3.19.29 \(\int \frac {e (-75-27 x^2-4 x^3)+e^{e^x} (e (-3-x^2)+e^{1+x} (3 x-x^2-x^3))}{5625-2850 x-3689 x^2+726 x^3+805 x^4+108 x^5+4 x^6+e^{2 e^x} (9-6 x-5 x^2+2 x^3+x^4)+e^{e^x} (450-264 x-274 x^2+80 x^3+58 x^4+4 x^5)} \, dx\)

Optimal. Leaf size=27 \[ \frac {e}{\left (25+e^{e^x}+2 x\right ) \left (1+\frac {-3+x^2}{x}\right )} \]

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Rubi [F]  time = 6.78, 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 {e \left (-75-27 x^2-4 x^3\right )+e^{e^x} \left (e \left (-3-x^2\right )+e^{1+x} \left (3 x-x^2-x^3\right )\right )}{5625-2850 x-3689 x^2+726 x^3+805 x^4+108 x^5+4 x^6+e^{2 e^x} \left (9-6 x-5 x^2+2 x^3+x^4\right )+e^{e^x} \left (450-264 x-274 x^2+80 x^3+58 x^4+4 x^5\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E*(-75 - 27*x^2 - 4*x^3) + E^E^x*(E*(-3 - x^2) + E^(1 + x)*(3*x - x^2 - x^3)))/(5625 - 2850*x - 3689*x^2
+ 726*x^3 + 805*x^4 + 108*x^5 + 4*x^6 + E^(2*E^x)*(9 - 6*x - 5*x^2 + 2*x^3 + x^4) + E^E^x*(450 - 264*x - 274*x
^2 + 80*x^3 + 58*x^4 + 4*x^5)),x]

[Out]

