3.61.90 \(\int \frac {e^{8+e^{12}} (-3+9 x-3 x^2)+e^8 (-3+12 x-3 x^2)+e^4 (-6 x+2 x^2)+e^8 (3 x-x^2) \log (-3+x)+e^8 (-3 x+x^2) \log (x)}{-12 x+4 x^2+e^4 (36 x^2-12 x^3)+e^8 (-27 x^3+9 x^4)+(e^4 (12 x-4 x^2)+e^8 (-18 x^2+6 x^3)) \log (-3+x)+e^8 (-3 x+x^2) \log ^2(-3+x)+(e^4 (-12 x+4 x^2)+e^8 (18 x^2-6 x^3)+e^8 (6 x-2 x^2) \log (-3+x)) \log (x)+e^8 (-3 x+x^2) \log ^2(x)} \, dx\)

Optimal. Leaf size=30 \[ \frac {1+e^{e^{12}}-x}{-\frac {2}{e^4}+3 x+\log (-3+x)-\log (x)} \]

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Rubi [F]  time = 4.22, 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 {e^{8+e^{12}} \left (-3+9 x-3 x^2\right )+e^8 \left (-3+12 x-3 x^2\right )+e^4 \left (-6 x+2 x^2\right )+e^8 \left (3 x-x^2\right ) \log (-3+x)+e^8 \left (-3 x+x^2\right ) \log (x)}{-12 x+4 x^2+e^4 \left (36 x^2-12 x^3\right )+e^8 \left (-27 x^3+9 x^4\right )+\left (e^4 \left (12 x-4 x^2\right )+e^8 \left (-18 x^2+6 x^3\right )\right ) \log (-3+x)+e^8 \left (-3 x+x^2\right ) \log ^2(-3+x)+\left (e^4 \left (-12 x+4 x^2\right )+e^8 \left (18 x^2-6 x^3\right )+e^8 \left (6 x-2 x^2\right ) \log (-3+x)\right ) \log (x)+e^8 \left (-3 x+x^2\right ) \log ^2(x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^(8 + E^12)*(-3 + 9*x - 3*x^2) + E^8*(-3 + 12*x - 3*x^2) + E^4*(-6*x + 2*x^2) + E^8*(3*x - x^2)*Log[-3 +
x] + E^8*(-3*x + x^2)*Log[x])/(-12*x + 4*x^2 + E^4*(36*x^2 - 12*x^3) + E^8*(-27*x^3 + 9*x^4) + (E^4*(12*x - 4
*x^2) + E^8*(-18*x^2 + 6*x^3))*Log[-3 + x] + E^8*(-3*x + x^2)*Log[-3 + x]^2 + (E^4*(-12*x + 4*x^2) + E^8*(18*x
^2 - 6*x^3) + E^8*(6*x - 2*x^2)*Log[-3 + x])*Log[x] + E^8*(-3*x + x^2)*Log[x]^2),x]

[Out]

