3.9.77 \(\int \frac {-14+12 x-6 x^2+x^3+(-8+12 x-6 x^2+x^3) \log (x)+e^{-3 e^x+3 x} (1+\log (x))+e^{-2 e^x+2 x} (-6+3 x+(-6+3 x) \log (x))+e^{-e^x+x} (6+6 e^x-12 x+3 x^2+(12-12 x+3 x^2) \log (x))}{-8+e^{-3 e^x+3 x}+12 x-6 x^2+x^3+e^{-2 e^x+2 x} (-6+3 x)+e^{-e^x+x} (12-12 x+3 x^2)} \, dx\) [877]
Optimal. Leaf size=22 \[ -3+\frac {3}{\left (-2+e^{-e^x+x}+x\right )^2}+x \log (x) \]
[Out]
3/(x+exp(x-exp(x))-2)^2-3+x*ln(x)
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Rubi [F]
time = 3.28, 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 {-14+12 x-6 x^2+x^3+\left (-8+12 x-6 x^2+x^3\right ) \log (x)+e^{-3 e^x+3 x} (1+\log (x))+e^{-2 e^x+2 x} (-6+3 x+(-6+3 x) \log (x))+e^{-e^x+x} \left (6+6 e^x-12 x+3 x^2+\left (12-12 x+3 x^2\right ) \log (x)\right )}{-8+e^{-3 e^x+3 x}+12 x-6 x^2+x^3+e^{-2 e^x+2 x} (-6+3 x)+e^{-e^x+x} \left (12-12 x+3 x^2\right )} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
Int[(-14 + 12*x - 6*x^2 + x^3 + (-8 + 12*x - 6*x^2 + x^3)*Log[x] + E^(-3*E^x + 3*x)*(1 + Log[x]) + E^(-2*E^x +
2*x)*(-6 + 3*x + (-6 + 3*x)*Log[x]) + E^(-E^x + x)*(6 + 6*E^x - 12*x + 3*x^2 + (12 - 12*x + 3*x^2)*Log[x]))/(
-8 + E^(-3*E^x + 3*x) + 12*x - 6*x^2 + x^3 + E^(-2*E^x + 2*x)*(-6 + 3*x) + E^(-E^x + x)*(12 - 12*x + 3*x^2)),x
]
[Out]
x*Log[x] - 18*Defer[Int][E^(3*E^x)/(-2*E^E^x + E^x + E^E^x*x)^3, x] + 24*Defer[Int][E^(4*E^x)/(-2*E^E^x + E^x
+ E^E^x*x)^3, x] + 6*Defer[Int][(E^(3*E^x)*x)/(-2*E^E^x + E^x + E^E^x*x)^3, x] - 24*Defer[Int][(E^(4*E^x)*x)/(
-2*E^E^x + E^x + E^E^x*x)^3, x] + 6*Defer[Int][(E^(4*E^x)*x^2)/(-2*E^E^x + E^x + E^E^x*x)^3, x] - 6*Defer[Int]
[E^(2*E^x)/(-2*E^E^x + E^x + E^E^x*x)^2, x] + 24*Defer[Int][E^(3*E^x)/(-2*E^E^x + E^x + E^E^x*x)^2, x] - 12*De
fer[Int][(E^(3*E^x)*x)/(-2*E^E^x + E^x + E^E^x*x)^2, x] + 6*Defer[Int][E^(2*E^x)/(-2*E^E^x + E^x + E^E^x*x), x
]
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^{3 x}+6 e^{2 \left (e^x+x\right )}+3 e^{e^x+2 x} (-2+x)+3 e^{2 e^x+x} \left (2-4 x+x^2\right )+e^{3 e^x} \left (-14+12 x-6 x^2+x^3\right )+\left (e^x+e^{e^x} (-2+x)\right )^3 \log (x)}{\left (e^x+e^{e^x} (-2+x)\right )^3} \, dx\\ &=\int \left (1+\frac {6 e^{2 e^x}}{-2 e^{e^x}+e^x+e^{e^x} x}-\frac {6 e^{2 e^x} \left (1-4 e^{e^x}+2 e^{e^x} x\right )}{\left (-2 e^{e^x}+e^x+e^{e^x} x\right )^2}+\frac {6 e^{3 e^x} \left (-3+4 e^{e^x}+x-4 