(46*E*Defer[Int][1/((-1 + Sqrt[13] - 2*x)*(25 + E^E^x + 2*x)^2), x])/Sqrt[13] + (2*E*Defer[Int][E^E^x/((-1 + S
qrt[13] - 2*x)*(25 + E^E^x + 2*x)^2), x])/Sqrt[13] - (4*(13 - Sqrt[13])*E*Defer[Int][1/((1 - Sqrt[13] + 2*x)*(
25 + E^E^x + 2*x)^2), x])/13 - ((13 - Sqrt[13])*E*Defer[Int][E^(E^x + x)/((1 - Sqrt[13] + 2*x)*(25 + E^E^x + 2
*x)^2), x])/13 + (46*E*Defer[Int][1/((1 + Sqrt[13] + 2*x)*(25 + E^E^x + 2*x)^2), x])/Sqrt[13] - (4*(13 + Sqrt[
13])*E*Defer[Int][1/((1 + Sqrt[13] + 2*x)*(25 + E^E^x + 2*x)^2), x])/13 + (2*E*Defer[Int][E^E^x/((1 + Sqrt[13]
+ 2*x)*(25 + E^E^x + 2*x)^2), x])/Sqrt[13] - ((13 + Sqrt[13])*E*Defer[Int][E^(E^x + x)/((1 + Sqrt[13] + 2*x)*
(25 + E^E^x + 2*x)^2), x])/13 - 144*E*Defer[Int][1/((25 + E^E^x + 2*x)^2*(-3 + x + x^2)^2), x] - 6*E*Defer[Int
][E^E^x/((25 + E^E^x + 2*x)^2*(-3 + x + x^2)^2), x] + 11*E*Defer[Int][x/((25 + E^E^x + 2*x)^2*(-3 + x + x^2)^2
), x] + E*Defer[Int][(E^E^x*x)/((25 + E^E^x + 2*x)^2*(-3 + x + x^2)^2), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e \left (-75-27 x^2-4 x^3-e^{e^x} \left (3+x^2\right )-e^{e^x+x} x \left (-3+x+x^2\right )\right )}{\left (25+e^{e^x}+2 x\right )^2 \left (3-x-x^2\right )^2} \, dx\\ &=e \int \frac {-75-27 x^2-4 x^3-e^{e^x} \left (3+x^2\right )-e^{e^x+x} x \left (-3+x+x^2\right )}{\left (25+e^{e^x}+2 x\right )^2 \left (3-x-x^2\right )^2} \, dx\\ &=e \int \left (-\frac {75}{\left (25+e^{e^x}+2 x\right )^2 \left (-3+x+x^2\right )^2}-\frac {27 x^2}{\left (25+e^{e^x}+2 x\right )^2 \left (-3+x+x^2\right )^2}-\frac {4 x^3}{\left (25+e^{e^x}+2 x\right )^2 \left (-3+x+x^2\right )^2}-\frac {e^{e^x} \left (3+x^2\right )}{\left (25+e^{e^x}+2 x\right )^2 \left (-3+x+x^2\right )^2}-\frac {e^{e^x+x} x}{\left (25+e^{e^x}+2 x\right )^2 \left (-3+x+x^2\right )}\right ) \, dx\\ &=-\left (e \int \frac {e^{e^x} \left (3+x^2\right )}{\left (25+e^{e^x}+2 x\right )^2 \left (-3+x+x^2\right )^2} \, dx\right )-e \int \frac {e^{e^x+x} x}{\left (25+e^{e^x}+2 x\right )^2 \left (-3+x+x^2\right )} \, dx-(4 e) \int \frac {x^3}{\left (25+e^{e^x}+2 x\right )^2 \left (-3+x+x^2\right )^2} \, dx-(27 e) \int \frac {x^2}{\left (25+e^{e^x}+2 x\right )^2 \left (-3+x+x^2\right )^2} \, dx-(75 e) \int \frac {1}{\left (25+e^{e^x}+2 x\right )^2 \left (-3+x+x^2\right )^2} \, dx\\ &=-\left (e \int \left (\frac {\left (1-\frac {1}{\sqrt {13}}\right ) e^{e^x+x}}{\left (1-\sqrt {13}+2 x\right ) \left (25+e^{e^x}+2 x\right )^2}+\frac {\left (1+\frac {1}{\sqrt {13}}\right ) e^{e^x+x}}{\left (1+\sqrt {13}+2 x\right ) \left (25+e^{e^x}+2 x\right )^2}\right ) \, dx\right )-e \int \left (-\frac {e^{e^x} (-6+x)}{\left (25+e^{e^x}+2 x\right )^2 \left (-3+x+x^2\right )^2}+\frac {e^{e^x}}{\left (25+e^{e^x}+2 x\right )^2 \left (-3+x+x^2\right )}\right ) \, dx-(4 e) \int \left (\frac {-3+4 x}{\left (25+e^{e^x}+2 x\right )^2 \left (-3+x+x^2\right )^2}+\frac {-1+x}{\left (25+e^{e^x}+2 