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3.46.60 \(\int \frac {15 x^2+e^{\frac {2 e^{6-x}}{3 x}} (27+12 x+3 x^2)+e^{\frac {e^{6-x}}{3 x}} (-30 x+e^{6-x} (4+8 x+5 x^2+x^3))}{12 x^2+12 x^3+3 x^4+e^{\frac {2 e^{6-x}}{3 x}} (12+12 x+3 x^2)+e^{\frac {e^{6-x}}{3 x}} (-24 x-24 x^2-6 x^3)} \, dx\)

Optimal. Leaf size=34 \[ 5-\frac {5}{2+x}+\frac {x}{1-e^{-\frac {e^{6-x}}{3 x}} x} \]

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Rubi [F]  time = 4.89, 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 {15 x^2+e^{\frac {2 e^{6-x}}{3 x}} \left (27+12 x+3 x^2\right )+e^{\frac {e^{6-x}}{3 x}} \left (-30 x+e^{6-x} \left (4+8 x+5 x^2+x^3\right )\right )}{12 x^2+12 x^3+3 x^4+e^{\frac {2 e^{6-x}}{3 x}} \left (12+12 x+3 x^2\right )+e^{\frac {e^{6-x}}{3 x}} \left (-24 x-24 x^2-6 x^3\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(15*x^2 + E^((2*E^(6 - x))/(3*x))*(27 + 12*x + 3*x^2) + E^(E^(6 - x)/(3*x))*(-30*x + E^(6 - x)*(4 + 8*x +
5*x^2 + x^3)))/(12*x^2 + 12*x^3 + 3*x^4 + E^((2*E^(6 - x))/(3*x))*(12 + 12*x + 3*x^2) + E^(E^(6 - x)/(3*x))*(-
24*x - 24*x^2 - 6*x^3)),x]

[Out]

