3.8.47 \(\int \frac {e^{9+9 e^{8 x}-18 x-9 x^2+18 x^3+9 x^4+e^{4 x} (18-18 x-18 x^2)} (55+e^{8 x} (-216+72 e^x-72 x)+72 x-144 x^2-162 x^3-36 x^4+e^x (-19-18 x+54 x^2+36 x^3)+e^{4 x} (-162+270 x+324 x^2+72 x^3+e^x (54-108 x-72 x^2)))+e^{9+9 e^{8 x}-18 x-9 x^2+18 x^3+9 x^4+e^{4 x} (18-18 x-18 x^2)} (54+e^{8 x} (-216+72 e^x-72 x)+72 x-144 x^2-162 x^3-36 x^4+e^x (-18-18 x+54 x^2+36 x^3)+e^{4 x} (-162+270 x+324 x^2+72 x^3+e^x (54-108 x-72 x^2))) \log (3-e^x+x)}{-3+e^x-x+(-6+2 e^x-2 x) \log (3-e^x+x)+(-3+e^x-x) \log ^2(3-e^x+x)} \, dx\)

Optimal. Leaf size=34 \[ \frac {e^{\left (3-3 \left (-e^{4 x}+x+x^2\right )\right )^2}}{1+\log \left (3-e^x+x\right )} \]

________________________________________________________________________________________

Rubi [F]  time = 125.12, 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 {\exp \left (9+9 e^{8 x}-18 x-9 x^2+18 x^3+9 x^4+e^{4 x} \left (18-18 x-18 x^2\right )\right ) \left (55+e^{8 x} \left (-216+72 e^x-72 x\right )+72 x-144 x^2-162 x^3-36 x^4+e^x \left (-19-18 x+54 x^2+36 x^3\right )+e^{4 x} \left (-162+270 x+324 x^2+72 x^3+e^x \left (54-108 x-72 x^2\right )\right )\right )+\exp \left (9+9 e^{8 x}-18 x-9 x^2+18 x^3+9 x^4+e^{4 x} \left (18-18 x-18 x^2\right )\right ) \left (54+e^{8 x} \left (-216+72 e^x-72 x\right )+72 x-144 x^2-162 x^3-36 x^4+e^x \left (-18-18 x+54 x^2+36 x^3\right )+e^{4 x} \left (-162+270 x+324 x^2+72 x^3+e^x \left (54-108 x-72 x^2\right )\right )\right ) \log \left (3-e^x+x\right )}{-3+e^x-x+\left (-6+2 e^x-2 x\right ) \log \left (3-e^x+x\right )+\left (-3+e^x-x\right ) \log ^2\left (3-e^x+x\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^(9 + 9*E^(8*x) - 18*x - 9*x^2 + 18*x^3 + 9*x^4 + E^(4*x)*(18 - 18*x - 18*x^2))*(55 + E^(8*x)*(-216 + 72
*E^x - 72*x) + 72*x - 144*x^2 - 162*x^3 - 36*x^4 + E^x*(-19 - 18*x + 54*x^2 + 36*x^3) + E^(4*x)*(-162 + 270*x
+ 324*x^2 + 72*x^3 + E^x*(54 - 108*x - 72*x^2))) + E^(9 + 9*E^(8*x) - 18*x - 9*x^2 + 18*x^3 + 9*x^4 + E^(4*x)*
(18 - 18*x - 18*x^2))*(54 + E^(8*x)*(-216 + 72*E^x - 72*x) + 72*x - 144*x^2 - 162*x^3 - 36*x^4 + E^x*(-18 - 18
*x + 54*x^2 + 36*x^3) + E^(4*x)*(-162 + 270*x + 324*x^2 + 72*x^3 + E^x*(54 - 108*x - 72*x^2)))*Log[3 - E^x + x
])/(-3 + E^x - x + (-6 + 2*E^x - 2*x)*Log[3 - E^x + x] + (-3 + E^x - x)*Log[3 - E^x + x]^2),x]

[Out]

