^2}}}{(-1+x{)}^2(6+e^{e^{-5x^2}{x}^{x^2}}x)}dx-4\int \frac{e^{e^{-5x^2}{x}^{x^2}}}{(-1+x)(6+e^{e^{-5x^2}{x}^{x^2}}x)}dx-6\int \frac{1}{(-1+x)(6+e^{e^{-5x^2}{x}^{x^2}}x)}dx-6\int \frac{1}{x^2(6+e^{e^{-5x^2}{x}^{x^2}}x)}dx+6\int \frac{1}{x(6+e^{e^{-5x^2}{x}^{x^2}}x)}dx+9\int \frac{e^{-5x^2+e^{-5x^2}{x}^{x^2}}{x}^{1+x^2}}{(-1+x)(6+e^{e^{-5x^2}{x}^{x^2}}x)}dx+12\int \frac{1}{(-1+x)(6+e^{e^{-5x^2}{x}^{x^2}}x)}dx-12\int \frac{1}{x(6+e^{e^{-5x^2}{x}^{x^2}}x)}dx-24\int \frac{1}{(-1+x{)}^2(6+e^{e^{-5x^2}{x}^{x^2}}x)}dx-\int (\frac{6}{(-1+x)x^2(6+e^{e^{-5x^2}{x}^{x^2}}x)}-\frac{e^{-5x^2+e^{-5x^2}{x}^{x^2}}{x}^{1+x^2}(-9+2\log (x))}{(-1+x)(6+e^{e^{-5x^2}{x}^{x^2}}x)})dx\\ & =\frac{\log (e^{e^{-5x^2}{x}^{x^2}}+\frac{6}{x})}{(1-x)x}+2\int \frac{\int \frac{e^{-5x^2+e^{-5x^2}{x}^{x^2}}{x}^{1+x^2}}{(-1+x)(6+e^{e^{-5x^2}{x}^{x^2}}x)}dx}{x}dx-4\int \frac{e^{e^{-5x^2}{x}^{x^2}}}{(-1+x{)}^2(6+e^{e^{-5x^2}{x}^{x^2}}x)}dx-4\int \frac{e^{e^{-5x^2}{x}^{x^2}}}{(-1+x)(6+e^{e^{-5x^2}{x}^{x^2}}x)}dx-6\int \frac{1}{(-1+x)(6+e^{e^{-5x^2}{x}^{x^2}}x)}dx-6\int \frac{1}{x^2(6+e^{e^{-5x^2}{x}^{x^2}}x)}dx-6\int \frac{1}{(-1+x)x^2(6+e^{e^{-5x^2}{x}^{x^2}}x)}dx+6\int \frac{1}{x(6+e^{e^{-5x^2}{x}^{x^2}}x)}dx+9\int \frac{e^{-5x^2+e^{-5x^2}{x}^{x^2}}{x}^{1+x^2}}{(-1+x)(6+e^{e^{-5x^2}{x}^{x^2}}x)}dx+12\int \frac{1}{(-1+x)(6+e^{e^{-5x^2}{x}^{x^2}}x)}dx-12\int \frac{1}{x(6+e^{e^{-5x^2}{x}^{x^2}}x)}dx-24\int \frac{1}{(-1+x{)}^2(6+e^{e^{-5x^2}{x}^{x^2}}x)}dx-(2\log (x))\int \frac{e^{-5x^2+e^{-5x^2}{x}^{x^2}}{x}^{1+x^2}}{(-1+x)(6+e^{e^{-5x^2}{x}^{x^2}}x)}dx+\int \frac{e^{-5x^2+e^{-5x^2}{x}^{x^2}}{x}^{1+x^2}(-9+2\log (x))}{(-1+x)(6+e^{e^{-5x^2}{x}^{x^2}}x)}dx\\ & =\frac{\log (e^{e^{-5x^2}{x}^{x^2}}+\frac{6}{x})}{(1-x)x}+2\int \frac{\int \frac{e^{-5x^2+e^{-5x^2}{x}^{x^2}}{x}^{1+x^2}}{(-1+x)(6+e^{e^{-5x^2}{x}^{x^2}}x)}dx}{x}dx-4\int \frac{e^{e^{-5x^2}{x}^{x^2}}}{(-1+x{)}^2(6+e^{e^{-5x^2}{x}^{x^2}}x)}dx-4\int \frac{e^{e^{-5x^2}{x}^{x^2}}}{(-1+x)(6+e^{e^{-5x^2}{x}^{x^2}}x)}dx-6\int \frac{1}{(-1+x)(6+e^{e^{-5x^2}{x}^{x^2}}x)}dx-6\int \frac{1}{x^2(6+e^{e^{-5x^2}{x}^{x^2}}x)}dx+6\int \frac{1}{x(6+e^{e^{-5x^2}{x}^{x^2}}x)}dx-6\int (\frac{1}{(-1+x)(6+e^{e^{-5x^2}{x}^{x^2}}x)}-\frac{1}{x^2(6+e^{e^{-5x^2}{x}^{x^2}}x)}-\frac{1}{x(6+e^{e^{-5x^2}{x}^{x^2}}x)})dx+9\int \frac{e^{-5x^2+e^{-5x^2}{x}^{x^2}}{x}^{1+x^2}}{(-1+x)(6+e^{e^{-5x^2}{x}^{x^2}}x)}dx+12\int \frac{1}{(-1+x)(6+e^{e^{-5x^2}{x}^{x^2}}x)}dx-12\int \frac{1}{x(6+e^{e^{-5x^2}{x}^{x^2}}x)}dx-24\int \frac{1}{(-1+x{)}^2(6+e^{e^{-5x^2}{x}^{x^2}}x)}dx-(2\log (x))\int \frac{e^{-5x^2+e^{-5x^2}{x}^{x^2}}{x}^{1+x^2}}{(-1+x)(6+e^{e^{-5x^2}{x}^{x^2}}x)}dx+\int (-\frac{9e^{-5x^2+e^{-5x^2}{x}^{x^2}}{x}^{1+x^2}}{(-1+x)(6+e^{e^{-5x^2}{x}^{x^2}}x)}+\frac{2e^{-5x^2+e^{-5x^2}{x}^{x^2}}{x}^{1+x^2}\log (x)}{(-1+x)(6+e^{e^{-5x^2}{x}^{x^2}}x)})dx\\ & =\frac{\log (e^{e^{-5x^2}{x}^{x^2}}+\frac{6}{x})}{(1-x)x}+2\int \frac{e^{-5x^2+e^{-5x^2}{x}^{x^2}}{x}^{1+x^2}\log (x)}{(-1+x)(6+e^{e^{-5x^2}{x}^{x^2}}x)}dx+2\int \frac{\int \frac{e^{-5x^2+e^{-5x^2}{x}^{x^2}}{x}^{1+x^2}}{(-1+x)(6+e^{e^{-5x^2}{x}^{x^2}}x)}dx}{x}dx-4\int \frac{e^{e^{-5x^2}{x}^{x^2}}}{(-1+x{)}^2(6+e^{e^{-5x^2}{x}^{x^2}}x)}dx-4\int \frac{e^{e^{-5x^2}{x}^{x^2}}}{(-1+x)(6+e^{e^{-5x^2}{x}^{x^2}}x)}dx-2(6\int \frac{1}{(-1+x)(6+e^{e^{-5x^2}{x}^{x^2}}x)}dx)+2(6\int \frac{1}{x(6+e^{e^{-5x^2}{x}^{x^2}}x)}dx)+12\int \frac{1}{(-1+x)(6+e^{e^{-5x^2}{x}^{x^2}}x)}dx-12\int \frac{1}{x(6+e^{e^{-5x^2}{x}^{x^2}}x)}dx-24\int \frac{1}{(-1+x{)}^2(6+e^{e^{-5x^2}{x}^{x^2}}x)}dx-(2\log (x))\int \frac{e^{-5x^2+e^{-5x^2}{x}^{x^2}}{x}^{1+x^2}}{(-1+x)(6+e^{e^{-5x^2}{x}^{x^2}}x)}dx\\ & =\frac{\log (e^{e^{-5x^2}{x}^{x^2}}+\frac{6}{x})}{(1-x)x}-4\int \frac{e^{e^{-5x^2}{x}^{x^2}}}{(-1+x{)}^2(6+e^{e^{-5x^2}{x}^{x^2}}x)}dx-4\int \frac{e^{e^{-5x^2}{x}^{x^2}}}{(-1+x)(6+e^{e^{-5x^2}{x}^{x^2}}x)}dx-2(6\int \frac{1}{(-1+x)(6+e^{e^{-5x^2}{x}^{x^2}}x)}dx)+2(6\int \frac{1}{x(6+e^{e^{-5x^2}{x}^{x^2}}x)}dx)+12\int \frac{1}{(-1+x)(6+e^{e^{-5x^2}{x}^{x^2}}x)}dx-12\int \frac{1}{x(6+e^{e^{-5x^2}{x}^{x^2}}x)}dx-24\int \frac{1}{(-1+x{)}^2(6+e^{e^{-5x^2}{x}^{x^2}}x)}dx\end{array}\end{array}$$

