3.44.86 \(\int \frac {e^{-2+\frac {e^{4 x}+4 e^{3 x} x^2-9 e^2 x^3+6 e^{2 x} x^4+4 e^x x^6+x^8}{9 e^2 x^2}} (18 x^8+6 x^9+e^{4 x} (-6+10 x+4 x^2)+e^2 (-36 x^3-9 x^4)+e^{3 x} (36 x^3+12 x^4)+e^{2 x} (36 x^4+48 x^5+12 x^6)+e^x (48 x^6+28 x^7+4 x^8))}{243 x^3+162 x^4+27 x^5} \, dx\)

Optimal. Leaf size=34 \[ \frac {e^{-x+\frac {\left (e^x+x^2\right )^4}{9 e^2 x^2}}}{3 (3+x)} \]

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Rubi [F]  time = 19.62, 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 (-2+\frac {e^{4 x}+4 e^{3 x} x^2-9 e^2 x^3+6 e^{2 x} x^4+4 e^x x^6+x^8}{9 e^2 x^2}\right ) \left (18 x^8+6 x^9+e^{4 x} \left (-6+10 x+4 x^2\right )+e^2 \left (-36 x^3-9 x^4\right )+e^{3 x} \left (36 x^3+12 x^4\right )+e^{2 x} \left (36 x^4+48 x^5+12 x^6\right )+e^x \left (48 x^6+28 x^7+4 x^8\right )\right )}{243 x^3+162 x^4+27 x^5} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^(-2 + (E^(4*x) + 4*E^(3*x)*x^2 - 9*E^2*x^3 + 6*E^(2*x)*x^4 + 4*E^x*x^6 + x^8)/(9*E^2*x^2))*(18*x^8 + 6*
x^9 + E^(4*x)*(-6 + 10*x + 4*x^2) + E^2*(-36*x^3 - 9*x^4) + E^(3*x)*(36*x^3 + 12*x^4) + E^(2*x)*(36*x^4 + 48*x
^5 + 12*x^6) + E^x*(48*x^6 + 28*x^7 + 4*x^8)))/(243*x^3 + 162*x^4 + 27*x^5),x]

[Out]

