3.34.62 \(\int \frac {1728 x^2+864 e x^2-864 x^3+e^{2 x} (12 x^2+12 x^3-6 x^4+e (6 x^2+6 x^3))+e^x (288 x^2+72 x^3-72 x^4+e (144 x^2+72 x^3))+(e^x (216 x+72 e x-72 x^2)+e^{2 x} (18 x+6 e x-6 x^2)) \log ^2(3+e-x)+(-432 x-144 e x+144 x^2+e^x (-36 x-12 e x+12 x^2)) \log (x)+(-144 x-72 e x+72 x^2+e^x (-12 x-12 x^2+6 x^3+e (-6 x-6 x^2))) \log ^2(x)+(36+12 e-12 x) \log ^3(x)+\log (3+e-x) (1728 x+864 e x-864 x^2+e^{2 x} (12 x+30 x^2-12 x^3+e (6 x+12 x^2))+e^x (288 x+288 x^2-144 x^3+e (144 x+144 x^2))+(-432-144 e+144 x+e^x (-36-12 e+12 x)) \log (x)+e^x (-18 x-6 e x+6 x^2) \log ^2(x))}{3 x+e x-x^2} \, dx\)

Optimal. Leaf size=25 \[ 3 \left (-\left (\left (12+e^x\right ) (x+\log (3+e-x))\right )+\log ^2(x)\right )^2 \]

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Rubi [F]  time = 180.00, 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*} \text {\$Aborted} \end {gather*}

Verification is not applicable to the result.

[In]

Int[(1728*x^2 + 864*E*x^2 - 864*x^3 + E^(2*x)*(12*x^2 + 12*x^3 - 6*x^4 + E*(6*x^2 + 6*x^3)) + E^x*(288*x^2 + 7
2*x^3 - 72*x^4 + E*(144*x^2 + 72*x^3)) + (E^x*(216*x + 72*E*x - 72*x^2) + E^(2*x)*(18*x + 6*E*x - 6*x^2))*Log[
3 + E - x]^2 + (-432*x - 144*E*x + 144*x^2 + E^x*(-36*x - 12*E*x + 12*x^2))*Log[x] + (-144*x - 72*E*x + 72*x^2
+ E^x*(-12*x - 12*x^2 + 6*x^3 + E*(-6*x - 6*x^2)))*Log[x]^2 + (36 + 12*E - 12*x)*Log[x]^3 + Log[3 + E - x]*(1
728*x + 864*E*x - 864*x^2 + E^(2*x)*(12*x + 30*x^2 - 12*x^3 + E*(6*x + 12*x^2)) + E^x*(288*x + 288*x^2 - 144*x
^3 + E*(144*x + 144*x^2)) + (-432 - 144*E + 144*x + E^x*(-36 - 12*E + 12*x))*Log[x] + E^x*(-18*x - 6*E*x + 6*x
^2)*Log[x]^2))/(3*x + E*x - x^2),x]

[Out]

$Aborted

Rubi steps

Aborted

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Mathematica [A]  time = 0.27, size = 31, normalized size = 1.24 \begin {gather*} 3 \left (\left (12+e^x\right ) x+\left (12+e^x\right ) \log (3+e-x)-\log ^2(x)\right )^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(1728*x^2 + 864*E*x^2 - 864*x^3 + E^(2*x)*(12*x^2 + 12*x^3 - 6*x^4 + E*(6*x^2 + 6*x^3)) + E^x*(288*x
^2 + 72*x^3 - 72*x^4 + E*(144*x^2 + 72*x^3)) + (E^x*(216*x + 72*E*x - 72*x^2) + E^(2*x)*(18*x + 6*E*x - 6*x^2)
)*Log[3 + E - x]^2 + (-432*x - 144*E*x + 144*x^2 + E^x*(-36*x - 12*E*x + 12*x^2))*Log[x] + (-144*x - 72*E*x +
72*x^2 + E^x*(-12*x - 12*x^2 + 6*x^3 + E*(-6*x - 6*x^2)))*Log[x]^2 + (36 + 12*E - 12*x)*Log[x]^3 + Log[3 + E -
x]*(1728*x + 864*E*x - 864*x^2 + E^(2*x)*(12*x + 30*x^2 - 12*x^3 + E*(6*x + 12*x^2)) + E^x*(288*x + 288*x^2 -
144*x^3 + E*(144*x + 144*x^2)) + (-432 - 144*E + 144*x + E^x*(-36 - 12*E + 12*x))*Log[x] + E^x*(-18*x - 6*E*x
+ 6*x^2)*Log[x]^2))/(3*x + E*x - x^2),x]