5*Defer[Int][(E^(E^(6 - x)/(3*x)) - x)^(-2), x] + Defer[Int][E^(6 + E^(6 - x)/(3*x) - x)/(E^(E^(6 - x)/(3*x))
- x)^2, x]/3 + Defer[Int][E^((2*E^(6 - x))/(3*x))/(E^(E^(6 - x)/(3*x)) - x)^2, x] + Defer[Int][(E^(6 + E^(6 -
x)/(3*x) - x)*x)/(E^(E^(6 - x)/(3*x)) - x)^2, x]/3 + 20*Defer[Int][1/((E^(E^(6 - x)/(3*x)) - x)^2*(2 + x)^2),
x] + 20*Defer[Int][E^(E^(6 - x)/(3*x))/((E^(E^(6 - x)/(3*x)) - x)^2*(2 + x)^2), x] + 5*Defer[Int][E^((2*E^(6 -
 x))/(3*x))/((E^(E^(6 - x)/(3*x)) - x)^2*(2 + x)^2), x] - 20*Defer[Int][1/((E^(E^(6 - x)/(3*x)) - x)^2*(2 + x)
), x] - 10*Defer[Int][E^(E^(6 - x)/(3*x))/((E^(E^(6 - x)/(3*x)) - x)^2*(2 + x)), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {15 x^2+e^{\frac {2 e^{6-x}}{3 x}} \left (27+12 x+3 x^2\right )+e^{\frac {e^{6-x}}{3 x}} \left (-30 x+e^{6-x} \left (4+8 x+5 x^2+x^3\right )\right )}{3 \left (e^{\frac {e^{6-x}}{3 x}}-x\right )^2 (2+x)^2} \, dx\\ &=\frac {1}{3} \int \frac {15 x^2+e^{\frac {2 e^{6-x}}{3 x}} \left (27+12 x+3 x^2\right )+e^{\frac {e^{6-x}}{3 x}} \left (-30 x+e^{6-x} \left (4+8 x+5 x^2+x^3\right )\right )}{\left (e^{\frac {e^{6-x}}{3 x}}-x\right )^2 (2+x)^2} \, dx\\ &=\frac {1}{3} \int \left (\frac {e^{6+\frac {e^{6-x}}{3 x}-x} (1+x)}{\left (e^{\frac {e^{6-x}}{3 x}}-x\right )^2}-\frac {30 e^{\frac {e^{6-x}}{3 x}} x}{\left (e^{\frac {e^{6-x}}{3 x}}-x\right )^2 (2+x)^2}+\frac {15 x^2}{\left (e^{\frac {e^{6-x}}{3 x}}-x\right )^2 (2+x)^2}+\frac {3 e^{\frac {2 e^{6-x}}{3 x}} \left (9+4 x+x^2\right )}{\left (e^{\frac {e^{6-x}}{3 x}}-x\right )^2 (2+x)^2}\right ) \, dx\\ &=\frac {1}{3} \int \frac {e^{6+\frac {e^{6-x}}{3 x}-x} (1+x)}{\left (e^{\frac {e^{6-x}}{3 x}}-x\right )^2} \, dx+5 \int \frac {x^2}{\left (e^{\frac {e^{6-x}}{3 x}}-x\right )^2 (2+x)^2} \, dx-10 \int \frac {e^{\frac {e^{6-x}}{3 x}} x}{\left (e^{\frac {e^{6-x}}{3 x}}-x\right )^2 (2+x)^2} \, dx+\int \frac {e^{\frac {2 e^{6-x}}{3 x}} \left (9+4 x+x^2\right )}{\left (e^{\frac {e^{6-x}}{3 x}}-x\right )^2 (2+x)^2} \, dx\\ &=\frac {1}{3} \int \left (\frac {e^{6+\frac {e^{6-x}}{3 x}-x}}{\left (e^{\frac {e^{6-x}}{3 x}}-x\right )^2}+\frac {e^{6+\frac {e^{6-x}}{3 x}-x} x}{\left (e^{\frac {e^{6-x}}{3 x}}-x\right )^2}\right ) \, dx+5 \int \left (\frac {1}{\left (e^{\frac {e^{6-x}}{3 x}}-x\right )^2}+\frac {4}{\left (e^{\frac {e^{6-x}}{3 x}}-x\right )^2 (2+x)^2}-\frac {4}{\left (e^{\frac {e^{6-x}}{3 x}}-x\right )^2 (2+x)}\right ) \, dx-10 \int \left (-\frac {2 e^{\frac {e^{6-x}}{3 x}}}{\left (e^{\frac {e^{6-x}}{3 x}}-x\right )^2 (2+x)^2}+\frac {e^{\frac {e^{6-x}}{3 x}}}{\left (e^{\frac {e^{6-x}}{3 x}}-x\right )^2 (2+x)}\right ) \, dx+\int \left (\frac {e^{\frac {2 e^{6-x}}{3 x}}}{\left (e^{\frac {e^{6-x}}{3 x}}-x\right )^2}+\frac {5 e^{\frac {2 e^{6-x}}{3 x}}}{\left (e^{\frac {e^{6-x}}{3 x}}-x\right )^2 (2+x)^2}\right ) \, dx\\ &=\frac {1}{3} \int \frac {e^{6+\frac {e^{6-x}}{3 x}-x}}{\left (e^{\frac {e^{6-x}}{3 x}}-x\right )^2} \, dx+\frac {1}{3} \int \frac {e^{6+\frac {e^{6-x}}{3 x}-x} x}{\left (e^{\frac {e^{6-x}}{3 x}}-x\right )^2} \, dx+5 \int \frac {1}{\left (e^{\frac {e^{6-x}}{3 x}}-x\right )^2} \, dx+5 \int \frac {e^{\frac {2 e^{6-x}}{3 x}}}{\left (e^{\frac {e^{6-x}}{3 x}}-x\right )^2 (2+x)^2} \, dx-10 \int \frac {e^{\frac {e^{6-x}}{3 x}}}{\left (e^{\frac {e^{6-x}}{3 x}}-x\right )^2 (2+x)} \, dx+20 \int \frac {1}{\left (e^{\frac {e^{6-x}}{3 x}}-x\right )^2 (2+x)^2} \, dx+20 \int \frac {e^{\frac {e^{6-x}}{3 x}}}{\left (e^{\frac {e^{6-x}}{3 x}}-x\right )^2 (2+x)^2} \, dx-20 \int \frac {1}{\left (e^{\frac {e^{6-x}}{3 x}}-x\right )^2 (2+x)} \, dx+\int \frac {e^{\frac {2 e^{6-x}}{3 x}}}{\left (e^{\frac {e^{6-x}}{3 x}}-x\right )^2} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.11, size = 42, normalized size = 1.24 \begin {gather*} \frac {1}{3} \left (3 x+\frac {3 x^2}{e^{\frac {e^{6-x}}{3 x}}-x}-\frac {15}{2+x}\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(15*x^2 + E^((2*E^(6 - x))/(3*x))*(27 + 12*x + 3*x^2) + E^(E^(6 - x)/(3*x))*(-30*x + E^(6 - x)*(4 +
8*x + 5*x^2 + x^3)))/(12*x^2 + 12*x^3 + 3*x^4 + E^((2*E^(6 - x))/(3*x))*(12 + 12*x + 3*x^2) + E^(E^(6 - x)/(3*
x))*(-24*x - 24*x^2 - 6*x^3)),x]

