3.26.69 $\int \frac{16{\log }^2(x^2)+e^{2e^{e^{\frac{x}{\log (x^2)}}}+4x}((1+4x){\log }^2(x^2)+e^{e^{\frac{x}{\log (x^2)}}+\frac{x}{\log (x^2)}}(-4x+2x\log (x^2)))+e^{e^{e^{\frac{x}{\log (x^2)}}}+2x}((8+16x){\log }^2(x^2)+e^{e^{\frac{x}{\log (x^2)}}+\frac{x}{\log (x^2)}}(-16x+8x\log (x^2)))}{{\log }^2(x^2)}dx$

Optimal. Leaf size=26 $$-4+{(4+e^{e^{e^{\frac{x}{\log \left(x^2\right)}}}+2x})}^{2}x$$

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Rubi [F]  time = 4.99, 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 = {} $$\begin{array}{c}\int \frac{16{\log }^2\left(x^2\right)+e^{2e^{e^{\frac{x}{\log \left(x^2\right)}}}+4x}((1+4x){\log }^2\left(x^2\right)+e^{e^{\frac{x}{\log \left(x^2\right)}}+\frac{x}{\log \left(x^2\right)}}(-4x+2x\log \left(x^2\right)))+e^{e^{e^{\frac{x}{\log \left(x^2\right)}}}+2x}((8+16x){\log }^2\left(x^2\right)+e^{e^{\frac{x}{\log \left(x^2\right)}}+\frac{x}{\log \left(x^2\right)}}(-16x+8x\log \left(x^2\right)))}{{\log }^2\left(x^2\right)}dx\end{array}$$

Verification is not applicable to the result.

[In]

Int[(16*Log[x^2]^2 + E^(2*E^E^(x/Log[x^2]) + 4*x)*((1 + 4*x)*Log[x^2]^2 + E^(E^(x/Log[x^2]) + x/Log[x^2])*(-4*
x + 2*x*Log[x^2])) + E^(E^E^(x/Log[x^2]) + 2*x)*((8 + 16*x)*Log[x^2]^2 + E^(E^(x/Log[x^2]) + x/Log[x^2])*(-16*
x + 8*x*Log[x^2])))/Log[x^2]^2,x]

[Out]

16*x + 8*Defer[Int][E^(E^E^(x/Log[x^2]) + 2*x), x] + Defer[Int][E^(2*(E^E^(x/Log[x^2]) + 2*x)), x] + 16*Defer[
Int][E^(E^E^(x/Log[x^2]) + 2*x)*x, x] + 4*Defer[Int][E^(2*(E^E^(x/Log[x^2]) + 2*x))*x, x] - 16*Defer[Int][(E^(
E^E^(x/Log[x^2]) + E^(x/Log[x^2]) + 2*x + x/Log[x^2])*x)/Log[x^2]^2, x] - 4*Defer[Int][(E^(2*E^E^(x/Log[x^2])
+ E^(x/Log[x^2]) + 4*x + x/Log[x^2])*x)/Log[x^2]^2, x] + 8*Defer[Int][(E^(E^E^(x/Log[x^2]) + E^(x/Log[x^2]) +
2*x + x/Log[x^2])*x)/Log[x^2], x] + 2*Defer[Int][(E^(2*E^E^(x/Log[x^2]) + E^(x/Log[x^2]) + 4*x + x/Log[x^2])*x
)/Log[x^2], x]