[Out]

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

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fricas [B]  time = 0.56, size = 99, normalized size = 3.96 \begin {gather*} 3 \, \log \relax (x)^{4} + 3 \, x^{2} e^{\left (2 \, x\right )} + 72 \, x^{2} e^{x} - 6 \, {\left (x e^{x} + 12 \, x\right )} \log \relax (x)^{2} + 3 \, {\left (e^{\left (2 \, x\right )} + 24 \, e^{x} + 144\right )} \log \left (-x + e + 3\right )^{2} + 432 \, x^{2} - 6 \, {\left ({\left (e^{x} + 12\right )} \log \relax (x)^{2} - x e^{\left (2 \, x\right )} - 24 \, x e^{x} - 144 \, x\right )} \log \left (-x + e + 3\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((6*x*exp(1)-6*x^2+18*x)*exp(x)^2+(72*x*exp(1)-72*x^2+216*x)*exp(x))*log(3-x+exp(1))^2+((-6*x*exp(1
)+6*x^2-18*x)*exp(x)*log(x)^2+((-12*exp(1)+12*x-36)*exp(x)-144*exp(1)+144*x-432)*log(x)+((12*x^2+6*x)*exp(1)-1
2*x^3+30*x^2+12*x)*exp(x)^2+((144*x^2+144*x)*exp(1)-144*x^3+288*x^2+288*x)*exp(x)+864*x*exp(1)-864*x^2+1728*x)
*log(3-x+exp(1))+(12*exp(1)-12*x+36)*log(x)^3+(((-6*x^2-6*x)*exp(1)+6*x^3-12*x^2-12*x)*exp(x)-72*x*exp(1)+72*x
^2-144*x)*log(x)^2+((-12*x*exp(1)+12*x^2-36*x)*exp(x)-144*x*exp(1)+144*x^2-432*x)*log(x)+((6*x^3+6*x^2)*exp(1)
-6*x^4+12*x^3+12*x^2)*exp(x)^2+((72*x^3+144*x^2)*exp(1)-72*x^4+72*x^3+288*x^2)*exp(x)+864*x^2*exp(1)-864*x^3+1
728*x^2)/(x*exp(1)-x^2+3*x),x, algorithm="fricas")

[Out]

3*log(x)^4 + 3*x^2*e^(2*x) + 72*x^2*e^x - 6*(x*e^x + 12*x)*log(x)^2 + 3*(e^(2*x) + 24*e^x + 144)*log(-x + e +
3)^2 + 432*x^2 - 6*((e^x + 12)*log(x)^2 - x*e^(2*x) - 24*x*e^x - 144*x)*log(-x + e + 3)