e^{e^x} x+e^{e^x} x^2\right )}{\left (-2 e^{e^x}+e^x+e^{e^x} x\right )^3}+\log (x)\right ) \, dx\\ &=x+6 \int \frac {e^{2 e^x}}{-2 e^{e^x}+e^x+e^{e^x} x} \, dx-6 \int \frac {e^{2 e^x} \left (1-4 e^{e^x}+2 e^{e^x} x\right )}{\left (-2 e^{e^x}+e^x+e^{e^x} x\right )^2} \, dx+6 \int \frac {e^{3 e^x} \left (-3+4 e^{e^x}+x-4 e^{e^x} x+e^{e^x} x^2\right )}{\left (-2 e^{e^x}+e^x+e^{e^x} x\right )^3} \, dx+\int \log (x) \, dx\\ &=x \log (x)-6 \int \frac {e^{2 e^x} \left (1+2 e^{e^x} (-2+x)\right )}{\left (e^x+e^{e^x} (-2+x)\right )^2} \, dx+6 \int \frac {e^{3 e^x} \left (-3+e^{e^x} (-2+x)^2+x\right )}{\left (e^x+e^{e^x} (-2+x)\right )^3} \, dx+6 \int \frac {e^{2 e^x}}{-2 e^{e^x}+e^x+e^{e^x} x} \, dx\\ &=x \log (x)+6 \int \frac {e^{2 e^x}}{-2 e^{e^x}+e^x+e^{e^x} x} \, dx+6 \int \left (-\frac {3 e^{3 e^x}}{\left (-2 e^{e^x}+e^x+e^{e^x} x\right )^3}+\frac {4 e^{4 e^x}}{\left (-2 e^{e^x}+e^x+e^{e^x} x\right )^3}+\frac {e^{3 e^x} x}{\left (-2 e^{e^x}+e^x+e^{e^x} x\right )^3}-\frac {4 e^{4 e^x} x}{\left (-2 e^{e^x}+e^x+e^{e^x} x\right )^3}+\frac {e^{4 e^x} x^2}{\left (-2 e^{e^x}+e^x+e^{e^x} x\right )^3}\right ) \, dx-6 \int \left (\frac {e^{2 e^x}}{\left (-2 e^{e^x}+e^x+e^{e^x} x\right )^2}-\frac {4 e^{3 e^x}}{\left (-2 e^{e^x}+e^x+e^{e^x} x\right )^2}+\frac {2 e^{3 e^x} x}{\left (-2 e^{e^x}+e^x+e^{e^x} x\right )^2}\right ) \, dx\\ &=x \log (x)+6 \int \frac {e^{3 e^x} x}{\left (-2 e^{e^x}+e^x+e^{e^x} x\right )^3} \, dx+6 \int \frac {e^{4 e^x} x^2}{\left (-2 e^{e^x}+e^x+e^{e^x} x\right )^3} \, dx-6 \int \frac {e^{2 e^x}}{\left (-2 e^{e^x}+e^x+e^{e^x} x\right )^2} \, dx+6 \int \frac {e^{2 e^x}}{-2 e^{e^x}+e^x+e^{e^x} x} \, dx-12 \int \frac {e^{3 e^x} x}{\left (-2 e^{e^x}+e^x+e^{e^x} x\right )^2} \, dx-18 \int \frac {e^{3 e^x}}{\left (-2 e^{e^x}+e^x+e^{e^x} x\right )^3} \, dx+24 \int \frac {e^{4 e^x}}{\left (-2 e^{e^x}+e^x+e^{e^x} x\right )^3} \, dx-24 \int \frac {e^{4 e^x} x}{\left (-2 e^{e^x}+e^x+e^{e^x} x\right )^3} \, dx+24 \int \frac {e^{3 e^x}}{\left (-2 e^{e^x}+e^x+e^{e^x} x\right )^2} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(45\) vs. \(2(22)=44\).
time = 0.11, size = 45, normalized size = 2.05 \begin {gather*} \frac {3 e^{2 e^x}+\left (e^x+e^{e^x} (-2+x)\right )^2 x \log (x)}{\left (e^x+e^{e^x} (-2+x)\right )^2} \end {gather*}
Antiderivative was successfully verified.