Rubi steps

$$\begin{array}{c}\begin{array}{rl}\text{integral}& =\int ((4+e^{e^{e^{\frac{x}{\log \left(x^2\right)}}}+2x})(4+e^{e^{e^{\frac{x}{\log \left(x^2\right)}}}+2x}+4e^{e^{e^{\frac{x}{\log \left(x^2\right)}}}+2x}x)+\frac{2e^{e^{e^{\frac{x}{\log \left(x^2\right)}}}+e^{\frac{x}{\log \left(x^2\right)}}+2x+\frac{x}{\log \left(x^2\right)}}(4+e^{e^{e^{\frac{x}{\log \left(x^2\right)}}}+2x})x(-2+\log \left(x^2\right))}{{\log }^2\left(x^2\right)})dx\\ & =2\int \frac{e^{e^{e^{\frac{x}{\log \left(x^2\right)}}}+e^{\frac{x}{\log \left(x^2\right)}}+2x+\frac{x}{\log \left(x^2\right)}}(4+e^{e^{e^{\frac{x}{\log \left(x^2\right)}}}+2x})x(-2+\log \left(x^2\right))}{{\log }^2\left(x^2\right)}dx+\int (4+e^{e^{e^{\frac{x}{\log \left(x^2\right)}}}+2x})(4+e^{e^{e^{\frac{x}{\log \left(x^2\right)}}}+2x}+4e^{e^{e^{\frac{x}{\log \left(x^2\right)}}}+2x}x)dx\\ & =2\int (\frac{4e^{e^{e^{\frac{x}{\log \left(x^2\right)}}}+e^{\frac{x}{\log \left(x^2\right)}}+2x+\frac{x}{\log \left(x^2\right)}}x(-2+\log \left(x^2\right))}{{\log }^2\left(x^2\right)}+\frac{e^{2e^{e^{\frac{x}{\log \left(x^2\right)}}}+e^{\frac{x}{\log \left(x^2\right)}}+4x+\frac{x}{\log \left(x^2\right)}}x(-2+\log \left(x^2\right))}{{\log }^2\left(x^2\right)})dx+\int (4+e^{e^{e^{\frac{x}{\log \left(x^2\right)}}}+2x})(4+e^{e^{e^{\frac{x}{\log \left(x^2\right)}}}+2x}(1+4x))dx\\ & =2\int \frac{e^{2e^{e^{\frac{x}{\log \left(x^2\right)}}}+e^{\frac{x}{\log \left(x^2\right)}}+4x+\frac{x}{\log \left(x^2\right)}}x(-2+\log \left(x^2\right))}{{\log }^2\left(x^2\right)}dx+8\int \frac{e^{e^{e^{\frac{x}{\log \left(x^2\right)}}}+e^{\frac{x}{\log \left(x^2\right)}}+2x+\frac{x}{\log \left(x^2\right)}}x(-2+\log \left(x^2\right))}{{\log }^2\left(x^2\right)}dx+\int (16+8e^{e^{e^{\frac{x}{\log \left(x^2\right)}}}+2x}(1+2x)+e^{2(e^{e^{\frac{x}{\log \left(x^2\right)}}}+2x)}(1+4x))dx\\ & =16x+2\int (-\frac{2e^{2e^{e^{\frac{x}{\log \left(x^2\right)}}}+e^{\frac{x}{\log \left(x^2\right)}}+4x+\frac{x}{\log \left(x^2\right)}}x}{{\log }^2\left(x^2\right)}+\frac{e^{2e^{e^{\frac{x}{\log \left(x^2\right)}}}+e^{\frac{x}{\log \left(x^2\right)}}+4x+\frac{x}{\log \left(x^2\right)}}x}{\log \left(x^2\right)})dx+8\int e^{e^{e^{\frac{x}{\log \left(x^2\right)}}}+2x}(1+2x)dx+8\int (-\frac{2e^{e^{e^{\frac{x}{\log \left(x^2\right)}}}+e^{\frac{x}{\log \left(x^2\right)}}+2x+\frac{x}{\log \left(x^2\right)}}x}{{\log }^2\left(x^2\right)}+\frac{e^{e^{e^{\frac{x}{\log \left(x^2\right)}}}+e^{\frac{x}{\log \left(x^2\right)}}+2x+\frac{x}{\log \left(x^2\right)}}x}{\log \left(x^2\right)})dx+\int e^{2(e^{e^{\frac{x}{\log \left(x^2\right)}}}+2x)}(1+4x)dx\\ & =16x+2\int \frac{e^{2e^{e^{\frac{x}{\log \left(x^2\right)}}}+e^{\frac{x}{\log \left(x^2\right)}}+4x+\frac{x}{\log \left(x^2\right)}}x}{\log \left(x^2\right)}dx-4\int \frac{e^{2e^{e^{\frac{x}{\log \left(x^2\right)}}}+e^{\frac{x}{\log \left(x^2\right)}}+4x+\frac{x}{\log \left(x^2\right)}}x}{{\log }^2\left(x^2\right)}dx+8\int (e^{e^{e^{\frac{x}{\log \left(x^2\right)}}}+2x}+2e^{e^{e^{\frac{x}{\log \left(x^2\right)}}}+2x}x)dx+8\int \frac{e^{e^{e^{\frac{x}{\log \left(x^2\right)}}}+e^{\frac{x}{\log \left(x^2\right)}}+2x+\frac{x}{\log \left(x^2\right)}}x}{\log \left(x^2\right)}dx-16\int \frac{e^{e^{e^{\frac{x}{\log \left(x^2\right)}}}+e^{\frac{x}{\log \left(x^2\right)}}+2x+\frac{x}{\log \left(x^2\right)}}x}{{\log }^2\left(x^2\right)}dx+\int (e^{2(e^{e^{\frac{x}{\log \left(x^2\right)}}}+2x)}+4e^{2(e^{e^{\frac{x}{\log \left(x^2\right)}}}+2x)}x)dx\\ & =16x+2\int \frac{e^{2e^{e^{\frac{x}{\log \left(x^2\right)}}}+e^{\frac{x}{\log \left(x^2\right)}}+4x+\frac{x}{\log \left(x^2\right)}}x}{\log \left(x^2\right)}dx+4\int e^{2(e^{e^{\frac{x}{\log \left(x^2\right)}}}+2x)}xdx-4\int \frac{e^{2e^{e^{\frac{x}{\log \left(x^2\right)}}}+e^{\frac{x}{\log \left(x^2\right)}}+4x+\frac{x}{\log \left(x^2\right)}}x}{{\log }^2\left(x^2\right)}dx+8\int e^{e^{e^{\frac{x}{\log \left(x^2\right)}}}+2x}dx+8\int \frac{e^{e^{e^{\frac{x}{\log \left(x^2\right)}}}+e^{\frac{x}{\log \left(x^2\right)}}+2x+\frac{x}{\log \left(x^2\right)}}x}{\log \left(x^2\right)}dx+16\int e^{e^{e^{\frac{x}{\log \left(x^2\right)}}}+2x}xdx-16\int \frac{e^{e^{e^{\frac{x}{\log \left(x^2\right)}}}+e^{\frac{x}{\log \left(x^2\right)}}+2x+\frac{x}{\log \left(x^2\right)}}x}{{\log }^2\left(x^2\right)}dx+\int e^{2(e^{e^{\frac{x}{\log \left(x^2\right)}}}+2x)}dx\end{array}\end{array}$$