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giac [B]  time = 0.31, size = 173, normalized size = 6.92 \begin {gather*} -6 \, x e^{x} \log \relax (x)^{2} + 3 \, \log \relax (x)^{4} - 6 \, e^{x} \log \relax (x)^{2} \log \left (-x + e + 3\right ) + 3 \, x^{2} e^{\left (2 \, x\right )} + 72 \, x^{2} e^{x} - 72 \, x \log \relax (x)^{2} + 6 \, x e^{\left (2 \, x\right )} \log \left (-x + e + 3\right ) + 144 \, x e^{x} \log \left (-x + e + 3\right ) - 72 \, \log \relax (x)^{2} \log \left (-x + e + 3\right ) + 3 \, e^{\left (2 \, x\right )} \log \left (-x + e + 3\right )^{2} + 72 \, e^{x} \log \left (-x + e + 3\right )^{2} + 432 \, x^{2} - 432 \, \log \left (x - e - 3\right )^{2} + 864 \, x \log \left (-x + e + 3\right ) + 864 \, \log \left (x - e - 3\right ) \log \left (-x + e + 3\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((6*x*exp(1)-6*x^2+18*x)*exp(x)^2+(72*x*exp(1)-72*x^2+216*x)*exp(x))*log(3-x+exp(1))^2+((-6*x*exp(1
)+6*x^2-18*x)*exp(x)*log(x)^2+((-12*exp(1)+12*x-36)*exp(x)-144*exp(1)+144*x-432)*log(x)+((12*x^2+6*x)*exp(1)-1
2*x^3+30*x^2+12*x)*exp(x)^2+((144*x^2+144*x)*exp(1)-144*x^3+288*x^2+288*x)*exp(x)+864*x*exp(1)-864*x^2+1728*x)
*log(3-x+exp(1))+(12*exp(1)-12*x+36)*log(x)^3+(((-6*x^2-6*x)*exp(1)+6*x^3-12*x^2-12*x)*exp(x)-72*x*exp(1)+72*x
^2-144*x)*log(x)^2+((-12*x*exp(1)+12*x^2-36*x)*exp(x)-144*x*exp(1)+144*x^2-432*x)*log(x)+((6*x^3+6*x^2)*exp(1)
-6*x^4+12*x^3+12*x^2)*exp(x)^2+((72*x^3+144*x^2)*exp(1)-72*x^4+72*x^3+288*x^2)*exp(x)+864*x^2*exp(1)-864*x^3+1
728*x^2)/(x*exp(1)-x^2+3*x),x, algorithm="giac")

[Out]

-6*x*e^x*log(x)^2 + 3*log(x)^4 - 6*e^x*log(x)^2*log(-x + e + 3) + 3*x^2*e^(2*x) + 72*x^2*e^x - 72*x*log(x)^2 +
6*x*e^(2*x)*log(-x + e + 3) + 144*x*e^x*log(-x + e + 3) - 72*log(x)^2*log(-x + e + 3) + 3*e^(2*x)*log(-x + e
+ 3)^2 + 72*e^x*log(-x + e + 3)^2 + 432*x^2 - 432*log(x - e - 3)^2 + 864*x*log(-x + e + 3) + 864*log(x - e - 3
)*log(-x + e + 3)

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maple [B]  time = 0.53, size = 107, normalized size = 4.28

method	result	size
risch	\(\left (3 \,{\mathrm e}^{2 x}+72 \,{\mathrm e}^{x}+432\right ) \ln \left (3-x +{\mathrm e}\right )^{2}+\left (6 x \,{\mathrm e}^{2 x}-6 \,{\mathrm e}^{x} \ln \relax (x )^{2}+144 \,{\mathrm e}^{x} x -72 \ln \relax (x )^{2}+864 x \right ) \ln \left (3-x +{\mathrm e}\right )+3 \,{\mathrm e}^{2 x} x^{2}-6 x \,{\mathrm e}^{x} \ln \relax (x )^{2}+3 \ln \relax (x )^{4}+72 \,{\mathrm e}^{x} x^{2}-72 x \ln \relax (x )^{2}+432 x^{2}\)	\(107\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((6*x*exp(1)-6*x^2+18*x)*exp(x)^2+(72*x*exp(1)-72*x^2+216*x)*exp(x))*ln(3-x+exp(1))^2+((-6*x*exp(1)+6*x^2
-18*x)*exp(x)*ln(x)^2+((-12*exp(1)+12*x-36)*exp(x)-144*exp(1)+144*x-432)*ln(x)+((12*x^2+6*x)*exp(1)-12*x^3+30*
x^2+12*x)*exp(x)^2+((144*x^2+144*x)*exp(1)-144*x^3+288*x^2+288*x)*exp(x)+864*x*exp(1)-864*x^2+1728*x)*ln(3-x+e
xp(1))+(12*exp(1)-12*x+36)*ln(x)^3+(((-6*x^2-6*x)*exp(1)+6*x^3-12*x^2-12*x)*exp(x)-72*x*exp(1)+72*x^2-144*x)*l
n(x)^2+((-12*x*exp(1)+12*x^2-36*x)*exp(x)-144*x*exp(1)+144*x^2-432*x)*ln(x)+((6*x^3+6*x^2)*exp(1)-6*x^4+12*x^3
+12*x^2)*exp(x)^2+((72*x^3+144*x^2)*exp(1)-72*x^4+72*x^3+288*x^2)*exp(x)+864*x^2*exp(1)-864*x^3+1728*x^2)/(x*e
xp(1)-x^2+3*x),x,method=_RETURNVERBOSE)