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Mathematica [A]  time = 0.31, size = 37, normalized size = 1.12 $$\begin{array}{c}\frac{4x-\log (e^{e^{-5x^2}{x}^{x^2}}+\frac{6}{x})}{(-1+x)x}\end{array}$$

Antiderivative was successfully verified.

[In]

Integrate[(-6 + 6*x - 24*x^2 + E^E^(-5*x^2 + x^2*Log[x])*(-4*x^3 + E^(-5*x^2 + x^2*Log[x])*(-9*x^3 + 9*x^4 + (
2*x^3 - 2*x^4)*Log[x])) + (-6 + 12*x + E^E^(-5*x^2 + x^2*Log[x])*(-x + 2*x^2))*Log[(6 + E^E^(-5*x^2 + x^2*Log[
x])*x)/x])/(6*x^2 - 12*x^3 + 6*x^4 + E^E^(-5*x^2 + x^2*Log[x])*(x^3 - 2*x^4 + x^5)),x]

[Out]

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

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fricas [A]  time = 1.03, size = 39, normalized size = 1.18 $$\begin{array}{c}\frac{4x-\log \left(\frac{x{e}^{\left(e^{(x^2\log (x)-5x^2)}\right)}+6}{x}\right)}{x^2-x}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((2*x^2-x)*exp(exp(x^2*log(x)-5*x^2))+12*x-6)*log((x*exp(exp(x^2*log(x)-5*x^2))+6)/x)+(((-2*x^4+2*x
^3)*log(x)+9*x^4-9*x^3)*exp(x^2*log(x)-5*x^2)-4*x^3)*exp(exp(x^2*log(x)-5*x^2))-24*x^2+6*x-6)/((x^5-2*x^4+x^3)
*exp(exp(x^2*log(x)-5*x^2))+6*x^4-12*x^3+6*x^2),x, algorithm="fricas")

[Out]

(4*x - log((x*e^(e^(x^2*log(x) - 5*x^2)) + 6)/x))/(x^2 - x)

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giac [B]  time = 1.60, size = 78, normalized size = 2.36 $$\begin{array}{c}\frac{4x-\log \left((x{e}^{(x^2\log (x)-5x^2+e^{(x^2\log (x)-5x^2)})}+6e^{(x^2\log (x)-5x^2)})e^{(-x^2\log (x)+5x^2)}\right)+\log (x)}{x^2-x}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((2*x^2-x)*exp(exp(x^2*log(x)-5*x^2))+12*x-6)*log((x*exp(exp(x^2*log(x)-5*x^2))+6)/x)+(((-2*x^4+2*x
^3)*log(x)+9*x^4-9*x^3)*exp(x^2*log(x)-5*x^2)-4*x^3)*exp(exp(x^2*log(x)-5*x^2))-24*x^2+6*x-6)/((x^5-2*x^4+x^3)
*exp(exp(x^2*log(x)-5*x^2))+6*x^4-12*x^3+6*x^2),x, algorithm="giac")

[Out]

(4*x - log((x*e^(x^2*log(x) - 5*x^2 + e^(x^2*log(x) - 5*x^2)) + 6*e^(x^2*log(x) - 5*x^2))*e^(-x^2*log(x) + 5*x
^2)) + log(x))/(x^2 - x)

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maple [C]  time = 0.21, size = 222, normalized size = 6.73

method	result	size
risch	$-\frac{\ln (x{\mathrm{e}}^{x^{x^2}{\mathrm{e}}^{-5x^2}}+6)}{x(x-1)}+\frac{i\pi \mathrm{csgn}\left(\frac{i}{x}\right)\mathrm{csgn}\left(i(x{\mathrm{e}}^{x^{x^2}{\mathrm{e}}^{-5x^2}}+6)\right)\mathrm{csgn}\left(\frac{i(x{\mathrm{e}}^{x^{x^2}{\mathrm{e}}^{-5x^2}}+6)}{x}\right)-i\pi \mathrm{csgn}\left(\frac{i}{x}\right)\mathrm{csgn}{\left(\frac{i(x{\mathrm{e}}^{x^{x^2}{\mathrm{e}}^{-5x^2}}+6)}{x}\right)}^2-i\pi \mathrm{csgn}\left(i(x{\mathrm{e}}^{x^{x^2}{\mathrm{e}}^{-5x^2}}+6)\right)\mathrm{csgn}{\left(\frac{i(x{\mathrm{e}}^{x^{x^2}{\mathrm{e}}^{-5x^2}}+6)}{x}\right)}^2+i\pi \mathrm{csgn}{\left(\frac{i(x{\mathrm{e}}^{x^{x^2}{\mathrm{e}}^{-5x^2}}+6)}{x}\right)}^3+8x+2\ln (x)}{2x(x-1)}$	$222$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((2*x^2-x)*exp(exp(x^2*ln(x)-5*x^2))+12*x-6)*ln((x*exp(exp(x^2*ln(x)-5*x^2))+6)/x)+(((-2*x^4+2*x^3)*ln(x)
+9*x^4-9*x^3)*exp(x^2*ln(x)-5*x^2)-4*x^3)*exp(exp(x^2*ln(x)-5*x^2))-24*x^2+6*x-6)/((x^5-2*x^4+x^3)*exp(exp(x^2
*ln(x)-5*x^2))+6*x^4-12*x^3+6*x^2),x,method=_RETURNVERBOSE)