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Mathematica [A]  time = 0.27, size = 24, normalized size = 0.92 $$\begin{array}{c}{(4+e^{e^{e^{\frac{x}{\log \left(x^2\right)}}}+2x})}^{2}x\end{array}$$

Antiderivative was successfully verified.

[In]

Integrate[(16*Log[x^2]^2 + E^(2*E^E^(x/Log[x^2]) + 4*x)*((1 + 4*x)*Log[x^2]^2 + E^(E^(x/Log[x^2]) + x/Log[x^2]
)*(-4*x + 2*x*Log[x^2])) + E^(E^E^(x/Log[x^2]) + 2*x)*((8 + 16*x)*Log[x^2]^2 + E^(E^(x/Log[x^2]) + x/Log[x^2])
*(-16*x + 8*x*Log[x^2])))/Log[x^2]^2,x]

[Out]

(4 + E^(E^E^(x/Log[x^2]) + 2*x))^2*x

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fricas [B]  time = 0.55, size = 108, normalized size = 4.15 $$\begin{array}{c}x{e}^{\left(2(2x{e}^{\left(\frac{x}{\log \left(x^2\right)}\right)}+e^{\left(\frac{e^{\left(\frac{x}{\log \left(x^2\right)}\right)}\log \left(x^2\right)+x}{\log \left(x^2\right)}\right)})e^{(-\frac{x}{\log \left(x^2\right)})}\right)}+8x{e}^{\left((2x{e}^{\left(\frac{x}{\log \left(x^2\right)}\right)}+e^{\left(\frac{e^{\left(\frac{x}{\log \left(x^2\right)}\right)}\log \left(x^2\right)+x}{\log \left(x^2\right)}\right)})e^{(-\frac{x}{\log \left(x^2\right)})}\right)}+16x\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((2*x*log(x^2)-4*x)*exp(x/log(x^2))*exp(exp(x/log(x^2)))+(4*x+1)*log(x^2)^2)*exp(exp(exp(x/log(x^2)
))+2*x)^2+((8*x*log(x^2)-16*x)*exp(x/log(x^2))*exp(exp(x/log(x^2)))+(16*x+8)*log(x^2)^2)*exp(exp(exp(x/log(x^2
)))+2*x)+16*log(x^2)^2)/log(x^2)^2,x, algorithm="fricas")

[Out]

x*e^(2*(2*x*e^(x/log(x^2)) + e^((e^(x/log(x^2))*log(x^2) + x)/log(x^2)))*e^(-x/log(x^2))) + 8*x*e^((2*x*e^(x/l
og(x^2)) + e^((e^(x/log(x^2))*log(x^2) + x)/log(x^2)))*e^(-x/log(x^2))) + 16*x

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 $$\begin{array}{c}\mathit{undef}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((2*x*log(x^2)-4*x)*exp(x/log(x^2))*exp(exp(x/log(x^2)))+(4*x+1)*log(x^2)^2)*exp(exp(exp(x/log(x^2)
))+2*x)^2+((8*x*log(x^2)-16*x)*exp(x/log(x^2))*exp(exp(x/log(x^2)))+(16*x+8)*log(x^2)^2)*exp(exp(exp(x/log(x^2
)))+2*x)+16*log(x^2)^2)/log(x^2)^2,x, algorithm="giac")