-3*E^8*(1 + E^E^12)*Defer[Int][(-2 + 3*E^4*x + E^4*Log[-3 + x] - E^4*Log[x])^(-2), x] + E^8*(2 - E^E^12)*Defer
[Int][1/((-3 + x)*(-2 + 3*E^4*x + E^4*Log[-3 + x] - E^4*Log[x])^2), x] + E^8*(1 + E^E^12)*Defer[Int][1/(x*(-2
+ 3*E^4*x + E^4*Log[-3 + x] - E^4*Log[x])^2), x] + 3*E^8*Defer[Int][x/(-2 + 3*E^4*x + E^4*Log[-3 + x] - E^4*Lo
g[x])^2, x] + E^4*Defer[Int][(2 - 3*E^4*x - E^4*Log[-3 + x] + E^4*Log[x])^(-1), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^4 \left (3 e^4 \left (1+e^{e^{12}}\right )+6 \left (1-\frac {1}{2} e^4 \left (4+3 e^{e^{12}}\right )\right ) x-2 \left (1-\frac {3}{2} e^4 \left (1+e^{e^{12}}\right )\right ) x^2+e^4 (-3+x) x \log (-3+x)-e^4 (-3+x) x \log (x)\right )}{(3-x) x \left (2-3 e^4 x-e^4 \log (-3+x)+e^4 \log (x)\right )^2} \, dx\\ &=e^4 \int \frac {3 e^4 \left (1+e^{e^{12}}\right )+6 \left (1-\frac {1}{2} e^4 \left (4+3 e^{e^{12}}\right )\right ) x-2 \left (1-\frac {3}{2} e^4 \left (1+e^{e^{12}}\right )\right ) x^2+e^4 (-3+x) x \log (-3+x)-e^4 (-3+x) x \log (x)}{(3-x) x \left (2-3 e^4 x-e^4 \log (-3+x)+e^4 \log (x)\right )^2} \, dx\\ &=e^4 \int \left (\frac {3 e^4 \left (-1-e^{e^{12}}+x\right ) \left (1-3 x+x^2\right )}{(-3+x) x \left (-2+3 e^4 x+e^4 \log (-3+x)-e^4 \log (x)\right )^2}+\frac {1}{2-3 e^4 x-e^4 \log (-3+x)+e^4 \log (x)}\right ) \, dx\\ &=e^4 \int \frac {1}{2-3 e^4 x-e^4 \log (-3+x)+e^4 \log (x)} \, dx+\left (3 e^8\right ) \int \frac {\left (-1-e^{e^{12}}+x\right ) \left (1-3 x+x^2\right )}{(-3+x) x \left (-2+3 e^4 x+e^4 \log (-3+x)-e^4 \log (x)\right )^2} \, dx\\ &=e^4 \int \frac {1}{2-3 e^4 x-e^4 \log (-3+x)+e^4 \log (x)} \, dx+\left (3 e^8\right ) \int \left (-\frac {1+e^{e^{12}}}{\left (-2+3 e^4 x+e^4 \log (-3+x)-e^4 \log (x)\right )^2}-\frac {-2+e^{e^{12}}}{3 (-3+x) \left (-2+3 e^4 x+e^4 \log (-3+x)-e^4 \log (x)\right )^2}+\frac {1+e^{e^{12}}}{3 x \left (-2+3 e^4 x+e^4 \log (-3+x)-e^4 \log (x)\right )^2}+\frac {x}{\left (-2+3 e^4 x+e^4 \log (-3+x)-e^4 \log (x)\right )^2}\right ) \, dx\\ &=e^4 \int \frac {1}{2-3 e^4 x-e^4 \log (-3+x)+e^4 \log (x)} \, dx+\left (3 e^8\right ) \int \frac {x}{\left (-2+3 e^4 x+e^4 \log (-3+x)-e^4 \log (x)\right )^2} \, dx+\left (e^8 \left (2-e^{e^{12}}\right )\right ) \int \frac {1}{(-3+x) \left (-2+3 e^4 x+e^4 \log (-3+x)-e^4 \log (x)\right )^2} \, dx+\left (e^8 \left (1+e^{e^{12}}\right )\right ) \int \frac {1}{x \left (-2+3 e^4 x+e^4 \log (-3+x)-e^4 \log (x)\right )^2} \, dx-\left (3 e^8 \left (1+e^{e^{12}}\right )\right ) \int \frac {1}{\left (-2+3 e^4 x+e^4 \log (-3+x)-e^4 \log (x)\right )^2} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.12, size = 40, normalized size = 1.33 \begin {gather*} -\frac {e^4 \left (1+e^{e^{12}}-x\right )}{2-3 e^4 x-e^4 \log (-3+x)+e^4 \log (x)} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^(8 + E^12)*(-3 + 9*x - 3*x^2) + E^8*(-3 + 12*x - 3*x^2) + E^4*(-6*x + 2*x^2) + E^8*(3*x - x^2)*Lo
g[-3 + x] + E^8*(-3*x + x^2)*Log[x])/(-12*x + 4*x^2 + E^4*(36*x^2 - 12*x^3) + E^8*(-27*x^3 + 9*x^4) + (E^4*(12
*x - 4*x^2) + E^8*(-18*x^2 + 6*x^3))*Log[-3 + x] + E^8*(-3*x + x^2)*Log[-3 + x]^2 + (E^4*(-12*x + 4*x^2) + E^8
*(18*x^2 - 6*x^3) + E^8*(6*x - 2*x^2)*Log[-3 + x])*Log[x] + E^8*(-3*x + x^2)*Log[x]^2),x]

[Out]

-((E^4*(1 + E^E^12 - x))/(2 - 3*E^4*x - E^4*Log[-3 + x] + E^4*Log[x]))