18*Defer[Int][E^(9*(-1 - E^(4*x) + x + x^2)^2)/(-1 - Log[3 - E^x + x]), x] - Defer[Int][E^(9*(-1 - E^(4*x) + x
+ x^2)^2)/(1 + Log[3 - E^x + x])^2, x] - 2*Defer[Int][E^(9*(-1 - E^(4*x) + x + x^2)^2)/((-3 + E^x - x)*(1 + L
og[3 - E^x + x])^2), x] - Defer[Int][(E^(9*(-1 - E^(4*x) + x + x^2)^2)*x)/((-3 + E^x - x)*(1 + Log[3 - E^x + x
])^2), x] + 54*Defer[Int][E^(4*x + 9*(-1 - E^(4*x) + x + x^2)^2)/(1 + Log[3 - E^x + x]), x] + 72*Defer[Int][E^
(8*x + 9*(-1 - E^(4*x) + x + x^2)^2)/(1 + Log[3 - E^x + x]), x] - 18*Defer[Int][(E^(9*(-1 - E^(4*x) + x + x^2)
^2)*x)/(1 + Log[3 - E^x + x]), x] - 108*Defer[Int][(E^(4*x + 9*(-1 - E^(4*x) + x + x^2)^2)*x)/(1 + Log[3 - E^x
+ x]), x] + 54*Defer[Int][(E^(9*(-1 - E^(4*x) + x + x^2)^2)*x^2)/(1 + Log[3 - E^x + x]), x] - 72*Defer[Int][(
E^(4*x + 9*(-1 - E^(4*x) + x + x^2)^2)*x^2)/(1 + Log[3 - E^x + x]), x] + 36*Defer[Int][(E^(9*(-1 - E^(4*x) + x
+ x^2)^2)*x^3)/(1 + Log[3 - E^x + x]), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^{9 \left (-1-e^{4 x}+x+x^2\right )^2} \left (-55-72 e^{8 x} \left (-3+e^x-x\right )-72 x+144 x^2+162 x^3+36 x^4+18 e^{4 x} \left (-3+e^x-x\right ) \left (-3+6 x+4 x^2\right )-e^x \left (-19-18 x+54 x^2+36 x^3\right )-18 \left (3+4 e^{8 x} \left (-3+e^x-x\right )+4 x-8 x^2-9 x^3-2 x^4-e^{4 x} \left (-3+e^x-x\right ) \left (-3+6 x+4 x^2\right )+e^x \left (-1-x+3 x^2+2 x^3\right )\right ) \log \left (3-e^x+x\right )\right )}{\left (3-e^x+x\right ) \left (1+\log \left (3-e^x+x\right )\right )^2} \, dx\\ &=\int \left (\frac {e^{9 \left (-1-e^{4 x}+x+x^2\right )^2} (2+x)}{\left (3-e^x+x\right ) \left (1+\log \left (3-e^x+x\right )\right )^2}+\frac {72 e^{8 x+9 \left (-1-e^{4 x}+x+x^2\right )^2}}{1+\log \left (3-e^x+x\right )}-\frac {18 e^{4 x+9 \left (-1-e^{4 x}+x+x^2\right )^2} \left (-3+6 x+4 x^2\right )}{1+\log \left (3-e^x+x\right )}+\frac {e^{9 \left (-1-e^{4 x}+x+x^2\right )^2} \left (-19-18 x+54 x^2+36 x^3-18 \log \left (3-e^x+x\right )-18 x \log \left (3-e^x+x\right )+54 x^2 \log \left (3-e^x+x\right )+36 x^3 \log \left (3-e^x+x\right )\right )}{\left (1+\log \left (3-e^x+x\right )\right )^2}\right ) \, dx\\ &=-\left (18 \int \frac {e^{4 x+9 \left (-1-e^{4 x}+x+x^2\right )^2} \left (-3+6 x+4 x^2\right )}{1+\log \left (3-e^x+x\right )} \, dx\right )+72 \int \frac {e^{8 x+9 \left (-1-e^{4 x}+x+x^2\right )^2}}{1+\log \left (3-e^x+x\right )} \, dx+\int \frac {e^{9 \left (-1-e^{4 x}+x+x^2\right )^2} (2+x)}{\left (3-e^x+x\right ) \left (1+\log \left (3-e^x+x\right )\right )^2} \, dx+\int \frac {e^{9 \left (-1-e^{4 x}+x+x^2\right )^2} \left (-19-18 x+54 x^2+36 x^3-18 \log \left (3-e^x+x\right )-18 x \log \left (3-e^x+x\right )+54 x^2 \log \left (3-e^x+x\right )+36 x^3 \log \left (3-e^x+x\right )\right )}{\left (1+\log \left (3-e^x+x\right )\right )^2} \, dx\\ &=-\left (18 \int \left (-\frac {3 e^{4 x+9 \left (-1-e^{4 x}+x+x^2\right )^2}}{1+\log \left (3-e^x+x\right )}+\frac {6 e^{4 x+9 \left (-1-e^{4 x}+x+x^2\right )^2} x}{1+\log \left (3-e^x+x\right )}+\frac {4 e^{4 x+9 \left (-1-e^{4 x}+x+x^2\right )^2} x^2}{1+\log \left (3-e^x+x\right )}\right ) \, dx\right )+72 \int \frac {e^{8 x+9 \left (-1-e^{4 x}+x+x^2\right )^2}}{1+\log \left (3-e^x+x\right )} \, dx+\int \frac {e^{9 \left (-1-e^{4 x}+x+x^2\right )^2} \left (-19-18 x+54 x^2+36 x^3+18 \left (-1-x+3 x^2+2 x^3\right ) \log \left (3-e^x+x\right )\right )}{\left (1+\log \left (3-e^x+x\right )\right )^2} \, dx+\int \left (-\frac {2 e^{9 \left (-1-e^{4 x}+x+x^2\right )^2}}{\left (-3+e^x-x\right ) \left (1+\log \left (3-e^x+x\right )\right )^2}-\frac {e^{9 \left (-1-e^{4 x}+x+x^2\right )^2} x}{\left (-3+e^x-x\right ) \left (1+\log \left (3-e^x+x\right )\right )^2}\right ) \, dx\\ &=-\left (2 \int \frac {e^{9 \left (-1-e^{4 x}+x+x^2\right )^2}}{\left (-3+e^x-x\right ) \left (1+\log \left (3-e^x+x\right )\right )^2} \, dx\right )+54 \int \frac {e^{4 x+9 \left (-1-e^{4 x}+x+x^2\right )^2}}{1+\log \left (3-e^x+x\right )} \, dx+72 \int \frac {e^{8 x+9 \left (-1-e^{4 x}+x+x^2\right )^2}}{1+\log \left (3-e^x+x\right )} \, dx-72 \int \frac {e^{4 x+9 \left (-1-e^{4 x}+x+x^2\right )^2} x^2}{1+\log \left (3-e^x+x\right )} \, dx-108 \int \frac {e^{4 x+9 \left (-1-e^{4 x}+x+x^2\right )^2} x}{1+\log \left (3-e^x+x\right )} \, dx-\int \frac {e^{9 \left (-1-e^{4 x}+x+x^2\right )^2} x}{\left (-3+e^x-x\right ) \left (1+\log \left (3-e^x+x\right )\right )^2} \, dx+\int \left (-\frac {e^{9 \left (-1-e^{4 x}+x+x^2\right )^2}}{\left (1+\log \left (3-e^x+x\right )\right )^2}+\frac {18 e^{9 \left (-1-e^{4 x}+x+x^2\right )^2} \left (-1-x+3 x^2+2 x^3\right )}{1+\log \left (3-e^x+x\right )}\right ) \, dx\\ &=-\left (2 \int \frac {e^{9 \left (-1-e^{4 x}+x+x^2\right )^2}}{\left (-3+e^x-x\right ) \left (1+\log \left (3-e^x+x\right )\right )^2} \, dx\right )+18 \int \frac {e^{9 \left (-1-e^{4 x}+x+x^2\right )^2} \left (-1-x+3 x^2+2 x^3\right )}{1+\log \left (3-e^x+x\right )} \, dx+54 \int \frac {e^{4 x+9 \left (-1-e^{4 x}+x+x^2\right )^2}}{1+\log \left (3-e^x+x\right )} \, dx+72 \int \frac {e^{8 x+9 \left (-1-e^{4 x}+x+x^2\right )^2}}{1+\log \left (3-e^x+x\right )} \, dx-72 \int \frac {e^{4 x+9 \left (-1-e^{4 x}+x+x^2\right )^2} x^2}{1+\log \left (3-e^x+x\right )} \, dx-108 \int \frac {e^{4 x+9 \left (-1-e^{4 x}+x+x^2\right )^2} x}{1+\log \left (3-e^x+x\right )} \, dx-\int \frac {e^{9 \left (-1-e^{4 x}+x+x^2\right )^2}}{\left (1+\log \left (3-e^x+x\right )\right )^2} \, dx-\int \frac {e^{9 \left (-1-e^{4 x}+x+x^2\right )^2} x}{\left (-3+e^x-x\right ) \left (1+\log \left (3-e^x+x\right )\right )^2} \, dx\\ &=-\left (2 \int \frac {e^{9 \left (-1-e^{4 x}+x+x^2\right )^2}}{\left (-3+e^x-x\right ) \left (1+\log \left (3-e^x+x\right )\right )^2} \, dx\right )+18 \int \left (\frac {e^{9 \left (-1-e^{4 x}+x+x^2\right )^2}}{-1-\log \left (3-e^x+x\right )}-\frac {e^{9 \left (-1-e^{4 x}+x+x^2\right )^2} x}{1+\log \left (3-e^x+x\right )}+\frac {3 e^{9 \left (-1-e^{4 x}+x+x^2\right )^2} x^2}{1+\log \left (3-e^x+x\right )}+\frac {2 e^{9 \left (-1-e^{4 x}+x+x^2\right )^2} x^3}{1+\log \left (3-e^x+x\right )}\right ) \, dx+54 \int \frac {e^{4 x+9 \left (-1-e^{4 x}+x+x^2\right )^2}}{1+\log \left (3-e^x+x\right )} \, dx+72 \int \frac {e^{8 x+9 \left (-1-e^{4 x}+x+x^2\right )^2}}{1+\log \left (3-e^x+x\right )} \, dx-72 \int \frac {e^{4 x+9 \left (-1-e^{4 x}+x+x^2\right )^2} x^2}{1+\log \left (3-e^x+x\right )} \, dx-108 \int \frac {e^{4 x+9 \left (-1-e^{4 x}+x+x^2\right )^2} x}{1+\log \left (3-e^x+x\right )} \, dx-\int \frac {e^{9 \left (-1-e^{4 x}+x+x^2\right )^2}}{\left (1+\log \left (3-e^x+x\right )\right )^2} \, dx-\int \frac {e^{9 \left (-1-e^{4 x}+x+x^2\right )^2} x}{\left (-3+e^x-x\right ) \left (1+\log \left (3-e^x+x\right )\right )^2} \, dx\\ &=-\left (2 \int \frac {e^{9 \left (-1-e^{4 x}+x+x^2\right )^2}}{\left (-3+e^x-x\right ) \left (1+\log \left (3-e^x+x\right )\right )^2} \, dx\right )+18 \int \frac {e^{9 \left (-1-e^{4 x}+x+x^2\right )^2}}{-1-\log \left (3-e^x+x\right )} \, dx-18 \int \frac {e^{9 \left (-1-e^{4 x}+x+x^2\right )^2} x}{1+\log \left (3-e^x+x\right )} \, dx+36 \int \frac {e^{9 \left (-1-e^{4 x}+x+x^2\right )^2} x^3}{1+\log \left (3-e^x+x\right )} \, dx+54 \int \frac {e^{4 x+9 \left (-1-e^{4 x}+x+x^2\right )^2}}{1+\log \left (3-e^x+x\right )} \, dx+54 \int \frac {e^{9 \left (-1-e^{4 x}+x+x^2\right )^2} x^2}{1+\log \left (3-e^x+x\right )} \, dx+72 \int \frac {e^{8 x+9 \left (-1-e^{4 x}+x+x^2\right )^2}}{1+\log \left (3-e^x+x\right )} \, dx-72 \int \frac {e^{4 x+9 \left (-1-e^{4 x}+x+x^2\right )^2} x^2}{1+\log \left (3-e^x+x\right )} \, dx-108 \int \frac {e^{4 x+9 \left (-1-e^{4 x}+x+x^2\right )^2} x}{1+\log \left (3-e^x+x\right )} \, dx-\int \frac {e^{9 \left (-1-e^{4 x}+x+x^2\right )^2}}{\left (1+\log \left (3-e^x+x\right )\right )^2} \, dx-\int \frac {e^{9 \left (-1-e^{4 x}+x+x^2\right )^2} x}{\left (-3+e^x-x\right ) \left (1+\log \left (3-e^x+x\right )\right )^2} \, dx\\ \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [A]  time = 0.34, size = 33, normalized size = 0.97 \begin {gather*} \frac {e^{9 \left (-1-e^{4 x}+x+x^2\right )^2}}{1+\log \left (3-e^x+x\right )} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^(9 + 9*E^(8*x) - 18*x - 9*x^2 + 18*x^3 + 9*x^4 + E^(4*x)*(18 - 18*x - 18*x^2))*(55 + E^(8*x)*(-21
6 + 72*E^x - 72*x) + 72*x - 144*x^2 - 162*x^3 - 36*x^4 + E^x*(-19 - 18*x + 54*x^2 + 36*x^3) + E^(4*x)*(-162 +
270*x + 324*x^2 + 72*x^3 + E^x*(54 - 108*x - 72*x^2))) + E^(9 + 9*E^(8*x) - 18*x - 9*x^2 + 18*x^3 + 9*x^4 + E^
(4*x)*(18 - 18*x - 18*x^2))*(54 + E^(8*x)*(-216 + 72*E^x - 72*x) + 72*x - 144*x^2 - 162*x^3 - 36*x^4 + E^x*(-1
8 - 18*x + 54*x^2 + 36*x^3) + E^(4*x)*(-162 + 270*x + 324*x^2 + 72*x^3 + E^x*(54 - 108*x - 72*x^2)))*Log[3 - E
^x + x])/(-3 + E^x - x + (-6 + 2*E^x - 2*x)*Log[3 - E^x + x] + (-3 + E^x - x)*Log[3 - E^x + x]^2),x]