[Out]

undef

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maple [A]  time = 0.39, size = 42, normalized size = 1.62

method	result	size
risch	$x{\mathrm{e}}^{2{\mathrm{e}}^{{\mathrm{e}}^{\frac{x}{\ln \left(x^2\right)}}}+4x}+8x{\mathrm{e}}^{{\mathrm{e}}^{{\mathrm{e}}^{\frac{x}{\ln \left(x^2\right)}}}+2x}+16x$	$42$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((2*x*ln(x^2)-4*x)*exp(x/ln(x^2))*exp(exp(x/ln(x^2)))+(4*x+1)*ln(x^2)^2)*exp(exp(exp(x/ln(x^2)))+2*x)^2+(
(8*x*ln(x^2)-16*x)*exp(x/ln(x^2))*exp(exp(x/ln(x^2)))+(16*x+8)*ln(x^2)^2)*exp(exp(exp(x/ln(x^2)))+2*x)+16*ln(x
^2)^2)/ln(x^2)^2,x,method=_RETURNVERBOSE)

[Out]

x*exp(2*exp(exp(x/ln(x^2)))+4*x)+8*x*exp(exp(exp(x/ln(x^2)))+2*x)+16*x

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maxima [A]  time = 0.77, size = 39, normalized size = 1.50 $$\begin{array}{c}x{e}^{(4x+2e^{\left(e^{\left(\frac{x}{2\log (x)}\right)}\right)})}+8x{e}^{(2x+e^{\left(e^{\left(\frac{x}{2\log (x)}\right)}\right)})}+16x\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((2*x*log(x^2)-4*x)*exp(x/log(x^2))*exp(exp(x/log(x^2)))+(4*x+1)*log(x^2)^2)*exp(exp(exp(x/log(x^2)
))+2*x)^2+((8*x*log(x^2)-16*x)*exp(x/log(x^2))*exp(exp(x/log(x^2)))+(16*x+8)*log(x^2)^2)*exp(exp(exp(x/log(x^2
)))+2*x)+16*log(x^2)^2)/log(x^2)^2,x, algorithm="maxima")

[Out]

x*e^(4*x + 2*e^(e^(1/2*x/log(x)))) + 8*x*e^(2*x + e^(e^(1/2*x/log(x)))) + 16*x

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mupad [B]  time = 1.69, size = 41, normalized size = 1.58 $$\begin{array}{c}16x+x{\mathrm{e}}^{2{\mathrm{e}}^{{\mathrm{e}}^{\frac{x}{\ln \left(x^2\right)}}}}{\mathrm{e}}^{4x}+8x{\mathrm{e}}^{2x}{\mathrm{e}}^{{\mathrm{e}}^{{\mathrm{e}}^{\frac{x}{\ln \left(x^2\right)}}}}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(4*x + 2*exp(exp(x/log(x^2))))*(log(x^2)^2*(4*x + 1) - exp(exp(x/log(x^2)))*exp(x/log(x^2))*(4*x - 2*x
*log(x^2))) + 16*log(x^2)^2 + exp(2*x + exp(exp(x/log(x^2))))*(log(x^2)^2*(16*x + 8) - exp(exp(x/log(x^2)))*ex
p(x/log(x^2))*(16*x - 8*x*log(x^2))))/log(x^2)^2,x)

[Out]

16*x + x*exp(2*exp(exp(x/log(x^2))))*exp(4*x) + 8*x*exp(2*x)*exp(exp(exp(x/log(x^2))))

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sympy [A]  time = 18.87, size = 39, normalized size = 1.50 $$\begin{array}{c}8x{e}^{2x+e^{e^{\frac{x}{\log \left(x^2\right)}}}}+x{e}^{4x+2e^{e^{\frac{x}{\log \left(x^2\right)}}}}+16x\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((2*x*ln(x**2)-4*x)*exp(x/ln(x**2))*exp(exp(x/ln(x**2)))+(4*x+1)*ln(x**2)**2)*exp(exp(exp(x/ln(x**2
)))+2*x)**2+((8*x*ln(x**2)-16*x)*exp(x/ln(x**2))*exp(exp(x/ln(x**2)))+(16*x+8)*ln(x**2)**2)*exp(exp(exp(x/ln(x
**2)))+2*x)+16*ln(x**2)**2)/ln(x**2)**2,x)

[Out]

8*x*exp(2*x + exp(exp(x/log(x**2)))) + x*exp(4*x + 2*exp(exp(x/log(x**2)))) + 16*x

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