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fricas [A]  time = 0.56, size = 41, normalized size = 1.37 \begin {gather*} -\frac {{\left (x - 1\right )} e^{8} - e^{\left (e^{12} + 8\right )}}{3 \, x e^{8} + e^{8} \log \left (x - 3\right ) - e^{8} \log \relax (x) - 2 \, e^{4}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((x^2-3*x)*exp(4)^2*log(x)+(-x^2+3*x)*exp(4)^2*log(x-3)+(-3*x^2+9*x-3)*exp(4)^2*exp(exp(12))+(-3*x^2
+12*x-3)*exp(4)^2+(2*x^2-6*x)*exp(4))/((x^2-3*x)*exp(4)^2*log(x)^2+((-2*x^2+6*x)*exp(4)^2*log(x-3)+(-6*x^3+18*
x^2)*exp(4)^2+(4*x^2-12*x)*exp(4))*log(x)+(x^2-3*x)*exp(4)^2*log(x-3)^2+((6*x^3-18*x^2)*exp(4)^2+(-4*x^2+12*x)
*exp(4))*log(x-3)+(9*x^4-27*x^3)*exp(4)^2+(-12*x^3+36*x^2)*exp(4)+4*x^2-12*x),x, algorithm="fricas")

[Out]

-((x - 1)*e^8 - e^(e^12 + 8))/(3*x*e^8 + e^8*log(x - 3) - e^8*log(x) - 2*e^4)

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giac [A]  time = 0.25, size = 43, normalized size = 1.43 \begin {gather*} -\frac {x e^{8} - e^{8} - e^{\left (e^{12} + 8\right )}}{3 \, x e^{8} + e^{8} \log \left (x - 3\right ) - e^{8} \log \relax (x) - 2 \, e^{4}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((x^2-3*x)*exp(4)^2*log(x)+(-x^2+3*x)*exp(4)^2*log(x-3)+(-3*x^2+9*x-3)*exp(4)^2*exp(exp(12))+(-3*x^2
+12*x-3)*exp(4)^2+(2*x^2-6*x)*exp(4))/((x^2-3*x)*exp(4)^2*log(x)^2+((-2*x^2+6*x)*exp(4)^2*log(x-3)+(-6*x^3+18*
x^2)*exp(4)^2+(4*x^2-12*x)*exp(4))*log(x)+(x^2-3*x)*exp(4)^2*log(x-3)^2+((6*x^3-18*x^2)*exp(4)^2+(-4*x^2+12*x)
*exp(4))*log(x-3)+(9*x^4-27*x^3)*exp(4)^2+(-12*x^3+36*x^2)*exp(4)+4*x^2-12*x),x, algorithm="giac")

[Out]

-(x*e^8 - e^8 - e^(e^12 + 8))/(3*x*e^8 + e^8*log(x - 3) - e^8*log(x) - 2*e^4)

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maple [A]  time = 0.06, size = 34, normalized size = 1.13

method	result	size
risch	\(\frac {\left ({\mathrm e}^{{\mathrm e}^{12}}-x +1\right ) {\mathrm e}^{4}}{3 x \,{\mathrm e}^{4}-{\mathrm e}^{4} \ln \relax (x )+{\mathrm e}^{4} \ln \left (x -3\right )-2}\)	\(34\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((x^2-3*x)*exp(4)^2*ln(x)+(-x^2+3*x)*exp(4)^2*ln(x-3)+(-3*x^2+9*x-3)*exp(4)^2*exp(exp(12))+(-3*x^2+12*x-3)
*exp(4)^2+(2*x^2-6*x)*exp(4))/((x^2-3*x)*exp(4)^2*ln(x)^2+((-2*x^2+6*x)*exp(4)^2*ln(x-3)+(-6*x^3+18*x^2)*exp(4
)^2+(4*x^2-12*x)*exp(4))*ln(x)+(x^2-3*x)*exp(4)^2*ln(x-3)^2+((6*x^3-18*x^2)*exp(4)^2+(-4*x^2+12*x)*exp(4))*ln(
x-3)+(9*x^4-27*x^3)*exp(4)^2+(-12*x^3+36*x^2)*exp(4)+4*x^2-12*x),x,method=_RETURNVERBOSE)

[Out]

(exp(exp(12))-x+1)*exp(4)/(3*x*exp(4)-exp(4)*ln(x)+exp(4)*ln(x-3)-2)