[In]
Integrate[(-14 + 12*x - 6*x^2 + x^3 + (-8 + 12*x - 6*x^2 + x^3)*Log[x] + E^(-3*E^x + 3*x)*(1 + Log[x]) + E^(-2
*E^x + 2*x)*(-6 + 3*x + (-6 + 3*x)*Log[x]) + E^(-E^x + x)*(6 + 6*E^x - 12*x + 3*x^2 + (12 - 12*x + 3*x^2)*Log[
x]))/(-8 + E^(-3*E^x + 3*x) + 12*x - 6*x^2 + x^3 + E^(-2*E^x + 2*x)*(-6 + 3*x) + E^(-E^x + x)*(12 - 12*x + 3*x
^2)),x]
[Out]
(3*E^(2*E^x) + (E^x + E^E^x*(-2 + x))^2*x*Log[x])/(E^x + E^E^x*(-2 + x))^2
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Maple [A]
time = 0.10, size = 20, normalized size = 0.91
| | |
| method |
result |
size |
| | |
| risch |
\(x \ln \left (x \right )+\frac {3}{\left (x +{\mathrm e}^{x -{\mathrm e}^{x}}-2\right )^{2}}\) |
\(20\) |
| | |
|
|
|
|
Verification of antiderivative is not currently implemented for this CAS.
[In]
int(((ln(x)+1)*exp(x-exp(x))^3+((3*x-6)*ln(x)+3*x-6)*exp(x-exp(x))^2+((3*x^2-12*x+12)*ln(x)+6*exp(x)+3*x^2-12*
x+6)*exp(x-exp(x))+(x^3-6*x^2+12*x-8)*ln(x)+x^3-6*x^2+12*x-14)/(exp(x-exp(x))^3+(3*x-6)*exp(x-exp(x))^2+(3*x^2
-12*x+12)*exp(x-exp(x))+x^3-6*x^2+12*x-8),x,method=_RETURNVERBOSE)
[Out]
x*ln(x)+3/(x+exp(x-exp(x))-2)^2
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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 80 vs.
\(2 (20) = 40\).
time = 0.38, size = 80, normalized size = 3.64 \begin {gather*} \frac {x e^{\left (2 \, x\right )} \log \left (x\right ) + 2 \, {\left (x^{2} - 2 \, x\right )} e^{\left (x + e^{x}\right )} \log \left (x\right ) + {\left ({\left (x^{3} - 4 \, x^{2} + 4 \, x\right )} \log \left (x\right ) + 3\right )} e^{\left (2 \, e^{x}\right )}}{2 \, {\left (x - 2\right )} e^{\left (x + e^{x}\right )} + {\left (x^{2} - 4 \, x + 4\right )} e^{\left (2 \, e^{x}\right )} + e^{\left (2 \, x\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((log(x)+1)*exp(x-exp(x))^3+((-6+3*x)*log(x)+3*x-6)*exp(x-exp(x))^2+((3*x^2-12*x+12)*log(x)+6*exp(x)
+3*x^2-12*x+6)*exp(x-exp(x))+(x^3-6*x^2+12*x-8)*log(x)+x^3-6*x^2+12*x-14)/(exp(x-exp(x))^3+(-6+3*x)*exp(x-exp(
x))^2+(3*x^2-12*x+12)*exp(x-exp(x))+x^3-6*x^2+12*x-8),x, algorithm="maxima")
[Out]
(x*e^(2*x)*log(x) + 2*(x^2 - 2*x)*e^(x + e^x)*log(x) + ((x^3 - 4*x^2 + 4*x)*log(x) + 3)*e^(2*e^x))/(2*(x - 2)*
e^(x + e^x) + (x^2 - 4*x + 4)*e^(2*e^x) + e^(2*x))
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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 80 vs.