(4*Defer[Int][E^(-1/9*(-E^(4*x) + 18*E^2*x^2 - 4*E^(3*x)*x^2 - 6*E^(2*x)*x^4 - 4*E^x*x^6 - x^8)/(E^2*x^2)), x]
)/3 + 18*Defer[Int][E^(-2 + (E^(4*x) + 4*E^(3*x)*x^2 - 9*E^2*x^3 + 6*E^(2*x)*x^4 + 4*E^x*x^6 + x^8)/(9*E^2*x^2
)), x] - (8*Defer[Int][E^(-2 + 2*x + (E^(4*x) + 4*E^(3*x)*x^2 - 9*E^2*x^3 + 6*E^(2*x)*x^4 + 4*E^x*x^6 + x^8)/(
9*E^2*x^2)), x])/9 - (2*Defer[Int][E^(-2 + 4*x + (E^(4*x) + 4*E^(3*x)*x^2 - 9*E^2*x^3 + 6*E^(2*x)*x^4 + 4*E^x*
x^6 + x^8)/(9*E^2*x^2))/x^3, x])/81 + (14*Defer[Int][E^(-2 + 4*x + (E^(4*x) + 4*E^(3*x)*x^2 - 9*E^2*x^3 + 6*E^
(2*x)*x^4 + 4*E^x*x^6 + x^8)/(9*E^2*x^2))/x^2, x])/243 - (14*Defer[Int][E^(-2 + 4*x + (E^(4*x) + 4*E^(3*x)*x^2
- 9*E^2*x^3 + 6*E^(2*x)*x^4 + 4*E^x*x^6 + x^8)/(9*E^2*x^2))/x, x])/729 - (4*Defer[Int][x/E^((-E^(4*x) + 18*E^
2*x^2 - 4*E^(3*x)*x^2 - 6*E^(2*x)*x^4 - 4*E^x*x^6 - x^8)/(9*E^2*x^2)), x])/9 - 6*Defer[Int][E^(-2 + (E^(4*x) +
4*E^(3*x)*x^2 - 9*E^2*x^3 + 6*E^(2*x)*x^4 + 4*E^x*x^6 + x^8)/(9*E^2*x^2))*x, x] + (4*Defer[Int][E^(-2 + 2*x +
(E^(4*x) + 4*E^(3*x)*x^2 - 9*E^2*x^3 + 6*E^(2*x)*x^4 + 4*E^x*x^6 + x^8)/(9*E^2*x^2))*x, x])/9 + (4*Defer[Int]
[x^2/E^((-E^(4*x) + 18*E^2*x^2 - 4*E^(3*x)*x^2 - 6*E^(2*x)*x^4 - 4*E^x*x^6 - x^8)/(9*E^2*x^2)), x])/27 + 2*Def
er[Int][E^(-2 + (E^(4*x) + 4*E^(3*x)*x^2 - 9*E^2*x^3 + 6*E^(2*x)*x^4 + 4*E^x*x^6 + x^8)/(9*E^2*x^2))*x^2, x] +
(4*Defer[Int][x^3/E^((-E^(4*x) + 18*E^2*x^2 - 4*E^(3*x)*x^2 - 6*E^(2*x)*x^4 - 4*E^x*x^6 - x^8)/(9*E^2*x^2)),
x])/27 - (2*Defer[Int][E^(-2 + (E^(4*x) + 4*E^(3*x)*x^2 - 9*E^2*x^3 + 6*E^(2*x)*x^4 + 4*E^x*x^6 + x^8)/(9*E^2*
x^2))*x^3, x])/3 + (2*Defer[Int][E^(-2 + (E^(4*x) + 4*E^(3*x)*x^2 - 9*E^2*x^3 + 6*E^(2*x)*x^4 + 4*E^x*x^6 + x^
8)/(9*E^2*x^2))*x^4, x])/9 - Defer[Int][E^((E^(4*x) + 4*E^(3*x)*x^2 - 9*E^2*x^3 + 6*E^(2*x)*x^4 + 4*E^x*x^6 +
x^8)/(9*E^2*x^2))/(3 + x)^2, x]/3 - 4*Defer[Int][1/(E^((-E^(4*x) + 18*E^2*x^2 - 4*E^(3*x)*x^2 - 6*E^(2*x)*x^4
- 4*E^x*x^6 - x^8)/(9*E^2*x^2))*(3 + x)), x] - ((162 + E^2)*Defer[Int][E^(-2 + (E^(4*x) + 4*E^(3*x)*x^2 - 9*E^
2*x^3 + 6*E^(2*x)*x^4 + 4*E^x*x^6 + x^8)/(9*E^2*x^2))/(3 + x), x])/3 + (8*Defer[Int][E^(-2 + 2*x + (E^(4*x) +
4*E^(3*x)*x^2 - 9*E^2*x^3 + 6*E^(2*x)*x^4 + 4*E^x*x^6 + x^8)/(9*E^2*x^2))/(3 + x), x])/3 + (4*Defer[Int][E^(-2
+ 3*x + (E^(4*x) + 4*E^(3*x)*x^2 - 9*E^2*x^3 + 6*E^(2*x)*x^4 + 4*E^x*x^6 + x^8)/(9*E^2*x^2))/(3 + x), x])/9 +
(14*Defer[Int][E^(-2 + 4*x + (E^(4*x) + 4*E^(3*x)*x^2 - 9*E^2*x^3 + 6*E^(2*x)*x^4 + 4*E^x*x^6 + x^8)/(9*E^2*x
^2))/(3 + x), x])/729