[Out]

(3*x + (3*x^2)/(E^(E^(6 - x)/(3*x)) - x) - 15/(2 + x))/3

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fricas [A]  time = 0.72, size = 53, normalized size = 1.56 \begin {gather*} -\frac {{\left (x^{2} + 2 \, x - 5\right )} e^{\left (\frac {e^{\left (-x + 6\right )}}{3 \, x}\right )} + 5 \, x}{x^{2} - {\left (x + 2\right )} e^{\left (\frac {e^{\left (-x + 6\right )}}{3 \, x}\right )} + 2 \, x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((3*x^2+12*x+27)*exp(1/3*exp(-x+6)/x)^2+((x^3+5*x^2+8*x+4)*exp(-x+6)-30*x)*exp(1/3*exp(-x+6)/x)+15*x
^2)/((3*x^2+12*x+12)*exp(1/3*exp(-x+6)/x)^2+(-6*x^3-24*x^2-24*x)*exp(1/3*exp(-x+6)/x)+3*x^4+12*x^3+12*x^2),x,
algorithm="fricas")

[Out]

-((x^2 + 2*x - 5)*e^(1/3*e^(-x + 6)/x) + 5*x)/(x^2 - (x + 2)*e^(1/3*e^(-x + 6)/x) + 2*x)

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giac [B]  time = 0.34, size = 2098, normalized size = 61.71 result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((3*x^2+12*x+27)*exp(1/3*exp(-x+6)/x)^2+((x^3+5*x^2+8*x+4)*exp(-x+6)-30*x)*exp(1/3*exp(-x+6)/x)+15*x
^2)/((3*x^2+12*x+12)*exp(1/3*exp(-x+6)/x)^2+(-6*x^3-24*x^2-24*x)*exp(1/3*exp(-x+6)/x)+3*x^4+12*x^3+12*x^2),x,
algorithm="giac")

[Out]

