3.48.17 \(\int \frac {2 x+e^{e^5} x+25 e^{-2 e^{1+x}} (-4 e^{1+3 e^5+x}+e^{1+2 e^5+x} (-24+12 x)+e^{1+e^5+x} (-48+48 x-12 x^2)+e^{1+x} (-32+48 x-24 x^2+4 x^3))+5 e^{-e^{1+x}} (8-4 x+e^{2 e^5} (2-2 e^{1+x} x)+e^{1+x} (-8 x+8 x^2-2 x^3)+e^{e^5} (8-2 x+e^{1+x} (-8 x+4 x^2)))}{16+2 e^{3 e^5}+e^{2 e^5} (12-6 x)-24 x+12 x^2-2 x^3+e^{e^5} (24-24 x+6 x^2)} \, dx\)

Optimal. Leaf size=31 \[ \left (5 e^{-e^{1+x}}-\frac {x}{2 \left (-2-e^{e^5}+x\right )}\right )^2 \]

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Rubi [F]  time = 3.55, 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 {2 x+e^{e^5} x+25 e^{-2 e^{1+x}} \left (-4 e^{1+3 e^5+x}+e^{1+2 e^5+x} (-24+12 x)+e^{1+e^5+x} \left (-48+48 x-12 x^2\right )+e^{1+x} \left (-32+48 x-24 x^2+4 x^3\right )\right )+5 e^{-e^{1+x}} \left (8-4 x+e^{2 e^5} \left (2-2 e^{1+x} x\right )+e^{1+x} \left (-8 x+8 x^2-2 x^3\right )+e^{e^5} \left (8-2 x+e^{1+x} \left (-8 x+4 x^2\right )\right )\right )}{16+2 e^{3 e^5}+e^{2 e^5} (12-6 x)-24 x+12 x^2-2 x^3+e^{e^5} \left (24-24 x+6 x^2\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(2*x + E^E^5*x + (25*(-4*E^(1 + 3*E^5 + x) + E^(1 + 2*E^5 + x)*(-24 + 12*x) + E^(1 + E^5 + x)*(-48 + 48*x
- 12*x^2) + E^(1 + x)*(-32 + 48*x - 24*x^2 + 4*x^3)))/E^(2*E^(1 + x)) + (5*(8 - 4*x + E^(2*E^5)*(2 - 2*E^(1 +
x)*x) + E^(1 + x)*(-8*x + 8*x^2 - 2*x^3) + E^E^5*(8 - 2*x + E^(1 + x)*(-8*x + 4*x^2))))/E^E^(1 + x))/(16 + 2*E
^(3*E^5) + E^(2*E^5)*(12 - 6*x) - 24*x + 12*x^2 - 2*x^3 + E^E^5*(24 - 24*x + 6*x^2)),x]

[Out]