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {\exp \left (-2+\frac {e^{4 x}+4 e^{3 x} x^2-9 e^2 x^3+6 e^{2 x} x^4+4 e^x x^6+x^8}{9 e^2 x^2}\right ) \left (18 x^8+6 x^9+e^{4 x} \left (-6+10 x+4 x^2\right )+e^2 \left (-36 x^3-9 x^4\right )+e^{3 x} \left (36 x^3+12 x^4\right )+e^{2 x} \left (36 x^4+48 x^5+12 x^6\right )+e^x \left (48 x^6+28 x^7+4 x^8\right )\right )}{x^3 \left (243+162 x+27 x^2\right )} \, dx\\ &=\int \frac {\exp \left (-2+\frac {e^{4 x}+4 e^{3 x} x^2-9 e^2 x^3+6 e^{2 x} x^4+4 e^x x^6+x^8}{9 e^2 x^2}\right ) \left (18 x^8+6 x^9+e^{4 x} \left (-6+10 x+4 x^2\right )+e^2 \left (-36 x^3-9 x^4\right )+e^{3 x} \left (36 x^3+12 x^4\right )+e^{2 x} \left (36 x^4+48 x^5+12 x^6\right )+e^x \left (48 x^6+28 x^7+4 x^8\right )\right )}{27 x^3 (3+x)^2} \, dx\\ &=\frac {1}{27} \int \frac {\exp \left (-2+\frac {e^{4 x}+4 e^{3 x} x^2-9 e^2 x^3+6 e^{2 x} x^4+4 e^x x^6+x^8}{9 e^2 x^2}\right ) \left (18 x^8+6 x^9+e^{4 x} \left (-6+10 x+4 x^2\right )+e^2 \left (-36 x^3-9 x^4\right )+e^{3 x} \left (36 x^3+12 x^4\right )+e^{2 x} \left (36 x^4+48 x^5+12 x^6\right )+e^x \left (48 x^6+28 x^7+4 x^8\right )\right )}{x^3 (3+x)^2} \, dx\\ &=\frac {1}{27} \int \left (\frac {12 \exp \left (-2+3 x+\frac {e^{4 x}+4 e^{3 x} x^2-9 e^2 x^3+6 e^{2 x} x^4+4 e^x x^6+x^8}{9 e^2 x^2}\right )}{3+x}+\frac {12 \exp \left (-2+2 x+\frac {e^{4 x}+4 e^{3 x} x^2-9 e^2 x^3+6 e^{2 x} x^4+4 e^x x^6+x^8}{9 e^2 x^2}\right ) x (1+x)}{3+x}+\frac {4 \exp \left (-2+x+\frac {e^{4 x}+4 e^{3 x} x^2-9 e^2 x^3+6 e^{2 x} x^4+4 e^x x^6+x^8}{9 e^2 x^2}\right ) x^3 (4+x)}{3+x}+\frac {2 \exp \left (-2+4 x+\frac {e^{4 x}+4 e^{3 x} x^2-9 e^2 x^3+6 e^{2 x} x^4+4 e^x x^6+x^8}{9 e^2 x^2}\right ) (-1+2 x)}{x^3 (3+x)}+\frac {3 \exp \left (-2+\frac {e^{4 x}+4 e^{3 x} x^2-9 e^2 x^3+6 e^{2 x} x^4+4 e^x x^6+x^8}{9 e^2 x^2}\right ) \left (-12 e^2-3 e^2 x+6 x^5+2 x^6\right )}{(3+x)^2}\right ) \, dx\\ &=\frac {2}{27} \int \frac {\exp \left (-2+4 x+\frac {e^{4 x}+4 e^{3 x} x^2-9 e^2 x^3+6 e^{2 x} x^4+4 e^x x^6+x^8}{9 e^2 x^2}\right ) (-1+2 x)}{x^3 (3+x)} \, dx+\frac {1}{9} \int \frac {\exp \left (-2+\frac {e^{4 x}+4 e^{3 x} x^2-9 e^2 x^3+6 e^{2 x} x^4+4 e^x x^6+x^8}{9 e^2 x^2}\right ) \left (-12 e^2-3 e^2 x+6 x^5+2 x^6\right )}{(3+x)^2} \, dx+\frac {4}{27} \int \frac {\exp \left (-2+x+\frac {e^{4 x}+4 e^{3 x} x^2-9 e^2 x^3+6 e^{2 x} x^4+4 e^x x^6+x^8}{9 e^2 x^2}\right ) x^3 (4+x)}{3+x} \, dx+\frac {4}{9} \int \frac {\exp \left (-2+3 x+\frac {e^{4 x}+4 e^{3 x} x^2-9 e^2 x^3+6 e^{2 x} x^4+4 e^x x^6+x^8}{9 e^2 x^2}\right )}{3+x} \, dx+\frac {4}{9} \int \frac {\exp \left (-2+2 x+\frac {e^{4 x}+4 e^{3 x} x^2-9 e^2 x^3+6 e^{2 x} x^4+4 e^x x^6+x^8}{9 e^2 x^2}\right ) x (1+x)}{3+x} \, dx\\ &=\frac {2}{27} \int \left (-\frac {e^{-2+4 x+\frac {e^{4 x}+4 e^{3 x} x^2-9 e^2 x^3+6 e^{2 x} x^4+4 e^x x^6+x^8}{9 e^2 x^2}}}{3 x^3}+\frac {7 e^{-2+4 x+\frac {e^{4 x}+4 e^{3 x} x^2-9 e^2 x^3+6 e^{2 x} x^4+4 e^x x^6+x^8}{9 e^2 x^2}}}{9 x^2}-\frac {7 e^{-2+4 x+\frac {e^{4 x}+4 e^{3 x} x^2-9 e^2 x^3+6 e^{2 x} x^4+4 e^x x^6+x^8}{9 e^2 x^2}}}{27 x}+\frac {7 e^{-2+4 x+\frac {e^{4 x}+4 e^{3 x} x^2-9 e^2 x^3+6 e^{2 x} x^4+4 e^x x^6+x^8}{9 e^2 x^2}}}{27 (3+x)}\right ) \, dx+\frac {1}{9} \int \left (162 e^{-2+\frac {e^{4 x}+4 e^{3 x} x^2-9 e^2 x^3+6 e^{2 x} x^4+4 e^x x^6+x^8}{9 e^2 x^2}}-54 e^{-2+\frac {e^{4 x}+4 e^{3 x} x^2-9 e^2 x^3+6 e^{2 x} x^4+4 e^x x^6+x^8}{9 e^2 x^2}} x+18 e^{-2+\frac {e^{4 x}+4 e^{3 x} x^2-9 e^2 x^3+6 e^{2 x} x^4+4 e^x x^6+x^8}{9 e^2 x^2}} x^2-6 e^{-2+\frac {e^{4 x}+4 e^{3 x} x^2-9 e^2 x^3+6 e^{2 x} x^4+4 e^x x^6+x^8}{9 e^2 x^2}} x^3+2 e^{-2+\frac {e^{4 x}+4 e^{3 x} x^2-9 e^2 x^3+6 e^{2 x} x^4+4 e^x x^6+x^8}{9 e^2 x^2}} x^4-\frac {3 e^{\frac {e^{4 x}+4 e^{3 x} x^2-9 e^2 x^3+6 e^{2 x} x^4+4 e^x x^6+x^8}{9 e^2 x^2}}}{(3+x)^2}-\frac {3 e^{-2+\frac {e^{4 x}+4 e^{3 x} x^2-9 e^2 x^3+6 e^{2 x} x^4+4 e^x x^6+x^8}{9 e^2 x^2}} \left (162+e^2\right )}{3+x}\right ) \, dx+\frac {4}{27} \int \frac {e^{-\frac {-e^{4 x}+18 e^2 x^2-4 e^{3 x} x^2-6 e^{2 x} x^4-4 e^x x^6-x^8}{9 e^2 x^2}} x^3 (4+x)}{3+x} \, dx+\frac {4}{9} \int \frac {e^{-2+3 x+\frac {e^{4 x}+4 e^{3 x} x^2-9 e^2 x^3+6 e^{2 x} x^4+4 e^x x^6+x^8}{9 e^2 x^2}}}{3+x} \, dx+\frac {4}{9} \int \left (-2 e^{-2+2 x+\frac {e^{4 x}+4 e^{3 x} x^2-9 e^2 x^3+6 e^{2 x} x^4+4 e^x x^6+x^8}{9 e^2 x^2}}+e^{-2+2 x+\frac {e^{4 x}+4 e^{3 x} x^2-9 e^2 x^3+6 e^{2 x} x^4+4 e^x x^6+x^8}{9 e^2 x^2}} x+\frac {6 e^{-2+2 x+\frac {e^{4 x}+4 e^{3 x} x^2-9 e^2 x^3+6 e^{2 x} x^4+4 e^x x^6+x^8}{9 e^2 x^2}}}{3+x}\right ) \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.19, size = 66, normalized size = 1.94 \begin {gather*} \frac {e^{\frac {e^{4 x}+4 e^{3 x} x^2-9 e^2 x^3+6 e^{2 x} x^4+4 e^x x^6+x^8}{9 e^2 x^2}}}{3 (3+x)} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^(-2 + (E^(4*x) + 4*E^(3*x)*x^2 - 9*E^2*x^3 + 6*E^(2*x)*x^4 + 4*E^x*x^6 + x^8)/(9*E^2*x^2))*(18*x^
8 + 6*x^9 + E^(4*x)*(-6 + 10*x + 4*x^2) + E^2*(-36*x^3 - 9*x^4) + E^(3*x)*(36*x^3 + 12*x^4) + E^(2*x)*(36*x^4
+ 48*x^5 + 12*x^6) + E^x*(48*x^6 + 28*x^7 + 4*x^8)))/(243*x^3 + 162*x^4 + 27*x^5),x]