[Out]

(3*exp(2*x)+72*exp(x)+432)*ln(3-x+exp(1))^2+(6*x*exp(2*x)-6*exp(x)*ln(x)^2+144*exp(x)*x-72*ln(x)^2+864*x)*ln(3
-x+exp(1))+3*exp(2*x)*x^2-6*x*exp(x)*ln(x)^2+3*ln(x)^4+72*exp(x)*x^2-72*x*ln(x)^2+432*x^2

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maxima [B]  time = 0.70, size = 269, normalized size = 10.76 \begin {gather*} 3 \, \log \relax (x)^{4} + 3 \, x^{2} e^{\left (2 \, x\right )} - 432 \, {\left (e + 3\right )} \log \left (x - e - 3\right )^{2} - 72 \, x \log \relax (x)^{2} - 864 \, e \log \left (x - e - 3\right ) \log \left (-x + e + 3\right ) + 3 \, {\left (e^{\left (2 \, x\right )} + 24 \, e^{x}\right )} \log \left (-x + e + 3\right )^{2} + 432 \, x^{2} + 864 \, x {\left (e + 3\right )} - 864 \, {\left ({\left (e + 3\right )} \log \left (x - e - 3\right ) + x\right )} e + 432 \, {\left (2 \, \log \left (x - e - 3\right ) \log \left (-x + e + 3\right ) - \log \left (-x + e + 3\right )^{2}\right )} e - 6 \, {\left (x \log \relax (x)^{2} - 12 \, x^{2}\right )} e^{x} + 864 \, {\left (e^{2} + 6 \, e + 9\right )} \log \left (x - e - 3\right ) - 2592 \, {\left (e + 3\right )} \log \left (x - e - 3\right ) + 6 \, {\left (x e^{\left (2 \, x\right )} - {\left (\log \relax (x)^{2} - 24 \, x\right )} e^{x} - 12 \, \log \relax (x)^{2}\right )} \log \left (-x + e + 3\right ) + 864 \, {\left ({\left (e + 3\right )} \log \left (x - e - 3\right ) + x\right )} \log \left (-x + e + 3\right ) - 864 \, \log \left (-x + e + 3\right )^{2} - 2592 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((6*x*exp(1)-6*x^2+18*x)*exp(x)^2+(72*x*exp(1)-72*x^2+216*x)*exp(x))*log(3-x+exp(1))^2+((-6*x*exp(1
)+6*x^2-18*x)*exp(x)*log(x)^2+((-12*exp(1)+12*x-36)*exp(x)-144*exp(1)+144*x-432)*log(x)+((12*x^2+6*x)*exp(1)-1
2*x^3+30*x^2+12*x)*exp(x)^2+((144*x^2+144*x)*exp(1)-144*x^3+288*x^2+288*x)*exp(x)+864*x*exp(1)-864*x^2+1728*x)
*log(3-x+exp(1))+(12*exp(1)-12*x+36)*log(x)^3+(((-6*x^2-6*x)*exp(1)+6*x^3-12*x^2-12*x)*exp(x)-72*x*exp(1)+72*x
^2-144*x)*log(x)^2+((-12*x*exp(1)+12*x^2-36*x)*exp(x)-144*x*exp(1)+144*x^2-432*x)*log(x)+((6*x^3+6*x^2)*exp(1)
-6*x^4+12*x^3+12*x^2)*exp(x)^2+((72*x^3+144*x^2)*exp(1)-72*x^4+72*x^3+288*x^2)*exp(x)+864*x^2*exp(1)-864*x^3+1
728*x^2)/(x*exp(1)-x^2+3*x),x, algorithm="maxima")