25/E^(2*E^(1 + x)) - 5/E^E^(1 + x) + x^2/(4*(2 + E^E^5 - x)^2) + 5*(2 + E^E^5)*Defer[Int][1/(E^E^(1 + x)*(2 +
E^E^5 - x)^2), x] - 5*(2 + E^E^5)*Defer[Int][E^(1 - E^(1 + x) + x)/(2 + E^E^5 - x), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {\left (2+e^{e^5}\right ) x+25 e^{-2 e^{1+x}} \left (-4 e^{1+3 e^5+x}+e^{1+2 e^5+x} (-24+12 x)+e^{1+e^5+x} \left (-48+48 x-12 x^2\right )+e^{1+x} \left (-32+48 x-24 x^2+4 x^3\right )\right )+5 e^{-e^{1+x}} \left (8-4 x+e^{2 e^5} \left (2-2 e^{1+x} x\right )+e^{1+x} \left (-8 x+8 x^2-2 x^3\right )+e^{e^5} \left (8-2 x+e^{1+x} \left (-8 x+4 x^2\right )\right )\right )}{16+2 e^{3 e^5}+e^{2 e^5} (12-6 x)-24 x+12 x^2-2 x^3+e^{e^5} \left (24-24 x+6 x^2\right )} \, dx\\ &=\int \frac {e^{-2 e^{1+x}} \left (10 e^{1+2 e^5+x}-2 e^{e^{1+x}} \left (1+\frac {e^{e^5}}{2}\right )-20 e^{1+e^5+x} (-2+x)+10 e^{1+x} (-2+x)^2\right ) \left (-20 \left (1+\frac {e^{e^5}}{2}\right )+10 x-e^{e^{1+x}} x\right )}{2 \left (2+e^{e^5}-x\right )^3} \, dx\\ &=\frac {1}{2} \int \frac {e^{-2 e^{1+x}} \left (10 e^{1+2 e^5+x}-2 e^{e^{1+x}} \left (1+\frac {e^{e^5}}{2}\right )-20 e^{1+e^5+x} (-2+x)+10 e^{1+x} (-2+x)^2\right ) \left (-20 \left (1+\frac {e^{e^5}}{2}\right )+10 x-e^{e^{1+x}} x\right )}{\left (2+e^{e^5}-x\right )^3} \, dx\\ &=\frac {1}{2} \int \left (\frac {10 e^{1-2 e^{1+x}+x} \left (-20 \left (1+\frac {e^{e^5}}{2}\right )+10 x-e^{e^{1+x}} x\right )}{2+e^{e^5}-x}+\frac {e^{-e^{1+x}} \left (2+e^{e^5}\right ) \left (20 \left (1+\frac {e^{e^5}}{2}\right )-10 x+e^{e^{1+x}} x\right )}{\left (2+e^{e^5}-x\right )^3}\right ) \, dx\\ &=5 \int \frac {e^{1-2 e^{1+x}+x} \left (-20 \left (1+\frac {e^{e^5}}{2}\right )+10 x-e^{e^{1+x}} x\right )}{2+e^{e^5}-x} \, dx+\frac {1}{2} \left (2+e^{e^5}\right ) \int \frac {e^{-e^{1+x}} \left (20 \left (1+\frac {e^{e^5}}{2}\right )-10 x+e^{e^{1+x}} x\right )}{\left (2+e^{e^5}-x\right )^3} \, dx\\ &=5 \int \left (-10 e^{1-2 e^{1+x}+x}-\frac {e^{1-e^{1+x}+x} x}{2+e^{e^5}-x}\right ) \, dx+\frac {1}{2} \left (2+e^{e^5}\right ) \int \left (\frac {10 e^{-e^{1+x}}}{\left (2+e^{e^5}-x\right )^2}+\frac {x}{\left (2+e^{e^5}-x\right )^3}\right ) \, dx\\ &=-\left (5 \int \frac {e^{1-e^{1+x}+x} x}{2+e^{e^5}-x} \, dx\right )-50 \int e^{1-2 e^{1+x}+x} \, dx+\frac {1}{2} \left (2+e^{e^5}\right ) \int \frac {x}{\left (2+e^{e^5}-x\right )^3} \, dx+\left (5 \left (2+e^{e^5}\right )\right ) \int \frac {e^{-e^{1+x}}}{\left (2+e^{e^5}-x\right )^2} \, dx\\ &=\frac {x^2}{4 \left (2+e^{e^5}-x\right )^2}-5 \int \left (-e^{1-e^{1+x}+x}+\frac {e^{1-e^{1+x}+x} \left (2+e^{e^5}\right )}{2+e^{e^5}-x}\right ) \, dx-50 \operatorname {Subst}\left (\int e^{1-2 e x} \, dx,x,e^x\right )+\left (5 \left (2+e^{e^5}\right )\right ) \int \frac {e^{-e^{1+x}}}{\left (2+e^{e^5}-x\right )^2} \, dx\\ &=25 e^{-2 e^{1+x}}+\frac {x^2}{4 \left (2+e^{e^5}-x\right )^2}+5 \int e^{1-e^{1+x}+x} \, dx+\left (5 \left (2+e^{e^5}\right )\right ) \int \frac {e^{-e^{1+x}}}{\left (2+e^{e^5}-x\right )^2} \, dx-\left (5 \left (2+e^{e^5}\right )\right ) \int \frac {e^{1-e^{1+x}+x}}{2+e^{e^5}-x} \, dx\\ &=25 e^{-2 e^{1+x}}+\frac {x^2}{4 \left (2+e^{e^5}-x\right )^2}+5 \operatorname {Subst}\left (\int e^{1-e x} \, dx,x,e^x\right )+\left (5 \left (2+e^{e^5}\right )\right ) \int \frac {e^{-e^{1+x}}}{\left (2+e^{e^5}-x\right )^2} \, dx-\left (5 \left (2+e^{e^5}\right )\right ) \int \frac {e^{1-e^{1+x}+x}}{2+e^{e^5}-x} \, dx\\ &=25 e^{-2 e^{1+x}}-5 e^{-e^{1+x}}+\frac {x^2}{4 \left (2+e^{e^5}-x\right )^2}+\left (5 \left (2+e^{e^5}\right )\right ) \int \frac {e^{-e^{1+x}}}{\left (2+e^{e^5}-x\right )^2} \, dx-\left (5 \left (2+e^{e^5}\right )\right ) \int \frac {e^{1-e^{1+x}+x}}{2+e^{e^5}-x} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [B]  time = 0.19, size = 86, normalized size = 2.77 \begin {gather*} \frac {1}{2} \left (50 e^{-2 e^{1+x}}+\frac {\left (2+e^{e^5}\right )^2}{2 \left (2+e^{e^5}-x\right )^2}-\frac {2+e^{e^5}}{2+e^{e^5}-x}+\frac {10 e^{-e^{1+x}} x}{2+e^{e^5}-x}\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(2*x + E^E^5*x + (25*(-4*E^(1 + 3*E^5 + x) + E^(1 + 2*E^5 + x)*(-24 + 12*x) + E^(1 + E^5 + x)*(-48 +
48*x - 12*x^2) + E^(1 + x)*(-32 + 48*x - 24*x^2 + 4*x^3)))/E^(2*E^(1 + x)) + (5*(8 - 4*x + E^(2*E^5)*(2 - 2*E
^(1 + x)*x) + E^(1 + x)*(-8*x + 8*x^2 - 2*x^3) + E^E^5*(8 - 2*x + E^(1 + x)*(-8*x + 4*x^2))))/E^E^(1 + x))/(16
+ 2*E^(3*E^5) + E^(2*E^5)*(12 - 6*x) - 24*x + 12*x^2 - 2*x^3 + E^E^5*(24 - 24*x + 6*x^2)),x]