[Out]

E^((E^(4*x) + 4*E^(3*x)*x^2 - 9*E^2*x^3 + 6*E^(2*x)*x^4 + 4*E^x*x^6 + x^8)/(9*E^2*x^2))/(3*(3 + x))

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fricas [B]  time = 0.71, size = 63, normalized size = 1.85 \begin {gather*} \frac {e^{\left (\frac {{\left (x^{8} + 4 \, x^{6} e^{x} + 6 \, x^{4} e^{\left (2 \, x\right )} + 4 \, x^{2} e^{\left (3 \, x\right )} - 9 \, {\left (x^{3} + 2 \, x^{2}\right )} e^{2} + e^{\left (4 \, x\right )}\right )} e^{\left (-2\right )}}{9 \, x^{2}} + 2\right )}}{3 \, {\left (x + 3\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*x^2+10*x-6)*exp(x)^4+(12*x^4+36*x^3)*exp(x)^3+(12*x^6+48*x^5+36*x^4)*exp(x)^2+(4*x^8+28*x^7+48*x
^6)*exp(x)+(-9*x^4-36*x^3)*exp(1)^2+6*x^9+18*x^8)*exp(1/9*(exp(x)^4+4*x^2*exp(x)^3+6*exp(x)^2*x^4+4*x^6*exp(x)
-9*x^3*exp(1)^2+x^8)/x^2/exp(1)^2)/(27*x^5+162*x^4+243*x^3)/exp(1)^2,x, algorithm="fricas")

[Out]

1/3*e^(1/9*(x^8 + 4*x^6*e^x + 6*x^4*e^(2*x) + 4*x^2*e^(3*x) - 9*(x^3 + 2*x^2)*e^2 + e^(4*x))*e^(-2)/x^2 + 2)/(
x + 3)