\(2 (20) = 40\).
time = 0.37, size = 80, normalized size = 3.64 \begin {gather*} \frac {x e^{\left (2 \, x - 2 \, e^{x}\right )} \log \left (x\right ) + 2 \, {\left (x^{2} - 2 \, x\right )} e^{\left (x - e^{x}\right )} \log \left (x\right ) + {\left (x^{3} - 4 \, x^{2} + 4 \, x\right )} \log \left (x\right ) + 3}{x^{2} + 2 \, {\left (x - 2\right )} e^{\left (x - e^{x}\right )} - 4 \, x + e^{\left (2 \, x - 2 \, e^{x}\right )} + 4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((log(x)+1)*exp(x-exp(x))^3+((-6+3*x)*log(x)+3*x-6)*exp(x-exp(x))^2+((3*x^2-12*x+12)*log(x)+6*exp(x)
+3*x^2-12*x+6)*exp(x-exp(x))+(x^3-6*x^2+12*x-8)*log(x)+x^3-6*x^2+12*x-14)/(exp(x-exp(x))^3+(-6+3*x)*exp(x-exp(
x))^2+(3*x^2-12*x+12)*exp(x-exp(x))+x^3-6*x^2+12*x-8),x, algorithm="fricas")
[Out]
(x*e^(2*x - 2*e^x)*log(x) + 2*(x^2 - 2*x)*e^(x - e^x)*log(x) + (x^3 - 4*x^2 + 4*x)*log(x) + 3)/(x^2 + 2*(x - 2
)*e^(x - e^x) - 4*x + e^(2*x - 2*e^x) + 4)
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Sympy [A]
time = 0.19, size = 36, normalized size = 1.64 \begin {gather*} x \log {\left (x \right )} + \frac {3}{x^{2} - 4 x + \left (2 x - 4\right ) e^{x - e^{x}} + e^{2 x - 2 e^{x}} + 4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((ln(x)+1)*exp(x-exp(x))**3+((-6+3*x)*ln(x)+3*x-6)*exp(x-exp(x))**2+((3*x**2-12*x+12)*ln(x)+6*exp(x)
+3*x**2-12*x+6)*exp(x-exp(x))+(x**3-6*x**2+12*x-8)*ln(x)+x**3-6*x**2+12*x-14)/(exp(x-exp(x))**3+(-6+3*x)*exp(x
-exp(x))**2+(3*x**2-12*x+12)*exp(x-exp(x))+x**3-6*x**2+12*x-8),x)
[Out]
x*log(x) + 3/(x**2 - 4*x + (2*x - 4)*exp(x - exp(x)) + exp(2*x - 2*exp(x)) + 4)
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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 6825 vs.
\(2 (20) = 40\).
time = 0.73, size = 6825, normalized size = 310.23 \begin {gather*} \text {Too large to display} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((log(x)+1)*exp(x-exp(x))^3+((-6+3*x)*log(x)+3*x-6)*exp(x-exp(x))^2+((3*x^2-12*x+12)*log(x)+6*exp(x)
+3*x^2-12*x+6)*exp(x-exp(x))+(x^3-6*x^2+12*x-8)*log(x)+x^3-6*x^2+12*x-14)/(exp(x-exp(x))^3+(-6+3*x)*exp(x-exp(
x))^2+(3*x^2-12*x+12)*exp(x-exp(x))+x^3-6*x^2+12*x-8),x, algorithm="giac")
[Out]