x\right )^2 \left (-3+x+x^2\right )}\right ) \, dx-(27 e) \int \left (-\frac {-3+x}{\left (25+e^{e^x}+2 x\right )^2 \left (-3+x+x^2\right )^2}+\frac {1}{\left (25+e^{e^x}+2 x\right )^2 \left (-3+x+x^2\right )}\right ) \, dx-(75 e) \int \frac {1}{\left (25+e^{e^x}+2 x\right )^2 \left (-3+x+x^2\right )^2} \, dx\\ &=e \int \frac {e^{e^x} (-6+x)}{\left (25+e^{e^x}+2 x\right )^2 \left (-3+x+x^2\right )^2} \, dx-e \int \frac {e^{e^x}}{\left (25+e^{e^x}+2 x\right )^2 \left (-3+x+x^2\right )} \, dx-(4 e) \int \frac {-3+4 x}{\left (25+e^{e^x}+2 x\right )^2 \left (-3+x+x^2\right )^2} \, dx-(4 e) \int \frac {-1+x}{\left (25+e^{e^x}+2 x\right )^2 \left (-3+x+x^2\right )} \, dx+(27 e) \int \frac {-3+x}{\left (25+e^{e^x}+2 x\right )^2 \left (-3+x+x^2\right )^2} \, dx-(27 e) \int \frac {1}{\left (25+e^{e^x}+2 x\right )^2 \left (-3+x+x^2\right )} \, dx-(75 e) \int \frac {1}{\left (25+e^{e^x}+2 x\right )^2 \left (-3+x+x^2\right )^2} \, dx-\frac {1}{13} \left (\left (13-\sqrt {13}\right ) e\right ) \int \frac {e^{e^x+x}}{\left (1-\sqrt {13}+2 x\right ) \left (25+e^{e^x}+2 x\right )^2} \, dx-\frac {1}{13} \left (\left (13+\sqrt {13}\right ) e\right ) \int \frac {e^{e^x+x}}{\left (1+\sqrt {13}+2 x\right ) \left (25+e^{e^x}+2 x\right )^2} \, dx\\ &=-\left (e \int \left (-\frac {2 e^{e^x}}{\sqrt {13} \left (-1+\sqrt {13}-2 x\right ) \left (25+e^{e^x}+2 x\right )^2}-\frac {2 e^{e^x}}{\sqrt {13} \left (1+\sqrt {13}+2 x\right ) \left (25+e^{e^x}+2 x\right )^2}\right ) \, dx\right )+e \int \left (-\frac {6 e^{e^x}}{\left (25+e^{e^x}+2 x\right )^2 \left (-3+x+x^2\right )^2}+\frac {e^{e^x} x}{\left (25+e^{e^x}+2 x\right )^2 \left (-3+x+x^2\right )^2}\right ) \, dx-(4 e) \int \left (-\frac {3}{\left (25+e^{e^x}+2 x\right )^2 \left (-3+x+x^2\right )^2}+\frac {4 x}{\left (25+e^{e^x}+2 x\right )^2 \left (-3+x+x^2\right )^2}\right ) \, dx-(4 e) \int \left (-\frac {1}{\left (25+e^{e^x}+2 x\right )^2 \left (-3+x+x^2\right )}+\frac {x}{\left (25+e^{e^x}+2 x\right )^2 \left (-3+x+x^2\right )}\right ) \, dx-(27 e) \int \left (-\frac {2}{\sqrt {13} \left (-1+\sqrt {13}-2 x\right ) \left (25+e^{e^x}+2 x\right )^2}-\frac {2}{\sqrt {13} \left (1+\sqrt {13}+2 x\right ) \left (25+e^{e^x}+2 x\right )^2}\right ) \, dx+(27 e) \int \left (-\frac {3}{\left (25+e^{e^x}+2 x\right )^2 \left (-3+x+x^2\right )^2}+\frac {x}{\left (25+e^{e^x}+2 x\right )^2 \left (-3+x+x^2\right )^2}\right ) \, dx-(75 e) \int \frac {1}{\left (25+e^{e^x}+2 x\right )^2 \left (-3+x+x^2\right )^2} \, dx-\frac {1}{13} \left (\left (13-\sqrt {13}\right ) e\right ) \int \frac {e^{e^x+x}}{\left (1-\sqrt {13}+2 x\right ) \left (25+e^{e^x}+2 x\right )^2} \, dx-\frac {1}{13} \left (\left (13+\sqrt {13}\right ) e\right ) \int \frac {e^{e^x+x}}{\left (1+\sqrt {13}+2 x\right ) \left (25+e^{e^x}+2 x\right )^2} \, dx\\ &=e \int \frac {e^{e^x} x}{\left (25+e^{e^x}+2 x\right )^2 \left (-3+x+x^2\right )^2} \, dx+(4 e) \int \frac {1}{\left (25+e^{e^x}+2 x\right )^2 \left (-3+x+x^2\right )} \, dx-(4 e) \int \frac {x}{\left (25+e^{e^x}+2 x\right )^2 \left (-3+x+x^2\right )} \, dx-(6 e) \int \frac {e^{e^x}}{\left (25+e^{e^x}+2 x\right )^2 \left (-3+x+x^2\right )^2} \, dx+(12 e) \int \frac {1}{\left (25+e^{e^x}+2 x\right )^2 \left (-3+x+x^2\right )^2} \, dx-(16 e) \int \frac {x}{\left (25+e^{e^x}+2 x\right )^2 \left (-3+x+x^2\right )^2} \, dx+(27 e) \int \frac {x}{\left (25+e^{e^x}+2 x\right )^2 \left (-3+x+x^2\right )^2} \, dx-(75 e) \int \frac {1}{\left (25+e^{e^x}+2 x\right )^2 \left (-3+x+x^2\right )^2} \, dx-(81 e) \int \frac {1}{\left (25+e^{e^x}+2 x\right )^2 \left (-3+x+x^2\right )^2} \, dx+\frac {(2 e) \int \frac {e^{e^x}}{\left (-1+\sqrt {13}-2 x\right ) \left (25+e^{e^x}+2 x\right )^2} \, dx}{\sqrt {13}}+\frac {(2 e) \int \frac {e^{e^x}}{\left (1+\sqrt {13}+2 x\right ) \left (25+e^{e^x}+2 x\right )^2} \, dx}{\sqrt {13}}+\frac {(54 e) \int \frac {1}{\left (-1+\sqrt {13}-2 x\right ) \left (25+e^{e^x}+2 x\right )^2} \, dx}{\sqrt {13}}+\frac {(54 e) \int \frac {1}{\left (1+\sqrt {13}+2 x\right ) \left (25+e^{e^x}+2 x\right )^2} \, dx}{\sqrt {13}}-\frac {1}{13} \left (\left (13-\sqrt {13}\right ) e\right ) \int \frac {e^{e^x+x}}{\left (1-\sqrt {13}+2 x\right ) \left (25+e^{e^x}+2 x\right )^2} \, dx-\frac {1}{13} \left (\left (13+\sqrt {13}\right ) e\right ) \int \frac {e^{e^x+x}}{\left (1+\sqrt {13}+2 x\right ) \left (25+e^{e^x}+2 x\right )^2} \, dx\\ &=e \int \frac {e^{e^x} x}{\left (25+e^{e^x}+2 x\right )^2 \left (-3+x+x^2\right )^2} \, dx+(4 e) \int \left (-\frac {2}{\sqrt {13} \left (-1+\sqrt {13}-2 x\right ) \left (25+e^{e^x}+2 x\right )^2}-\frac {2}{\sqrt {13} \left (1+\sqrt {13}+2 x\right ) \left (25+e^{e^x}+2 x\right )^2}\right ) \, dx-(4 e) \int \left (\frac {1-\frac {1}{\sqrt {13}}}{\left (1-\sqrt {13}+2 x\right ) \left (25+e^{e^x}+2 x\right )^2}+\frac {1+\frac {1}{\sqrt {13}}}{\left (1+\sqrt {13}+2 x\right ) \left (25+e^{e^x}+2 x\right )^2}\right ) \, dx-(6 e) \int \frac {e^{e^x}}{\left (25+e^{e^x}+2 x\right )^2 \left (-3+x+x^2\right )^2} \, dx+(12 e) \int \frac {1}{\left (25+e^{e^x}+2 x\right )^2 \left (-3+x+x^2\right )^2} \, dx-(16 e) \int \frac {x}{\left (25+e^{e^x}+2 x\right )^2 \left (-3+x+x^2\right )^2} \, dx+(27 e) \int \frac {x}{\left (25+e^{e^x}+2 x\right )^2 \left (-3+x+x^2\right )^2} \, dx-(75 e) \int \frac {1}{\left (25+e^{e^x}+2 x\right )^2 \left (-3+x+x^2\right )^2} \, dx-(81 e) \int \frac {1}{\left (25+e^{e^x}+2 x\right )^2 \left (-3+x+x^2\right )^2} \, dx+\frac {(2 e) \int \frac {e^{e^x}}{\left (-1+\sqrt {13}-2 x\right ) \left (25+e^{e^x}+2 x\right )^2} \, dx}{\sqrt {13}}+\frac {(2 e) \int \frac {e^{e^x}}{\left (1+\sqrt {13}+2 x\right ) \left (25+e^{e^x}+2 x\right )^2} \, dx}{\sqrt {13}}+\frac {(54 e) \int \frac {1}{\left (-1+\sqrt {13}-2 x\right ) \left (25+e^{e^x}+2 x\right )^2} \, dx}{\sqrt {13}}+\frac {(54 e) \int \frac {1}{\left (1+\sqrt {13}+2 x\right ) \left (25+e^{e^x}+2 x\right )^2} \, dx}{\sqrt {13}}-\frac {1}{13} \left (\left (13-\sqrt {13}\right ) e\right ) \int \frac {e^{e^x+x}}{\left (1-\sqrt {13}+2 x\right ) \left (25+e^{e^x}+2 x\right )^2} \, dx-\frac {1}{13} \left (\left (13+\sqrt {13}\right ) e\right ) \int \frac {e^{e^x+x}}{\left (1+\sqrt {13}+2 x\right ) \left (25+e^{e^x}+2 x\right )^2} \, dx\\ &=e \int \frac {e^{e^x} x}{\left (25+e^{e^x}+2 x\right )^2 \left (-3+x+x^2\right )^2} \, dx-(6 e) \int \frac {e^{e^x}}{\left (25+e^{e^x}+2 x\right )^2 \left (-3+x+x^2\right )^2} \, dx+(12 e) \int \frac {1}{\left (25+e^{e^x}+2 x\right )^2 \left (-3+x+x^2\right )^2} \, dx-(16 e) \int \frac {x}{\left (25+e^{e^x}+2 x\right )^2 \left (-3+x+x^2\right )^2} \, dx+(27 e) \int \frac {x}{\left (25+e^{e^x}+2 x\right )^2 \left (-3+x+x^2\right )^2} \, dx-(75 e) \int \frac {1}{\left (25+e^{e^x}+2 x\right )^2 \left (-3+x+x^2\right )^2} \, dx-(81 e) \int \frac {1}{\left (25+e^{e^x}+2 x\right )^2 \left (-3+x+x^2\right )^2} \, dx+\frac {(2 e) \int \frac {e^{e^x}}{\left (-1+\sqrt {13}-2 x\right ) \left (25+e^{e^x}+2 x\right )^2} \, dx}{\sqrt {13}}+\frac {(2 e) \int \frac {e^{e^x}}{\left (1+\sqrt {13}+2 x\right ) \left (25+e^{e^x}+2 x\right )^2} \, dx}{\sqrt {13}}-\frac {(8 e) \int \frac {1}{\left (-1+\sqrt {13}-2 x\right ) \left (25+e^{e^x}+2 x\right )^2} \, dx}{\sqrt {13}}-\frac {(8 e) \int \frac {1}{\left (1+\sqrt {13}+2 x\right ) \left (25+e^{e^x}+2 x\right )^2} \, dx}{\sqrt {13}}+\frac {(54 e) \int \frac {1}{\left (-1+\sqrt {13}-2 x\right ) \left (25+e^{e^x}+2 x\right )^2} \, dx}{\sqrt {13}}+\frac {(54 e) \int \frac {1}{\left (1+\sqrt {13}+2 x\right ) \left (25+e^{e^x}+2 x\right )^2} \, dx}{\sqrt {13}}-\frac {1}{13} \left (\left (13-\sqrt {13}\right ) e\right ) \int \frac {e^{e^x+x}}{\left (1-\sqrt {13}+2 x\right ) \left (25+e^{e^x}+2 x\right )^2} \, dx-\frac {1}{13} \left (4 \left (13-\sqrt {13}\right ) e\right ) \int \frac {1}{\left (1-\sqrt {13}+2 x\right ) \left (25+e^{e^x}+2 x\right )^2} \, dx-\frac {1}{13} \left (\left (13+\sqrt {13}\right ) e\right ) \int \frac {e^{e^x+x}}{\left (1+\sqrt {13}+2 x\right ) \left (25+e^{e^x}+2 x\right )^2} \, dx-\frac {1}{13} \left (4 \left (13+\sqrt {13}\right ) e\right ) \int \frac {1}{\left (1+\sqrt {13}+2 x\right ) \left (25+e^{e^x}+2 x\right )^2} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 1.52, size = 23, normalized size = 0.85 \begin {gather*} \frac {e x}{\left (25+e^{e^x}+2 x\right ) \left (-3+x+x^2\right )} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E*(-75 - 27*x^2 - 4*x^3) + E^E^x*(E*(-3 - x^2) + E^(1 + x)*(3*x - x^2 - x^3)))/(5625 - 2850*x - 368
9*x^2 + 726*x^3 + 805*x^4 + 108*x^5 + 4*x^6 + E^(2*E^x)*(9 - 6*x - 5*x^2 + 2*x^3 + x^4) + E^E^x*(450 - 264*x -
274*x^2 + 80*x^3 + 58*x^4 + 4*x^5)),x]