-(9*x^5*e^(2*x + 1/3*e^(-x + 6)/x) + 3*x^5*e^(x + 1/3*(18*x + e^(-x + 6))/x) + 3*x^5*e^(x + 1/3*e^(-x + 6)/x +
 6) + x^5*e^(1/3*(18*x + e^(-x + 6))/x + 6) + 5*x^4*e^12 + 45*x^4*e^(2*x) + 18*x^4*e^(2*x + 1/3*e^(-x + 6)/x)
- 9*x^4*e^(3/2*x + 1/6*(3*x^2 + 2*e^(-x + 6))/x + 1/3*e^(-x + 6)/x) - 3*x^4*e^(x + 1/3*(18*x + e^(-x + 6))/x +
 1/3*e^(-x + 6)/x) + 9*x^4*e^(x + 1/3*(18*x + e^(-x + 6))/x) + 9*x^4*e^(x + 1/3*e^(-x + 6)/x + 6) + 30*x^4*e^(
x + 6) - 3*x^4*e^(1/2*x + 1/6*(3*x^2 + 2*e^(-x + 6))/x + 1/3*e^(-x + 6)/x + 6) - x^4*e^(1/3*(18*x + e^(-x + 6)
)/x + 1/3*e^(-x + 6)/x + 6) + 4*x^4*e^(1/3*(18*x + e^(-x + 6))/x + 6) + 10*x^3*e^12 - 45*x^3*e^(2*x + 1/3*e^(-
x + 6)/x) - 18*x^3*e^(3/2*x + 1/6*(3*x^2 + 2*e^(-x + 6))/x + 1/3*e^(-x + 6)/x) - 45*x^3*e^(3/2*x + 1/6*(3*x^2
+ 2*e^(-x + 6))/x) - 9*x^3*e^(x + 1/3*(18*x + e^(-x + 6))/x + 1/3*e^(-x + 6)/x) + 6*x^3*e^(x + 1/3*(18*x + e^(
-x + 6))/x) - 24*x^3*e^(x + 1/3*e^(-x + 6)/x + 6) + 30*x^3*e^(x + 6) - 9*x^3*e^(1/2*x + 1/6*(3*x^2 + 2*e^(-x +
 6))/x + 1/3*e^(-x + 6)/x + 6) - 30*x^3*e^(1/2*x + 1/6*(3*x^2 + 2*e^(-x + 6))/x + 6) - 5*x^3*e^(-1/2*x + 1/6*(
3*x^2 + 2*e^(-x + 6))/x + 12) - 4*x^3*e^(1/3*(18*x + e^(-x + 6))/x + 1/3*e^(-x + 6)/x + 6) + 5*x^3*e^(1/3*(18*
x + e^(-x + 6))/x + 6) - 5*x^3*e^(1/3*e^(-x + 6)/x + 12) + 5*x^2*e^12 + 45*x^2*e^(3/2*x + 1/6*(3*x^2 + 2*e^(-x
 + 6))/x + 1/3*e^(-x + 6)/x) - 6*x^2*e^(x + 1/3*(18*x + e^(-x + 6))/x + 1/3*e^(-x + 6)/x) - 30*x^2*e^(x + 1/3*
e^(-x + 6)/x + 6) + 24*x^2*e^(1/2*x + 1/6*(3*x^2 + 2*e^(-x + 6))/x + 1/3*e^(-x + 6)/x + 6) - 30*x^2*e^(1/2*x +
 1/6*(3*x^2 + 2*e^(-x + 6))/x + 6) + 5*x^2*e^(-1/2*x + 1/6*(3*x^2 + 2*e^(-x + 6))/x + 1/3*e^(-x + 6)/x + 12) -
 10*x^2*e^(-1/2*x + 1/6*(3*x^2 + 2*e^(-x + 6))/x + 12) - 5*x^2*e^(1/3*(18*x + e^(-x + 6))/x + 1/3*e^(-x + 6)/x
 + 6) + 2*x^2*e^(1/3*(18*x + e^(-x + 6))/x + 6) - 10*x^2*e^(1/3*e^(-x + 6)/x + 12) + 30*x*e^(1/2*x + 1/6*(3*x^
2 + 2*e^(-x + 6))/x + 1/3*e^(-x + 6)/x + 6) + 10*x*e^(-1/2*x + 1/6*(3*x^2 + 2*e^(-x + 6))/x + 1/3*e^(-x + 6)/x
 + 12) - 5*x*e^(-1/2*x + 1/6*(3*x^2 + 2*e^(-x + 6))/x + 12) - 2*x*e^(1/3*(18*x + e^(-x + 6))/x + 1/3*e^(-x + 6
)/x + 6) - 5*x*e^(1/3*e^(-x + 6)/x + 12) + 5*e^(-1/2*x + 1/6*(3*x^2 + 2*e^(-x + 6))/x + 1/3*e^(-x + 6)/x + 12)
)/(x^5*e^12 + 9*x^5*e^(2*x) + 6*x^5*e^(x + 6) + 4*x^4*e^12 + 18*x^4*e^(2*x) - 9*x^4*e^(2*x + 1/3*e^(-x + 6)/x)
 - 9*x^4*e^(3/2*x + 1/6*(3*x^2 + 2*e^(-x + 6))/x) - 6*x^4*e^(x + 1/3*e^(-x + 6)/x + 6) + 18*x^4*e^(x + 6) - 6*
x^4*e^(1/2*x + 1/6*(3*x^2 + 2*e^(-x + 6))/x + 6) - x^4*e^(-1/2*x + 1/6*(3*x^2 + 2*e^(-x + 6))/x + 12) - x^4*e^
(1/3*e^(-x + 6)/x + 12) + 5*x^3*e^12 - 18*x^3*e^(2*x + 1/3*e^(-x + 6)/x) + 9*x^3*e^(3/2*x + 1/6*(3*x^2 + 2*e^(
-x + 6))/x + 1/3*e^(-x + 6)/x) - 18*x^3*e^(3/2*x + 1/6*(3*x^2 + 2*e^(-x + 6))/x) - 18*x^3*e^(x + 1/3*e^(-x + 6
)/x + 6) + 12*x^3*e^(x + 6) + 6*x^3*e^(1/2*x + 1/6*(3*x^2 + 2*e^(-x + 6))/x + 1/3*e^(-x + 6)/x + 6) - 18*x^3*e
^(1/2*x + 1/6*(3*x^2 + 2*e^(-x + 6))/x + 6) + x^3*e^(-1/2*x + 1/6*(3*x^2 + 2*e^(-x + 6))/x + 1/3*e^(-x + 6)/x
+ 12) - 4*x^3*e^(-1/2*x + 1/6*(3*x^2 + 2*e^(-x + 6))/x + 12) - 4*x^3*e^(1/3*e^(-x + 6)/x + 12) + 2*x^2*e^12 +
18*x^2*e^(3/2*x + 1/6*(3*x^2 + 2*e^(-x + 6))/x + 1/3*e^(-x + 6)/x) - 12*x^2*e^(x + 1/3*e^(-x + 6)/x + 6) + 18*
x^2*e^(1/2*x + 1/6*(3*x^2 + 2*e^(-x + 6))/x + 1/3*e^(-x + 6)/x + 6) - 12*x^2*e^(1/2*x + 1/6*(3*x^2 + 2*e^(-x +
 6))/x + 6) + 4*x^2*e^(-1/2*x + 1/6*(3*x^2 + 2*e^(-x + 6))/x + 1/3*e^(-x + 6)/x + 12) - 5*x^2*e^(-1/2*x + 1/6*
(3*x^2 + 2*e^(-x + 6))/x + 12) - 5*x^2*e^(1/3*e^(-x + 6)/x + 12) + 12*x*e^(1/2*x + 1/6*(3*x^2 + 2*e^(-x + 6))/
x + 1/3*e^(-x + 6)/x + 6) + 5*x*e^(-1/2*x + 1/6*(3*x^2 + 2*e^(-x + 6))/x + 1/3*e^(-x + 6)/x + 12) - 2*x*e^(-1/
2*x + 1/6*(3*x^2 + 2*e^(-x + 6))/x + 12) - 2*x*e^(1/3*e^(-x + 6)/x + 12) + 2*e^(-1/2*x + 1/6*(3*x^2 + 2*e^(-x
+ 6))/x + 1/3*e^(-x + 6)/x + 12))