[Out]

3*log(x)^4 + 3*x^2*e^(2*x) - 432*(e + 3)*log(x - e - 3)^2 - 72*x*log(x)^2 - 864*e*log(x - e - 3)*log(-x + e +
3) + 3*(e^(2*x) + 24*e^x)*log(-x + e + 3)^2 + 432*x^2 + 864*x*(e + 3) - 864*((e + 3)*log(x - e - 3) + x)*e + 4
32*(2*log(x - e - 3)*log(-x + e + 3) - log(-x + e + 3)^2)*e - 6*(x*log(x)^2 - 12*x^2)*e^x + 864*(e^2 + 6*e + 9
)*log(x - e - 3) - 2592*(e + 3)*log(x - e - 3) + 6*(x*e^(2*x) - (log(x)^2 - 24*x)*e^x - 12*log(x)^2)*log(-x +
e + 3) + 864*((e + 3)*log(x - e - 3) + x)*log(-x + e + 3) - 864*log(-x + e + 3)^2 - 2592*x

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mupad [F]  time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int \frac {{\mathrm {e}}^{2\,x}\,\left (\mathrm {e}\,\left (6\,x^3+6\,x^2\right )+12\,x^2+12\,x^3-6\,x^4\right )+\ln \left (\mathrm {e}-x+3\right )\,\left (1728\,x+{\mathrm {e}}^x\,\left (288\,x+\mathrm {e}\,\left (144\,x^2+144\,x\right )+288\,x^2-144\,x^3\right )+864\,x\,\mathrm {e}+{\mathrm {e}}^{2\,x}\,\left (12\,x+\mathrm {e}\,\left (12\,x^2+6\,x\right )+30\,x^2-12\,x^3\right )-\ln \relax (x)\,\left (144\,\mathrm {e}-144\,x+{\mathrm {e}}^x\,\left (12\,\mathrm {e}-12\,x+36\right )+432\right )-864\,x^2-{\mathrm {e}}^x\,{\ln \relax (x)}^2\,\left (18\,x+6\,x\,\mathrm {e}-6\,x^2\right )\right )+{\ln \left (\mathrm {e}-x+3\right )}^2\,\left ({\mathrm {e}}^{2\,x}\,\left (18\,x+6\,x\,\mathrm {e}-6\,x^2\right )+{\mathrm {e}}^x\,\left (216\,x+72\,x\,\mathrm {e}-72\,x^2\right )\right )-{\ln \relax (x)}^2\,\left (144\,x+{\mathrm {e}}^x\,\left (12\,x+\mathrm {e}\,\left (6\,x^2+6\,x\right )+12\,x^2-6\,x^3\right )+72\,x\,\mathrm {e}-72\,x^2\right )+864\,x^2\,\mathrm {e}+{\ln \relax (x)}^3\,\left (12\,\mathrm {e}-12\,x+36\right )+{\mathrm {e}}^x\,\left (\mathrm {e}\,\left (72\,x^3+144\,x^2\right )+288\,x^2+72\,x^3-72\,x^4\right )-\ln \relax (x)\,\left (432\,x+144\,x\,\mathrm {e}-144\,x^2+{\mathrm {e}}^x\,\left (36\,x+12\,x\,\mathrm {e}-12\,x^2\right )\right )+1728\,x^2-864\,x^3}{3\,x+x\,\mathrm {e}-x^2} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(2*x)*(exp(1)*(6*x^2 + 6*x^3) + 12*x^2 + 12*x^3 - 6*x^4) + log(exp(1) - x + 3)*(1728*x + exp(x)*(288*x
+ exp(1)*(144*x + 144*x^2) + 288*x^2 - 144*x^3) + 864*x*exp(1) + exp(2*x)*(12*x + exp(1)*(6*x + 12*x^2) + 30*
x^2 - 12*x^3) - log(x)*(144*exp(1) - 144*x + exp(x)*(12*exp(1) - 12*x + 36) + 432) - 864*x^2 - exp(x)*log(x)^2
*(18*x + 6*x*exp(1) - 6*x^2)) + log(exp(1) - x + 3)^2*(exp(2*x)*(18*x + 6*x*exp(1) - 6*x^2) + exp(x)*(216*x +
72*x*exp(1) - 72*x^2)) - log(x)^2*(144*x + exp(x)*(12*x + exp(1)*(6*x + 6*x^2) + 12*x^2 - 6*x^3) + 72*x*exp(1)
- 72*x^2) + 864*x^2*exp(1) + log(x)^3*(12*exp(1) - 12*x + 36) + exp(x)*(exp(1)*(144*x^2 + 72*x^3) + 288*x^2 +
72*x^3 - 72*x^4) - log(x)*(432*x + 144*x*exp(1) - 144*x^2 + exp(x)*(36*x + 12*x*exp(1) - 12*x^2)) + 1728*x^2
- 864*x^3)/(3*x + x*exp(1) - x^2),x)