[Out]

(E*x)/((25 + E^E^x + 2*x)*(-3 + x + x^2))

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fricas [A]  time = 0.87, size = 31, normalized size = 1.15 \begin {gather*} \frac {x e}{2 \, x^{3} + 27 \, x^{2} + {\left (x^{2} + x - 3\right )} e^{\left (e^{x}\right )} + 19 \, x - 75} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-x^3-x^2+3*x)*exp(1)*exp(x)+(-x^2-3)*exp(1))*exp(exp(x))+(-4*x^3-27*x^2-75)*exp(1))/((x^4+2*x^3-5
*x^2-6*x+9)*exp(exp(x))^2+(4*x^5+58*x^4+80*x^3-274*x^2-264*x+450)*exp(exp(x))+4*x^6+108*x^5+805*x^4+726*x^3-36
89*x^2-2850*x+5625),x, algorithm="fricas")

[Out]

x*e/(2*x^3 + 27*x^2 + (x^2 + x - 3)*e^(e^x) + 19*x - 75)

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giac [A]  time = 0.31, size = 38, normalized size = 1.41 \begin {gather*} \frac {x e}{2 \, x^{3} + x^{2} e^{\left (e^{x}\right )} + 27 \, x^{2} + x e^{\left (e^{x}\right )} + 19 \, x - 3 \, e^{\left (e^{x}\right )} - 75} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-x^3-x^2+3*x)*exp(1)*exp(x)+(-x^2-3)*exp(1))*exp(exp(x))+(-4*x^3-27*x^2-75)*exp(1))/((x^4+2*x^3-5
*x^2-6*x+9)*exp(exp(x))^2+(4*x^5+58*x^4+80*x^3-274*x^2-264*x+450)*exp(exp(x))+4*x^6+108*x^5+805*x^4+726*x^3-36
89*x^2-2850*x+5625),x, algorithm="giac")

[Out]

x*e/(2*x^3 + x^2*e^(e^x) + 27*x^2 + x*e^(e^x) + 19*x - 3*e^(e^x) - 75)

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maple [A]  time = 0.06, size = 23, normalized size = 0.85

method	result	size
risch	\(\frac {x \,{\mathrm e}}{\left (x^{2}+x -3\right ) \left (25+2 x +{\mathrm e}^{{\mathrm e}^{x}}\right )}\)	\(23\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((-x^3-x^2+3*x)*exp(1)*exp(x)+(-x^2-3)*exp(1))*exp(exp(x))+(-4*x^3-27*x^2-75)*exp(1))/((x^4+2*x^3-5*x^2-6
*x+9)*exp(exp(x))^2+(4*x^5+58*x^4+80*x^3-274*x^2-264*x+450)*exp(exp(x))+4*x^6+108*x^5+805*x^4+726*x^3-3689*x^2
-2850*x+5625),x,method=_RETURNVERBOSE)