(x^11*e^(5*x + 2*e^x)*log(x) - 3*x^11*e^(4*x + 2*e^x)*log(x) + 3*x^11*e^(3*x + 2*e^x)*log(x) - x^11*e^(2*x + 2
*e^x)*log(x) + 6*x^10*e^(6*x + e^x)*log(x) - 18*x^10*e^(5*x + 2*e^x)*log(x) - 18*x^10*e^(5*x + e^x)*log(x) + 5
7*x^10*e^(4*x + 2*e^x)*log(x) + 18*x^10*e^(4*x + e^x)*log(x) - 60*x^10*e^(3*x + 2*e^x)*log(x) - 6*x^10*e^(3*x
+ e^x)*log(x) + 21*x^10*e^(2*x + 2*e^x)*log(x) + 15*x^9*e^(7*x)*log(x) - 45*x^9*e^(6*x)*log(x) + 45*x^9*e^(5*x
)*log(x) - 15*x^9*e^(4*x)*log(x) - 96*x^9*e^(6*x + e^x)*log(x) + 144*x^9*e^(5*x + 2*e^x)*log(x) + 306*x^9*e^(5
*x + e^x)*log(x) - 480*x^9*e^(4*x + 2*e^x)*log(x) - 324*x^9*e^(4*x + e^x)*log(x) + 531*x^9*e^(3*x + 2*e^x)*log
(x) + 114*x^9*e^(3*x + e^x)*log(x) - 195*x^9*e^(2*x + 2*e^x)*log(x) - 210*x^8*e^(7*x)*log(x) + 675*x^8*e^(6*x)
*log(x) - 720*x^8*e^(5*x)*log(x) + 255*x^8*e^(4*x)*log(x) + 20*x^8*e^(8*x - e^x)*log(x) - 60*x^8*e^(7*x - e^x)
*log(x) + 672*x^8*e^(6*x + e^x)*log(x) + 60*x^8*e^(6*x - e^x)*log(x) - 672*x^8*e^(5*x + 2*e^x)*log(x) - 2268*x
^8*e^(5*x + e^x)*log(x) - 20*x^8*e^(5*x - e^x)*log(x) + 2352*x^8*e^(4*x + 2*e^x)*log(x) + 2538*x^8*e^(4*x + e^
x)*log(x) - 2730*x^8*e^(3*x + 2*e^x)*log(x) - 942*x^8*e^(3*x + e^x)*log(x) + 1051*x^8*e^(2*x + 2*e^x)*log(x) +
3*x^8*e^(5*x + 2*e^x) - 9*x^8*e^(4*x + 2*e^x) + 9*x^8*e^(3*x + 2*e^x) - 3*x^8*e^(2*x + 2*e^x) + 1260*x^7*e^(7
*x)*log(x) - 4320*x^7*e^(6*x)*log(x) + 4905*x^7*e^(5*x)*log(x) - 1845*x^7*e^(4*x)*log(x) + 15*x^7*e^(9*x - 2*e
^x)*log(x) - 240*x^7*e^(8*x - e^x)*log(x) - 45*x^7*e^(8*x - 2*e^x)*log(x) + 780*x^7*e^(7*x - e^x)*log(x) + 45*
x^7*e^(7*x - 2*e^x)*log(x) - 2688*x^7*e^(6*x + e^x)*log(x) - 840*x^7*e^(6*x - e^x)*log(x) - 15*x^7*e^(6*x - 2*
e^x)*log(x) + 2016*x^7*e^(5*x + 2*e^x)*log(x) + 9576*x^7*e^(5*x + e^x)*log(x) + 300*x^7*e^(5*x - e^x)*log(x) -
7392*x^7*e^(4*x + 2*e^x)*log(x) - 11304*x^7*e^(4*x + e^x)*log(x) + 8988*x^7*e^(3*x + 2*e^x)*log(x) + 4422*x^7
*e^(3*x + e^x)*log(x) - 3624*x^7*e^(2*x + 2*e^x)*log(x) + 12*x^7*e^(6*x + e^x) - 42*x^7*e^(5*x + 2*e^x) - 36*x
^7*e^(5*x + e^x) + 135*x^7*e^(4*x + 2*e^x) + 36*x^7*e^(4*x + e^x) - 144*x^7*e^(3*x + 2*e^x) - 12*x^7*e^(3*x +
e^x) + 51*x^7*e^(2*x + 2*e^x) - 4200*x^6*e^(7*x)*log(x) + 15300*x^6*e^(6*x)*log(x) - 18450*x^6*e^(5*x)*log(x)
