3.54.14 \(\int \frac {1-e^{e^{20}}-x^2-\log (x)}{e^{2 e^{20}}+4 x^2-4 x^3+x^4+e^{e^{20}} (4 x-2 x^2)+(2 e^{e^{20}}+4 x-2 x^2) \log (x)+\log ^2(x)} \, dx\)

Optimal. Leaf size=22 \[ \frac {x}{-e^{e^{20}}-2 x+x^2-\log (x)} \]

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Rubi [F]  time = 0.64, 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*} \int \frac {1-e^{e^{20}}-x^2-\log (x)}{e^{2 e^{20}}+4 x^2-4 x^3+x^4+e^{e^{20}} \left (4 x-2 x^2\right )+\left (2 e^{e^{20}}+4 x-2 x^2\right ) \log (x)+\log ^2(x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(1 - E^E^20 - x^2 - Log[x])/(E^(2*E^20) + 4*x^2 - 4*x^3 + x^4 + E^E^20*(4*x - 2*x^2) + (2*E^E^20 + 4*x - 2
*x^2)*Log[x] + Log[x]^2),x]

[Out]

2*Defer[Int][x/(-E^E^20 - 2*x + x^2 - Log[x])^2, x] - 2*Defer[Int][x^2/(-E^E^20 - 2*x + x^2 - Log[x])^2, x] +
Defer[Int][(E^E^20 + 2*x - x^2 + Log[x])^(-2), x] - Defer[Int][(E^E^20 + 2*x - x^2 + Log[x])^(-1), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {1-e^{e^{20}}-x^2-\log (x)}{\left (e^{e^{20}}-(-2+x) x+\log (x)\right )^2} \, dx\\ &=\int \left (-\frac {-1-2 x+2 x^2}{\left (-e^{e^{20}}-2 x+x^2-\log (x)\right )^2}-\frac {1}{e^{e^{20}}+2 x-x^2+\log (x)}\right ) \, dx\\ &=-\int \frac {-1-2 x+2 x^2}{\left (-e^{e^{20}}-2 x+x^2-\log (x)\right )^2} \, dx-\int \frac {1}{e^{e^{20}}+2 x-x^2+\log (x)} \, dx\\ &=-\int \frac {1}{e^{e^{20}}+2 x-x^2+\log (x)} \, dx-\int \left (-\frac {2 x}{\left (-e^{e^{20}}-2 x+x^2-\log (x)\right )^2}+\frac {2 x^2}{\left (-e^{e^{20}}-2 x+x^2-\log (x)\right )^2}-\frac {1}{\left (e^{e^{20}}+2 x-x^2+\log (x)\right )^2}\right ) \, dx\\ &=2 \int \frac {x}{\left (-e^{e^{20}}-2 x+x^2-\log (x)\right )^2} \, dx-2 \int \frac {x^2}{\left (-e^{e^{20}}-2 x+x^2-\log (x)\right )^2} \, dx+\int \frac {1}{\left (e^{e^{20}}+2 x-x^2+\log (x)\right )^2} \, dx-\int \frac {1}{e^{e^{20}}+2 x-x^2+\log (x)} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.23, size = 21, normalized size = 0.95 \begin {gather*} -\frac {x}{e^{e^{20}}+2 x-x^2+\log (x)} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(1 - E^E^20 - x^2 - Log[x])/(E^(2*E^20) + 4*x^2 - 4*x^3 + x^4 + E^E^20*(4*x - 2*x^2) + (2*E^E^20 + 4
*x - 2*x^2)*Log[x] + Log[x]^2),x]

[Out]

-(x/(E^E^20 + 2*x - x^2 + Log[x]))

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fricas [A]  time = 0.89, size = 20, normalized size = 0.91 \begin {gather*} \frac {x}{x^{2} - 2 \, x - e^{\left (e^{20}\right )} - \log \relax (x)} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-log(x)-exp(exp(20))-x^2+1)/(log(x)^2+(2*exp(exp(20))-2*x^2+4*x)*log(x)+exp(exp(20))^2+(-2*x^2+4*x)
*exp(exp(20))+x^4-4*x^3+4*x^2),x, algorithm="fricas")

[Out]

x/(x^2 - 2*x - e^(e^20) - log(x))

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giac [A]  time = 0.15, size = 20, normalized size = 0.91 \begin {gather*} \frac {x}{x^{2} - 2 \, x - e^{\left (e^{20}\right )} - \log \relax (x)} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-log(x)-exp(exp(20))-x^2+1)/(log(x)^2+(2*exp(exp(20))-2*x^2+4*x)*log(x)+exp(exp(20))^2+(-2*x^2+4*x)
*exp(exp(20))+x^4-4*x^3+4*x^2),x, algorithm="giac")

[Out]

x/(x^2 - 2*x - e^(e^20) - log(x))

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maple [A]  time = 0.14, size = 20, normalized size = 0.91

method	result	size
norman	\(-\frac {x}{-x^{2}+\ln \relax (x )+{\mathrm e}^{{\mathrm e}^{20}}+2 x}\)	\(20\)
risch	\(-\frac {x}{-x^{2}+\ln \relax (x )+{\mathrm e}^{{\mathrm e}^{20}}+2 x}\)	\(20\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((-ln(x)-exp(exp(20))-x^2+1)/(ln(x)^2+(2*exp(exp(20))-2*x^2+4*x)*ln(x)+exp(exp(20))^2+(-2*x^2+4*x)*exp(exp(
20))+x^4-4*x^3+4*x^2),x,method=_RETURNVERBOSE)

[Out]

-x/(-x^2+ln(x)+exp(exp(20))+2*x)

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maxima [A]  time = 0.47, size = 20, normalized size = 0.91 \begin {gather*} \frac {x}{x^{2} - 2 \, x - e^{\left (e^{20}\right )} - \log \relax (x)} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-log(x)-exp(exp(20))-x^2+1)/(log(x)^2+(2*exp(exp(20))-2*x^2+4*x)*log(x)+exp(exp(20))^2+(-2*x^2+4*x)
*exp(exp(20))+x^4-4*x^3+4*x^2),x, algorithm="maxima")

[Out]

x/(x^2 - 2*x - e^(e^20) - log(x))

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mupad [B]  time = 4.12, size = 19, normalized size = 0.86 \begin {gather*} -\frac {x}{2\,x+{\mathrm {e}}^{{\mathrm {e}}^{20}}+\ln \relax (x)-x^2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp(exp(20)) + log(x) + x^2 - 1)/(exp(2*exp(20)) + log(x)^2 + exp(exp(20))*(4*x - 2*x^2) + 4*x^2 - 4*x^3
+ x^4 + log(x)*(4*x + 2*exp(exp(20)) - 2*x^2)),x)

[Out]

-x/(2*x + exp(exp(20)) + log(x) - x^2)

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sympy [A]  time = 0.12, size = 17, normalized size = 0.77 \begin {gather*} - \frac {x}{- x^{2} + 2 x + \log {\relax (x )} + e^{e^{20}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-ln(x)-exp(exp(20))-x**2+1)/(ln(x)**2+(2*exp(exp(20))-2*x**2+4*x)*ln(x)+exp(exp(20))**2+(-2*x**2+4*
x)*exp(exp(20))+x**4-4*x**3+4*x**2),x)

[Out]

-x/(-x**2 + 2*x + log(x) + exp(exp(20)))

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