[Out]

E^(9*(-1 - E^(4*x) + x + x^2)^2)/(1 + Log[3 - E^x + x])

________________________________________________________________________________________

fricas [A]  time = 0.56, size = 52, normalized size = 1.53 \begin {gather*} \frac {e^{\left (9 \, x^{4} + 18 \, x^{3} - 9 \, x^{2} - 18 \, {\left (x^{2} + x - 1\right )} e^{\left (4 \, x\right )} - 18 \, x + 9 \, e^{\left (8 \, x\right )} + 9\right )}}{\log \left (x - e^{x} + 3\right ) + 1} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((72*exp(x)-72*x-216)*exp(4*x)^2+((-72*x^2-108*x+54)*exp(x)+72*x^3+324*x^2+270*x-162)*exp(4*x)+(36*
x^3+54*x^2-18*x-18)*exp(x)-36*x^4-162*x^3-144*x^2+72*x+54)*exp(9*exp(4*x)^2+(-18*x^2-18*x+18)*exp(4*x)+9*x^4+1
8*x^3-9*x^2-18*x+9)*log(-exp(x)+3+x)+((72*exp(x)-72*x-216)*exp(4*x)^2+((-72*x^2-108*x+54)*exp(x)+72*x^3+324*x^
2+270*x-162)*exp(4*x)+(36*x^3+54*x^2-18*x-19)*exp(x)-36*x^4-162*x^3-144*x^2+72*x+55)*exp(9*exp(4*x)^2+(-18*x^2
-18*x+18)*exp(4*x)+9*x^4+18*x^3-9*x^2-18*x+9))/((exp(x)-3-x)*log(-exp(x)+3+x)^2+(2*exp(x)-2*x-6)*log(-exp(x)+3
+x)+exp(x)-3-x),x, algorithm="fricas")

[Out]

e^(9*x^4 + 18*x^3 - 9*x^2 - 18*(x^2 + x - 1)*e^(4*x) - 18*x + 9*e^(8*x) + 9)/(log(x - e^x + 3) + 1)