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {{\left (6 \, x^{9} + 18 \, x^{8} - 9 \, {\left (x^{4} + 4 \, x^{3}\right )} e^{2} + 2 \, {\left (2 \, x^{2} + 5 \, x - 3\right )} e^{\left (4 \, x\right )} + 12 \, {\left (x^{4} + 3 \, x^{3}\right )} e^{\left (3 \, x\right )} + 12 \, {\left (x^{6} + 4 \, x^{5} + 3 \, x^{4}\right )} e^{\left (2 \, x\right )} + 4 \, {\left (x^{8} + 7 \, x^{7} + 12 \, x^{6}\right )} e^{x}\right )} e^{\left (\frac {{\left (x^{8} + 4 \, x^{6} e^{x} + 6 \, x^{4} e^{\left (2 \, x\right )} - 9 \, x^{3} e^{2} + 4 \, x^{2} e^{\left (3 \, x\right )} + e^{\left (4 \, x\right )}\right )} e^{\left (-2\right )}}{9 \, x^{2}} - 2\right )}}{27 \, {\left (x^{5} + 6 \, x^{4} + 9 \, x^{3}\right )}}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*x^2+10*x-6)*exp(x)^4+(12*x^4+36*x^3)*exp(x)^3+(12*x^6+48*x^5+36*x^4)*exp(x)^2+(4*x^8+28*x^7+48*x
^6)*exp(x)+(-9*x^4-36*x^3)*exp(1)^2+6*x^9+18*x^8)*exp(1/9*(exp(x)^4+4*x^2*exp(x)^3+6*exp(x)^2*x^4+4*x^6*exp(x)
-9*x^3*exp(1)^2+x^8)/x^2/exp(1)^2)/(27*x^5+162*x^4+243*x^3)/exp(1)^2,x, algorithm="giac")

[Out]

integrate(1/27*(6*x^9 + 18*x^8 - 9*(x^4 + 4*x^3)*e^2 + 2*(2*x^2 + 5*x - 3)*e^(4*x) + 12*(x^4 + 3*x^3)*e^(3*x)
+ 12*(x^6 + 4*x^5 + 3*x^4)*e^(2*x) + 4*(x^8 + 7*x^7 + 12*x^6)*e^x)*e^(1/9*(x^8 + 4*x^6*e^x + 6*x^4*e^(2*x) - 9
*x^3*e^2 + 4*x^2*e^(3*x) + e^(4*x))*e^(-2)/x^2 - 2)/(x^5 + 6*x^4 + 9*x^3), x)

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maple [B]  time = 0.14, size = 60, normalized size = 1.76

method	result	size
risch	\(\frac {{\mathrm e}^{-\frac {\left (-x^{8}-4 x^{6} {\mathrm e}^{x}-6 \,{\mathrm e}^{2 x} x^{4}+9 x^{3} {\mathrm e}^{2}-4 x^{2} {\mathrm e}^{3 x}-{\mathrm e}^{4 x}\right ) {\mathrm e}^{-2}}{9 x^{2}}}}{3 x +9}\)	\(60\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((4*x^2+10*x-6)*exp(x)^4+(12*x^4+36*x^3)*exp(x)^3+(12*x^6+48*x^5+36*x^4)*exp(x)^2+(4*x^8+28*x^7+48*x^6)*ex
p(x)+(-9*x^4-36*x^3)*exp(1)^2+6*x^9+18*x^8)*exp(1/9*(exp(x)^4+4*x^2*exp(x)^3+6*exp(x)^2*x^4+4*x^6*exp(x)-9*x^3
*exp(1)^2+x^8)/x^2/exp(1)^2)/(27*x^5+162*x^4+243*x^3)/exp(1)^2,x,method=_RETURNVERBOSE)

[Out]

1/3/(3+x)*exp(-1/9*(-x^8-4*x^6*exp(x)-6*exp(2*x)*x^4+9*x^3*exp(2)-4*x^2*exp(3*x)-exp(4*x))*exp(-2)/x^2)