+ 7365*x^6*e^(4*x)*log(x) + 6*x^6*e^(10*x - 3*e^x)*log(x) - 150*x^6*e^(9*x - 2*e^x)*log(x) - 18*x^6*e^(9*x - 3
*e^x)*log(x) + 1200*x^6*e^(8*x - e^x)*log(x) + 495*x^6*e^(8*x - 2*e^x)*log(x) + 18*x^6*e^(8*x - 3*e^x)*log(x)
- 4200*x^6*e^(7*x - e^x)*log(x) - 540*x^6*e^(7*x - 2*e^x)*log(x) - 6*x^6*e^(7*x - 3*e^x)*log(x) + 6720*x^6*e^(
6*x + e^x)*log(x) + 4860*x^6*e^(6*x - e^x)*log(x) + 195*x^6*e^(6*x - 2*e^x)*log(x) - 4032*x^6*e^(5*x + 2*e^x)*
log(x) - 25200*x^6*e^(5*x + e^x)*log(x) - 1860*x^6*e^(5*x - e^x)*log(x) + 15456*x^6*e^(4*x + 2*e^x)*log(x) + 3
1320*x^6*e^(4*x + e^x)*log(x) - 19656*x^6*e^(3*x + 2*e^x)*log(x) - 12900*x^6*e^(3*x + e^x)*log(x) + 8292*x^6*e
^(2*x + 2*e^x)*log(x) + 18*x^6*e^(7*x) - 54*x^6*e^(6*x) + 54*x^6*e^(5*x) - 18*x^6*e^(4*x) - 144*x^6*e^(6*x + e
^x) + 252*x^6*e^(5*x + 2*e^x) + 468*x^6*e^(5*x + e^x) - 864*x^6*e^(4*x + 2*e^x) - 504*x^6*e^(4*x + e^x) + 981*
x^6*e^(3*x + 2*e^x) + 180*x^6*e^(3*x + e^x) - 369*x^6*e^(2*x + 2*e^x) + 8400*x^5*e^(7*x)*log(x) - 32400*x^5*e^
(6*x)*log(x) + 41400*x^5*e^(5*x)*log(x) - 17520*x^5*e^(4*x)*log(x) + x^5*e^(11*x - 4*e^x)*log(x) - 48*x^5*e^(1
0*x - 3*e^x)*log(x) - 3*x^5*e^(10*x - 4*e^x)*log(x) + 600*x^5*e^(9*x - 2*e^x)*log(x) + 162*x^5*e^(9*x - 3*e^x)
*log(x) + 3*x^5*e^(9*x - 4*e^x)*log(x) - 3200*x^5*e^(8*x - e^x)*log(x) - 2160*x^5*e^(8*x - 2*e^x)*log(x) - 180
*x^5*e^(8*x - 3*e^x)*log(x) - x^5*e^(8*x - 4*e^x)*log(x) + 12000*x^5*e^(7*x - e^x)*log(x) + 2565*x^5*e^(7*x -
2*e^x)*log(x) + 66*x^5*e^(7*x - 3*e^x)*log(x) - 10752*x^5*e^(6*x + e^x)*log(x) - 14880*x^5*e^(6*x - e^x)*log(x
) - 1005*x^5*e^(6*x - 2*e^x)*log(x) + 5376*x^5*e^(5*x + 2*e^x)*log(x) + 42336*x^5*e^(5*x + e^x)*log(x) + 6100*
x^5*e^(5*x - e^x)*log(x) - 21504*x^5*e^(4*x + 2*e^x)*log(x) - 55296*x^5*e^(4*x + e^x)*log(x) + 28560*x^5*e^(3*
x + 2*e^x)*log(x) + 23952*x^5*e^(3*x + e^x)*log(x) - 12592*x^5*e^(2*x + 2*e^x)*log(x) - 180*x^5*e^(7*x) + 594*
x^5*e^(6*x) - 648*x^5*e^(5*x) + 234*x^5*e^(4*x) + 12*x^5*e^(8*x - e^x) - 36*x^5*e^(7*x - e^x) + 720*x^5*e^(6*x
+ e^x) + 36*x^5*e^(6*x - e^x) - 840*x^5*e^(5*x + 2*e^x) - 2520*x^5*e^(5*x + e^x) - 12*x^5*e^(5*x - e^x) + 306
0*x^5*e^(4*x + 2*e^x) + 2916*x^5*e^(4*x + e^x) - 3690*x^5*e^(3*x + 2*e^x) - 1116*x^5*e^(3*x + e^x) + 1473*x^5*