________________________________________________________________________________________

giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {18 \, {\left (2 \, x^{4} + 9 \, x^{3} + 8 \, x^{2} + 4 \, {\left (x - e^{x} + 3\right )} e^{\left (8 \, x\right )} - {\left (4 \, x^{3} + 18 \, x^{2} - {\left (4 \, x^{2} + 6 \, x - 3\right )} e^{x} + 15 \, x - 9\right )} e^{\left (4 \, x\right )} - {\left (2 \, x^{3} + 3 \, x^{2} - x - 1\right )} e^{x} - 4 \, x - 3\right )} e^{\left (9 \, x^{4} + 18 \, x^{3} - 9 \, x^{2} - 18 \, {\left (x^{2} + x - 1\right )} e^{\left (4 \, x\right )} - 18 \, x + 9 \, e^{\left (8 \, x\right )} + 9\right )} \log \left (x - e^{x} + 3\right ) + {\left (36 \, x^{4} + 162 \, x^{3} + 144 \, x^{2} + 72 \, {\left (x - e^{x} + 3\right )} e^{\left (8 \, x\right )} - 18 \, {\left (4 \, x^{3} + 18 \, x^{2} - {\left (4 \, x^{2} + 6 \, x - 3\right )} e^{x} + 15 \, x - 9\right )} e^{\left (4 \, x\right )} - {\left (36 \, x^{3} + 54 \, x^{2} - 18 \, x - 19\right )} e^{x} - 72 \, x - 55\right )} e^{\left (9 \, x^{4} + 18 \, x^{3} - 9 \, x^{2} - 18 \, {\left (x^{2} + x - 1\right )} e^{\left (4 \, x\right )} - 18 \, x + 9 \, e^{\left (8 \, x\right )} + 9\right )}}{{\left (x - e^{x} + 3\right )} \log \left (x - e^{x} + 3\right )^{2} + 2 \, {\left (x - e^{x} + 3\right )} \log \left (x - e^{x} + 3\right ) + x - e^{x} + 3}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((72*exp(x)-72*x-216)*exp(4*x)^2+((-72*x^2-108*x+54)*exp(x)+72*x^3+324*x^2+270*x-162)*exp(4*x)+(36*
x^3+54*x^2-18*x-18)*exp(x)-36*x^4-162*x^3-144*x^2+72*x+54)*exp(9*exp(4*x)^2+(-18*x^2-18*x+18)*exp(4*x)+9*x^4+1
8*x^3-9*x^2-18*x+9)*log(-exp(x)+3+x)+((72*exp(x)-72*x-216)*exp(4*x)^2+((-72*x^2-108*x+54)*exp(x)+72*x^3+324*x^
2+270*x-162)*exp(4*x)+(36*x^3+54*x^2-18*x-19)*exp(x)-36*x^4-162*x^3-144*x^2+72*x+55)*exp(9*exp(4*x)^2+(-18*x^2
-18*x+18)*exp(4*x)+9*x^4+18*x^3-9*x^2-18*x+9))/((exp(x)-3-x)*log(-exp(x)+3+x)^2+(2*exp(x)-2*x-6)*log(-exp(x)+3
+x)+exp(x)-3-x),x, algorithm="giac")

[Out]

integrate((18*(2*x^4 + 9*x^3 + 8*x^2 + 4*(x - e^x + 3)*e^(8*x) - (4*x^3 + 18*x^2 - (4*x^2 + 6*x - 3)*e^x + 15*
x - 9)*e^(4*x) - (2*x^3 + 3*x^2 - x - 1)*e^x - 4*x - 3)*e^(9*x^4 + 18*x^3 - 9*x^2 - 18*(x^2 + x - 1)*e^(4*x) -
18*x + 9*e^(8*x) + 9)*log(x - e^x + 3) + (36*x^4 + 162*x^3 + 144*x^2 + 72*(x - e^x + 3)*e^(8*x) - 18*(4*x^3 +
18*x^2 - (4*x^2 + 6*x - 3)*e^x + 15*x - 9)*e^(4*x) - (36*x^3 + 54*x^2 - 18*x - 19)*e^x - 72*x - 55)*e^(9*x^4
+ 18*x^3 - 9*x^2 - 18*(x^2 + x - 1)*e^(4*x) - 18*x + 9*e^(8*x) + 9))/((x - e^x + 3)*log(x - e^x + 3)^2 + 2*(x
- e^x + 3)*log(x - e^x + 3) + x - e^x + 3), x)