[Out]

x*exp(1)/(x^2+x-3)/(25+2*x+exp(exp(x)))

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maxima [A]  time = 0.87, size = 31, normalized size = 1.15 \begin {gather*} \frac {x e}{2 \, x^{3} + 27 \, x^{2} + {\left (x^{2} + x - 3\right )} e^{\left (e^{x}\right )} + 19 \, x - 75} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-x^3-x^2+3*x)*exp(1)*exp(x)+(-x^2-3)*exp(1))*exp(exp(x))+(-4*x^3-27*x^2-75)*exp(1))/((x^4+2*x^3-5
*x^2-6*x+9)*exp(exp(x))^2+(4*x^5+58*x^4+80*x^3-274*x^2-264*x+450)*exp(exp(x))+4*x^6+108*x^5+805*x^4+726*x^3-36
89*x^2-2850*x+5625),x, algorithm="maxima")

[Out]

x*e/(2*x^3 + 27*x^2 + (x^2 + x - 3)*e^(e^x) + 19*x - 75)

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mupad [B]  time = 1.25, size = 86, normalized size = 3.19 \begin {gather*} \frac {2\,x^4\,{\mathrm {e}}^{x+1}-x\,\left (75\,{\mathrm {e}}^{x+1}-6\,\mathrm {e}\right )+x^2\,\left (19\,{\mathrm {e}}^{x+1}-2\,\mathrm {e}\right )+x^3\,\left (27\,{\mathrm {e}}^{x+1}-2\,\mathrm {e}\right )}{\left (25\,{\mathrm {e}}^x+2\,x\,{\mathrm {e}}^x-2\right )\,\left (2\,x+{\mathrm {e}}^{{\mathrm {e}}^x}+25\right )\,{\left (x^2+x-3\right )}^2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp(exp(x))*(exp(1)*(x^2 + 3) + exp(1)*exp(x)*(x^2 - 3*x + x^3)) + exp(1)*(27*x^2 + 4*x^3 + 75))/(exp(2*
exp(x))*(2*x^3 - 5*x^2 - 6*x + x^4 + 9) - 2850*x + exp(exp(x))*(80*x^3 - 274*x^2 - 264*x + 58*x^4 + 4*x^5 + 45
0) - 3689*x^2 + 726*x^3 + 805*x^4 + 108*x^5 + 4*x^6 + 5625),x)

[Out]

(2*x^4*exp(x + 1) - x*(75*exp(x + 1) - 6*exp(1)) + x^2*(19*exp(x + 1) - 2*exp(1)) + x^3*(27*exp(x + 1) - 2*exp
(1)))/((25*exp(x) + 2*x*exp(x) - 2)*(2*x + exp(exp(x)) + 25)*(x + x^2 - 3)^2)

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sympy [A]  time = 0.27, size = 31, normalized size = 1.15 \begin {gather*} \frac {e x}{2 x^{3} + 27 x^{2} + 19 x + \left (x^{2} + x - 3\right ) e^{e^{x}} - 75} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-x**3-x**2+3*x)*exp(1)*exp(x)+(-x**2-3)*exp(1))*exp(exp(x))+(-4*x**3-27*x**2-75)*exp(1))/((x**4+2
*x**3-5*x**2-6*x+9)*exp(exp(x))**2+(4*x**5+58*x**4+80*x**3-274*x**2-264*x+450)*exp(exp(x))+4*x**6+108*x**5+805
*x**4+726*x**3-3689*x**2-2850*x+5625),x)

[Out]

E*x/(2*x**3 + 27*x**2 + 19*x + (x**2 + x - 3)*exp(exp(x)) - 75)

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