[Out]

int((exp(2*x)*(exp(1)*(6*x^2 + 6*x^3) + 12*x^2 + 12*x^3 - 6*x^4) + log(exp(1) - x + 3)*(1728*x + exp(x)*(288*x
+ exp(1)*(144*x + 144*x^2) + 288*x^2 - 144*x^3) + 864*x*exp(1) + exp(2*x)*(12*x + exp(1)*(6*x + 12*x^2) + 30*
x^2 - 12*x^3) - log(x)*(144*exp(1) - 144*x + exp(x)*(12*exp(1) - 12*x + 36) + 432) - 864*x^2 - exp(x)*log(x)^2
*(18*x + 6*x*exp(1) - 6*x^2)) + log(exp(1) - x + 3)^2*(exp(2*x)*(18*x + 6*x*exp(1) - 6*x^2) + exp(x)*(216*x +
72*x*exp(1) - 72*x^2)) - log(x)^2*(144*x + exp(x)*(12*x + exp(1)*(6*x + 6*x^2) + 12*x^2 - 6*x^3) + 72*x*exp(1)
- 72*x^2) + 864*x^2*exp(1) + log(x)^3*(12*exp(1) - 12*x + 36) + exp(x)*(exp(1)*(144*x^2 + 72*x^3) + 288*x^2 +
72*x^3 - 72*x^4) - log(x)*(432*x + 144*x*exp(1) - 144*x^2 + exp(x)*(36*x + 12*x*exp(1) - 12*x^2)) + 1728*x^2
- 864*x^3)/(3*x + x*exp(1) - x^2), x)

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sympy [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((6*x*exp(1)-6*x**2+18*x)*exp(x)**2+(72*x*exp(1)-72*x**2+216*x)*exp(x))*ln(3-x+exp(1))**2+((-6*x*ex
p(1)+6*x**2-18*x)*exp(x)*ln(x)**2+((-12*exp(1)+12*x-36)*exp(x)-144*exp(1)+144*x-432)*ln(x)+((12*x**2+6*x)*exp(
1)-12*x**3+30*x**2+12*x)*exp(x)**2+((144*x**2+144*x)*exp(1)-144*x**3+288*x**2+288*x)*exp(x)+864*x*exp(1)-864*x
**2+1728*x)*ln(3-x+exp(1))+(12*exp(1)-12*x+36)*ln(x)**3+(((-6*x**2-6*x)*exp(1)+6*x**3-12*x**2-12*x)*exp(x)-72*
x*exp(1)+72*x**2-144*x)*ln(x)**2+((-12*x*exp(1)+12*x**2-36*x)*exp(x)-144*x*exp(1)+144*x**2-432*x)*ln(x)+((6*x*
*3+6*x**2)*exp(1)-6*x**4+12*x**3+12*x**2)*exp(x)**2+((72*x**3+144*x**2)*exp(1)-72*x**4+72*x**3+288*x**2)*exp(x
)+864*x**2*exp(1)-864*x**3+1728*x**2)/(x*exp(1)-x**2+3*x),x)

[Out]

Timed out

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