________________________________________________________________________________________

maple [A]  time = 0.08, size = 63, normalized size = 1.85

method	result	size
risch	\(\frac {{\mathrm e}^{9 x^{4}-18 x^{2} {\mathrm e}^{4 x}+18 x^{3}-18 x \,{\mathrm e}^{4 x}-9 x^{2}+18 \,{\mathrm e}^{4 x}+9 \,{\mathrm e}^{8 x}-18 x +9}}{1+\ln \left (-{\mathrm e}^{x}+3+x \right )}\)	\(63\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((72*exp(x)-72*x-216)*exp(4*x)^2+((-72*x^2-108*x+54)*exp(x)+72*x^3+324*x^2+270*x-162)*exp(4*x)+(36*x^3+54
*x^2-18*x-18)*exp(x)-36*x^4-162*x^3-144*x^2+72*x+54)*exp(9*exp(4*x)^2+(-18*x^2-18*x+18)*exp(4*x)+9*x^4+18*x^3-
9*x^2-18*x+9)*ln(-exp(x)+3+x)+((72*exp(x)-72*x-216)*exp(4*x)^2+((-72*x^2-108*x+54)*exp(x)+72*x^3+324*x^2+270*x
-162)*exp(4*x)+(36*x^3+54*x^2-18*x-19)*exp(x)-36*x^4-162*x^3-144*x^2+72*x+55)*exp(9*exp(4*x)^2+(-18*x^2-18*x+1
8)*exp(4*x)+9*x^4+18*x^3-9*x^2-18*x+9))/((exp(x)-3-x)*ln(-exp(x)+3+x)^2+(2*exp(x)-2*x-6)*ln(-exp(x)+3+x)+exp(x
)-3-x),x,method=_RETURNVERBOSE)

[Out]

exp(9*x^4-18*x^2*exp(4*x)+18*x^3-18*x*exp(4*x)-9*x^2+18*exp(4*x)+9*exp(8*x)-18*x+9)/(1+ln(-exp(x)+3+x))

________________________________________________________________________________________

maxima [B]  time = 1.23, size = 81, normalized size = 2.38 \begin {gather*} \frac {e^{\left (9 \, x^{4} + 18 \, x^{3} - 18 \, x^{2} e^{\left (4 \, x\right )} + 9 \, e^{\left (8 \, x\right )} + 18 \, e^{\left (4 \, x\right )} + 9\right )}}{e^{\left (9 \, x^{2} + 18 \, x e^{\left (4 \, x\right )} + 18 \, x\right )} \log \left (x - e^{x} + 3\right ) + e^{\left (9 \, x^{2} + 18 \, x e^{\left (4 \, x\right )} + 18 \, x\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((72*exp(x)-72*x-216)*exp(4*x)^2+((-72*x^2-108*x+54)*exp(x)+72*x^3+324*x^2+270*x-162)*exp(4*x)+(36*
x^3+54*x^2-18*x-18)*exp(x)-36*x^4-162*x^3-144*x^2+72*x+54)*exp(9*exp(4*x)^2+(-18*x^2-18*x+18)*exp(4*x)+9*x^4+1
8*x^3-9*x^2-18*x+9)*log(-exp(x)+3+x)+((72*exp(x)-72*x-216)*exp(4*x)^2+((-72*x^2-108*x+54)*exp(x)+72*x^3+324*x^
2+270*x-162)*exp(4*x)+(36*x^3+54*x^2-18*x-19)*exp(x)-36*x^4-162*x^3-144*x^2+72*x+55)*exp(9*exp(4*x)^2+(-18*x^2
-18*x+18)*exp(4*x)+9*x^4+18*x^3-9*x^2-18*x+9))/((exp(x)-3-x)*log(-exp(x)+3+x)^2+(2*exp(x)-2*x-6)*log(-exp(x)+3
+x)+exp(x)-3-x),x, algorithm="maxima")

[Out]

e^(9*x^4 + 18*x^3 - 18*x^2*e^(4*x) + 9*e^(8*x) + 18*e^(4*x) + 9)/(e^(9*x^2 + 18*x*e^(4*x) + 18*x)*log(x - e^x
+ 3) + e^(9*x^2 + 18*x*e^(4*x) + 18*x))