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maxima [A]  time = 0.40, size = 38, normalized size = 1.27 \begin {gather*} -\frac {x e^{4} - {\left (e^{\left (e^{12}\right )} + 1\right )} e^{4}}{3 \, x e^{4} + e^{4} \log \left (x - 3\right ) - e^{4} \log \relax (x) - 2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((x^2-3*x)*exp(4)^2*log(x)+(-x^2+3*x)*exp(4)^2*log(x-3)+(-3*x^2+9*x-3)*exp(4)^2*exp(exp(12))+(-3*x^2
+12*x-3)*exp(4)^2+(2*x^2-6*x)*exp(4))/((x^2-3*x)*exp(4)^2*log(x)^2+((-2*x^2+6*x)*exp(4)^2*log(x-3)+(-6*x^3+18*
x^2)*exp(4)^2+(4*x^2-12*x)*exp(4))*log(x)+(x^2-3*x)*exp(4)^2*log(x-3)^2+((6*x^3-18*x^2)*exp(4)^2+(-4*x^2+12*x)
*exp(4))*log(x-3)+(9*x^4-27*x^3)*exp(4)^2+(-12*x^3+36*x^2)*exp(4)+4*x^2-12*x),x, algorithm="maxima")

[Out]

-(x*e^4 - (e^(e^12) + 1)*e^4)/(3*x*e^4 + e^4*log(x - 3) - e^4*log(x) - 2)

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mupad [B]  time = 5.00, size = 55, normalized size = 1.83 \begin {gather*} \frac {{\mathrm {e}}^{-4}\,\left (3\,{\mathrm {e}}^{{\mathrm {e}}^{12}+8}-2\,{\mathrm {e}}^4+3\,{\mathrm {e}}^8+\ln \left (x-3\right )\,{\mathrm {e}}^8-{\mathrm {e}}^8\,\ln \relax (x)\right )}{3\,\left (\ln \left (x-3\right )\,{\mathrm {e}}^4+3\,x\,{\mathrm {e}}^4-{\mathrm {e}}^4\,\ln \relax (x)-2\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(4)*(6*x - 2*x^2) + exp(8)*(3*x^2 - 12*x + 3) + exp(8)*log(x)*(3*x - x^2) - log(x - 3)*exp(8)*(3*x - x
^2) + exp(8)*exp(exp(12))*(3*x^2 - 9*x + 3))/(12*x + exp(8)*(27*x^3 - 9*x^4) - exp(4)*(36*x^2 - 12*x^3) - log(
x - 3)*(exp(4)*(12*x - 4*x^2) - exp(8)*(18*x^2 - 6*x^3)) - 4*x^2 - log(x)*(exp(8)*(18*x^2 - 6*x^3) - exp(4)*(1
2*x - 4*x^2) + log(x - 3)*exp(8)*(6*x - 2*x^2)) + exp(8)*log(x)^2*(3*x - x^2) + log(x - 3)^2*exp(8)*(3*x - x^2
)),x)

[Out]

(exp(-4)*(3*exp(exp(12) + 8) - 2*exp(4) + 3*exp(8) + log(x - 3)*exp(8) - exp(8)*log(x)))/(3*(log(x - 3)*exp(4)
+ 3*x*exp(4) - exp(4)*log(x) - 2))

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sympy [A]  time = 0.41, size = 39, normalized size = 1.30 \begin {gather*} \frac {- x e^{4} + e^{4} + e^{4} e^{e^{12}}}{3 x e^{4} - e^{4} \log {\relax (x )} + e^{4} \log {\left (x - 3 \right )} - 2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((x**2-3*x)*exp(4)**2*ln(x)+(-x**2+3*x)*exp(4)**2*ln(x-3)+(-3*x**2+9*x-3)*exp(4)**2*exp(exp(12))+(-3
*x**2+12*x-3)*exp(4)**2+(2*x**2-6*x)*exp(4))/((x**2-3*x)*exp(4)**2*ln(x)**2+((-2*x**2+6*x)*exp(4)**2*ln(x-3)+(
-6*x**3+18*x**2)*exp(4)**2+(4*x**2-12*x)*exp(4))*ln(x)+(x**2-3*x)*exp(4)**2*ln(x-3)**2+((6*x**3-18*x**2)*exp(4
)**2+(-4*x**2+12*x)*exp(4))*ln(x-3)+(9*x**4-27*x**3)*exp(4)**2+(-12*x**3+36*x**2)*exp(4)+4*x**2-12*x),x)

[Out]

(-x*exp(4) + exp(4) + exp(4)*exp(exp(12)))/(3*x*exp(4) - exp(4)*log(x) + exp(4)*log(x - 3) - 2)

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