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maple [A]  time = 0.49, size = 33, normalized size = 0.97

method result size
risch \(x -\frac {5}{2+x}-\frac {x^{2}}{x -{\mathrm e}^{\frac {{\mathrm e}^{-x +6}}{3 x}}}\) \(33\)
norman \(\frac {-5 x +5 \,{\mathrm e}^{\frac {{\mathrm e}^{-x +6}}{3 x}}-2 \,{\mathrm e}^{\frac {{\mathrm e}^{-x +6}}{3 x}} x -{\mathrm e}^{\frac {{\mathrm e}^{-x +6}}{3 x}} x^{2}}{x^{2}-{\mathrm e}^{\frac {{\mathrm e}^{-x +6}}{3 x}} x +2 x -2 \,{\mathrm e}^{\frac {{\mathrm e}^{-x +6}}{3 x}}}\) \(90\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((3*x^2+12*x+27)*exp(1/3*exp(-x+6)/x)^2+((x^3+5*x^2+8*x+4)*exp(-x+6)-30*x)*exp(1/3*exp(-x+6)/x)+15*x^2)/((
3*x^2+12*x+12)*exp(1/3*exp(-x+6)/x)^2+(-6*x^3-24*x^2-24*x)*exp(1/3*exp(-x+6)/x)+3*x^4+12*x^3+12*x^2),x,method=
_RETURNVERBOSE)