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maxima [B]  time = 1.69, size = 58, normalized size = 1.71 \begin {gather*} \frac {e^{\left (\frac {1}{9} \, x^{6} e^{\left (-2\right )} + \frac {4}{9} \, x^{4} e^{\left (x - 2\right )} + \frac {2}{3} \, x^{2} e^{\left (2 \, x - 2\right )} - x + \frac {e^{\left (4 \, x - 2\right )}}{9 \, x^{2}} + \frac {4}{9} \, e^{\left (3 \, x - 2\right )}\right )}}{3 \, {\left (x + 3\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*x^2+10*x-6)*exp(x)^4+(12*x^4+36*x^3)*exp(x)^3+(12*x^6+48*x^5+36*x^4)*exp(x)^2+(4*x^8+28*x^7+48*x
^6)*exp(x)+(-9*x^4-36*x^3)*exp(1)^2+6*x^9+18*x^8)*exp(1/9*(exp(x)^4+4*x^2*exp(x)^3+6*exp(x)^2*x^4+4*x^6*exp(x)
-9*x^3*exp(1)^2+x^8)/x^2/exp(1)^2)/(27*x^5+162*x^4+243*x^3)/exp(1)^2,x, algorithm="maxima")

[Out]

1/3*e^(1/9*x^6*e^(-2) + 4/9*x^4*e^(x - 2) + 2/3*x^2*e^(2*x - 2) - x + 1/9*e^(4*x - 2)/x^2 + 4/9*e^(3*x - 2))/(
x + 3)

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mupad [B]  time = 3.62, size = 56, normalized size = 1.65 \begin {gather*} \frac {{\mathrm {e}}^{\frac {{\mathrm {e}}^{-2}\,\left ({\mathrm {e}}^{4\,x}+4\,x^6\,{\mathrm {e}}^x+4\,x^2\,{\mathrm {e}}^{3\,x}+6\,x^4\,{\mathrm {e}}^{2\,x}-9\,x^3\,{\mathrm {e}}^2+x^8\right )}{9\,x^2}}}{3\,\left (x+3\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(-2)*exp((exp(-2)*(exp(4*x)/9 + (4*x^6*exp(x))/9 + (4*x^2*exp(3*x))/9 + (2*x^4*exp(2*x))/3 - x^3*exp(2
) + x^8/9))/x^2)*(exp(4*x)*(10*x + 4*x^2 - 6) + exp(x)*(48*x^6 + 28*x^7 + 4*x^8) + exp(3*x)*(36*x^3 + 12*x^4)
- exp(2)*(36*x^3 + 9*x^4) + exp(2*x)*(36*x^4 + 48*x^5 + 12*x^6) + 18*x^8 + 6*x^9))/(243*x^3 + 162*x^4 + 27*x^5
),x)

[Out]

exp((exp(-2)*(exp(4*x) + 4*x^6*exp(x) + 4*x^2*exp(3*x) + 6*x^4*exp(2*x) - 9*x^3*exp(2) + x^8))/(9*x^2))/(3*(x
+ 3))

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sympy [B]  time = 0.49, size = 65, normalized size = 1.91 \begin {gather*} \frac {e^{\frac {\frac {x^{8}}{9} + \frac {4 x^{6} e^{x}}{9} + \frac {2 x^{4} e^{2 x}}{3} - x^{3} e^{2} + \frac {4 x^{2} e^{3 x}}{9} + \frac {e^{4 x}}{9}}{x^{2} e^{2}}}}{3 x + 9} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*x**2+10*x-6)*exp(x)**4+(12*x**4+36*x**3)*exp(x)**3+(12*x**6+48*x**5+36*x**4)*exp(x)**2+(4*x**8+2
8*x**7+48*x**6)*exp(x)+(-9*x**4-36*x**3)*exp(1)**2+6*x**9+18*x**8)*exp(1/9*(exp(x)**4+4*x**2*exp(x)**3+6*exp(x
)**2*x**4+4*x**6*exp(x)-9*x**3*exp(1)**2+x**8)/x**2/exp(1)**2)/(27*x**5+162*x**4+243*x**3)/exp(1)**2,x)

[Out]

exp((x**8/9 + 4*x**6*exp(x)/9 + 2*x**4*exp(2*x)/3 - x**3*exp(2) + 4*x**2*exp(3*x)/9 + exp(4*x)/9)*exp(-2)/x**2
)/(3*x + 9)

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