________________________________________________________________________________________

mupad [B]  time = 1.18, size = 69, normalized size = 2.03 \begin {gather*} \frac {{\mathrm {e}}^{9\,{\mathrm {e}}^{8\,x}}\,{\mathrm {e}}^{18\,{\mathrm {e}}^{4\,x}}\,{\mathrm {e}}^{-18\,x}\,{\mathrm {e}}^9\,{\mathrm {e}}^{-18\,x\,{\mathrm {e}}^{4\,x}}\,{\mathrm {e}}^{-9\,x^2}\,{\mathrm {e}}^{9\,x^4}\,{\mathrm {e}}^{18\,x^3}\,{\mathrm {e}}^{-18\,x^2\,{\mathrm {e}}^{4\,x}}}{\ln \left (x-{\mathrm {e}}^x+3\right )+1} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(9*exp(8*x) - 18*x - exp(4*x)*(18*x + 18*x^2 - 18) - 9*x^2 + 18*x^3 + 9*x^4 + 9)*(exp(8*x)*(72*x - 72*
exp(x) + 216) - 72*x + 144*x^2 + 162*x^3 + 36*x^4 + exp(x)*(18*x - 54*x^2 - 36*x^3 + 19) - exp(4*x)*(270*x - e
xp(x)*(108*x + 72*x^2 - 54) + 324*x^2 + 72*x^3 - 162) - 55) + exp(9*exp(8*x) - 18*x - exp(4*x)*(18*x + 18*x^2
- 18) - 9*x^2 + 18*x^3 + 9*x^4 + 9)*log(x - exp(x) + 3)*(exp(8*x)*(72*x - 72*exp(x) + 216) - 72*x + 144*x^2 +
162*x^3 + 36*x^4 + exp(x)*(18*x - 54*x^2 - 36*x^3 + 18) - exp(4*x)*(270*x - exp(x)*(108*x + 72*x^2 - 54) + 324
*x^2 + 72*x^3 - 162) - 54))/(x - exp(x) + log(x - exp(x) + 3)*(2*x - 2*exp(x) + 6) + log(x - exp(x) + 3)^2*(x
- exp(x) + 3) + 3),x)

[Out]

(exp(9*exp(8*x))*exp(18*exp(4*x))*exp(-18*x)*exp(9)*exp(-18*x*exp(4*x))*exp(-9*x^2)*exp(9*x^4)*exp(18*x^3)*exp
(-18*x^2*exp(4*x)))/(log(x - exp(x) + 3) + 1)

________________________________________________________________________________________

sympy [A]  time = 2.31, size = 53, normalized size = 1.56 \begin {gather*} \frac {e^{9 x^{4} + 18 x^{3} - 9 x^{2} - 18 x + \left (- 18 x^{2} - 18 x + 18\right ) e^{4 x} + 9 e^{8 x} + 9}}{\log {\left (x - e^{x} + 3 \right )} + 1} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((72*exp(x)-72*x-216)*exp(4*x)**2+((-72*x**2-108*x+54)*exp(x)+72*x**3+324*x**2+270*x-162)*exp(4*x)+
(36*x**3+54*x**2-18*x-18)*exp(x)-36*x**4-162*x**3-144*x**2+72*x+54)*exp(9*exp(4*x)**2+(-18*x**2-18*x+18)*exp(4
*x)+9*x**4+18*x**3-9*x**2-18*x+9)*ln(-exp(x)+3+x)+((72*exp(x)-72*x-216)*exp(4*x)**2+((-72*x**2-108*x+54)*exp(x
)+72*x**3+324*x**2+270*x-162)*exp(4*x)+(36*x**3+54*x**2-18*x-19)*exp(x)-36*x**4-162*x**3-144*x**2+72*x+55)*exp
(9*exp(4*x)**2+(-18*x**2-18*x+18)*exp(4*x)+9*x**4+18*x**3-9*x**2-18*x+9))/((exp(x)-3-x)*ln(-exp(x)+3+x)**2+(2*
exp(x)-2*x-6)*ln(-exp(x)+3+x)+exp(x)-3-x),x)

[Out]

exp(9*x**4 + 18*x**3 - 9*x**2 - 18*x + (-18*x**2 - 18*x + 18)*exp(4*x) + 9*exp(8*x) + 9)/(log(x - exp(x) + 3)
+ 1)

________________________________________________________________________________________