[Out]

x-5/(2+x)-x^2/(x-exp(1/3*exp(-x+6)/x))

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maxima [A]  time = 0.45, size = 53, normalized size = 1.56 \begin {gather*} -\frac {{\left (x^{2} + 2 \, x - 5\right )} e^{\left (\frac {e^{\left (-x + 6\right )}}{3 \, x}\right )} + 5 \, x}{x^{2} - {\left (x + 2\right )} e^{\left (\frac {e^{\left (-x + 6\right )}}{3 \, x}\right )} + 2 \, x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((3*x^2+12*x+27)*exp(1/3*exp(-x+6)/x)^2+((x^3+5*x^2+8*x+4)*exp(-x+6)-30*x)*exp(1/3*exp(-x+6)/x)+15*x
^2)/((3*x^2+12*x+12)*exp(1/3*exp(-x+6)/x)^2+(-6*x^3-24*x^2-24*x)*exp(1/3*exp(-x+6)/x)+3*x^4+12*x^3+12*x^2),x,
algorithm="maxima")

[Out]

-((x^2 + 2*x - 5)*e^(1/3*e^(-x + 6)/x) + 5*x)/(x^2 - (x + 2)*e^(1/3*e^(-x + 6)/x) + 2*x)

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mupad [B]  time = 3.25, size = 74, normalized size = 2.18 \begin {gather*} -\frac {5\,x-5\,{\mathrm {e}}^{\frac {{\mathrm {e}}^{-x}\,{\mathrm {e}}^6}{3\,x}}+2\,x\,{\mathrm {e}}^{\frac {{\mathrm {e}}^{-x}\,{\mathrm {e}}^6}{3\,x}}+x^2\,{\mathrm {e}}^{\frac {{\mathrm {e}}^{-x}\,{\mathrm {e}}^6}{3\,x}}}{\left (x-{\mathrm {e}}^{\frac {{\mathrm {e}}^{-x}\,{\mathrm {e}}^6}{3\,x}}\right )\,\left (x+2\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp((2*exp(6 - x))/(3*x))*(12*x + 3*x^2 + 27) - exp(exp(6 - x)/(3*x))*(30*x - exp(6 - x)*(8*x + 5*x^2 + x
^3 + 4)) + 15*x^2)/(exp((2*exp(6 - x))/(3*x))*(12*x + 3*x^2 + 12) - exp(exp(6 - x)/(3*x))*(24*x + 24*x^2 + 6*x
^3) + 12*x^2 + 12*x^3 + 3*x^4),x)

[Out]

-(5*x - 5*exp((exp(-x)*exp(6))/(3*x)) + 2*x*exp((exp(-x)*exp(6))/(3*x)) + x^2*exp((exp(-x)*exp(6))/(3*x)))/((x
 - exp((exp(-x)*exp(6))/(3*x)))*(x + 2))

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sympy [A]  time = 0.31, size = 20, normalized size = 0.59 \begin {gather*} \frac {x^{2}}{- x + e^{\frac {e^{6 - x}}{3 x}}} + x - \frac {5}{x + 2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((3*x**2+12*x+27)*exp(1/3*exp(-x+6)/x)**2+((x**3+5*x**2+8*x+4)*exp(-x+6)-30*x)*exp(1/3*exp(-x+6)/x)+
15*x**2)/((3*x**2+12*x+12)*exp(1/3*exp(-x+6)/x)**2+(-6*x**3-24*x**2-24*x)*exp(1/3*exp(-x+6)/x)+3*x**4+12*x**3+
12*x**2),x)

[Out]

x**2/(-x + exp(exp(6 - x)/(3*x))) + x - 5/(x + 2)

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