e^(2*x + 2*e^x) - 10080*x^4*e^(7*x)*log(x) + 41040*x^4*e^(6*x)*log(x) - 55440*x^4*e^(5*x)*log(x) + 24840*x^4*e
^(4*x)*log(x) - 6*x^4*e^(11*x - 4*e^x)*log(x) + 144*x^4*e^(10*x - 3*e^x)*log(x) + 21*x^4*e^(10*x - 4*e^x)*log(
x) - 1200*x^4*e^(9*x - 2*e^x)*log(x) - 540*x^4*e^(9*x - 3*e^x)*log(x) - 24*x^4*e^(9*x - 4*e^x)*log(x) + 4800*x
^4*e^(8*x - e^x)*log(x) + 4680*x^4*e^(8*x - 2*e^x)*log(x) + 666*x^4*e^(8*x - 3*e^x)*log(x) + 9*x^4*e^(8*x - 4*
e^x)*log(x) - 19200*x^4*e^(7*x - e^x)*log(x) - 6030*x^4*e^(7*x - 2*e^x)*log(x) - 270*x^4*e^(7*x - 3*e^x)*log(x
) + 10752*x^4*e^(6*x + e^x)*log(x) + 25440*x^4*...
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Mupad [F]
time = 0.00, size = -1, normalized size = -0.05 \begin {gather*} \int \frac {12\,x+{\mathrm {e}}^{x-{\mathrm {e}}^x}\,\left (6\,{\mathrm {e}}^x-12\,x+\ln \left (x\right )\,\left (3\,x^2-12\,x+12\right )+3\,x^2+6\right )+{\mathrm {e}}^{3\,x-3\,{\mathrm {e}}^x}\,\left (\ln \left (x\right )+1\right )+\ln \left (x\right )\,\left (x^3-6\,x^2+12\,x-8\right )-6\,x^2+x^3+{\mathrm {e}}^{2\,x-2\,{\mathrm {e}}^x}\,\left (3\,x+\ln \left (x\right )\,\left (3\,x-6\right )-6\right )-14}{12\,x+{\mathrm {e}}^{3\,x-3\,{\mathrm {e}}^x}+{\mathrm {e}}^{x-{\mathrm {e}}^x}\,\left (3\,x^2-12\,x+12\right )+{\mathrm {e}}^{2\,x-2\,{\mathrm {e}}^x}\,\left (3\,x-6\right )-6\,x^2+x^3-8} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
int((12*x + exp(x - exp(x))*(6*exp(x) - 12*x + log(x)*(3*x^2 - 12*x + 12) + 3*x^2 + 6) + exp(3*x - 3*exp(x))*(
log(x) + 1) + log(x)*(12*x - 6*x^2 + x^3 - 8) - 6*x^2 + x^3 + exp(2*x - 2*exp(x))*(3*x + log(x)*(3*x - 6) - 6)
- 14)/(12*x + exp(3*x - 3*exp(x)) + exp(x - exp(x))*(3*x^2 - 12*x + 12) + exp(2*x - 2*exp(x))*(3*x - 6) - 6*x
^2 + x^3 - 8),x)
[Out]
int((12*x + exp(x - exp(x))*(6*exp(x) - 12*x + log(x)*(3*x^2 - 12*x + 12) + 3*x^2 + 6) + exp(3*x - 3*exp(x))*(
log(x) + 1) + log(x)*(12*x - 6*x^2 + x^3 - 8) - 6*x^2 + x^3 + exp(2*x - 2*exp(x))*(3*x + log(x)*(3*x - 6) - 6)
- 14)/(12*x + exp(3*x - 3*exp(x)) + exp(x - exp(x))*(3*x^2 - 12*x + 12) + exp(2*x - 2*exp(x))*(3*x - 6) - 6*x
^2 + x^3 - 8), x)
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