[Out]

-1/x/(x-1)*ln(x*exp(x^(x^2)*exp(-5*x^2))+6)+1/2*(I*Pi*csgn(I/x)*csgn(I*(x*exp(x^(x^2)*exp(-5*x^2))+6))*csgn(I/
x*(x*exp(x^(x^2)*exp(-5*x^2))+6))-I*Pi*csgn(I/x)*csgn(I/x*(x*exp(x^(x^2)*exp(-5*x^2))+6))^2-I*Pi*csgn(I*(x*exp
(x^(x^2)*exp(-5*x^2))+6))*csgn(I/x*(x*exp(x^(x^2)*exp(-5*x^2))+6))^2+I*Pi*csgn(I/x*(x*exp(x^(x^2)*exp(-5*x^2))
+6))^3+8*x+2*ln(x))/x/(x-1)

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maxima [A]  time = 0.44, size = 37, normalized size = 1.12 $$\begin{array}{c}\frac{4x-\log (x{e}^{\left(e^{(x^2\log (x)-5x^2)}\right)}+6)+\log (x)}{x^2-x}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((2*x^2-x)*exp(exp(x^2*log(x)-5*x^2))+12*x-6)*log((x*exp(exp(x^2*log(x)-5*x^2))+6)/x)+(((-2*x^4+2*x
^3)*log(x)+9*x^4-9*x^3)*exp(x^2*log(x)-5*x^2)-4*x^3)*exp(exp(x^2*log(x)-5*x^2))-24*x^2+6*x-6)/((x^5-2*x^4+x^3)
*exp(exp(x^2*log(x)-5*x^2))+6*x^4-12*x^3+6*x^2),x, algorithm="maxima")

[Out]

(4*x - log(x*e^(e^(x^2*log(x) - 5*x^2)) + 6) + log(x))/(x^2 - x)

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mupad [B]  time = 4.85, size = 37, normalized size = 1.12 $$\begin{array}{c}\frac{4x-\ln \left(\frac{x{\mathrm{e}}^{x^{x^2}{\mathrm{e}}^{-5x^2}}+6}{x}\right)}{x(x-1)}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(log((x*exp(exp(x^2*log(x) - 5*x^2)) + 6)/x)*(exp(exp(x^2*log(x) - 5*x^2))*(x - 2*x^2) - 12*x + 6) - exp(
exp(x^2*log(x) - 5*x^2))*(exp(x^2*log(x) - 5*x^2)*(log(x)*(2*x^3 - 2*x^4) - 9*x^3 + 9*x^4) - 4*x^3) - 6*x + 24
*x^2 + 6)/(exp(exp(x^2*log(x) - 5*x^2))*(x^3 - 2*x^4 + x^5) + 6*x^2 - 12*x^3 + 6*x^4),x)

[Out]

(4*x - log((x*exp(x^(x^2)*exp(-5*x^2)) + 6)/x))/(x*(x - 1))

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sympy [A]  time = 33.23, size = 31, normalized size = 0.94 $$\begin{array}{c}-\frac{\log \left(\frac{x{e}^{e^{x^2\log (x)-5x^2}}+6}{x}\right)}{x^2-x}+\frac{4}{x-1}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((2*x**2-x)*exp(exp(x**2*ln(x)-5*x**2))+12*x-6)*ln((x*exp(exp(x**2*ln(x)-5*x**2))+6)/x)+(((-2*x**4+
2*x**3)*ln(x)+9*x**4-9*x**3)*exp(x**2*ln(x)-5*x**2)-4*x**3)*exp(exp(x**2*ln(x)-5*x**2))-24*x**2+6*x-6)/((x**5-
2*x**4+x**3)*exp(exp(x**2*ln(x)-5*x**2))+6*x**4-12*x**3+6*x**2),x)

[Out]

-log((x*exp(exp(x**2*log(x) - 5*x**2)) + 6)/x)/(x**2 - x) + 4/(x - 1)

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