[Out]

(50/E^(2*E^(1 + x)) + (2 + E^E^5)^2/(2*(2 + E^E^5 - x)^2) - (2 + E^E^5)/(2 + E^E^5 - x) + (10*x)/(E^E^(1 + x)*
(2 + E^E^5 - x)))/2

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fricas [B]  time = 0.71, size = 136, normalized size = 4.39 \begin {gather*} \frac {4 \, {\left (x^{2} - 2 \, {\left (x - 2\right )} e^{\left (e^{5}\right )} - 4 \, x + e^{\left (2 \, e^{5}\right )} + 4\right )} e^{\left (2 \, {\left (e^{\left (3 \, e^{5}\right )} \log \relax (5) - e^{\left (x + 3 \, e^{5} + 1\right )}\right )} e^{\left (-3 \, e^{5}\right )}\right )} - 4 \, {\left (x^{2} - x e^{\left (e^{5}\right )} - 2 \, x\right )} e^{\left ({\left (e^{\left (3 \, e^{5}\right )} \log \relax (5) - e^{\left (x + 3 \, e^{5} + 1\right )}\right )} e^{\left (-3 \, e^{5}\right )}\right )} + 2 \, {\left (x - 2\right )} e^{\left (e^{5}\right )} + 4 \, x - e^{\left (2 \, e^{5}\right )} - 4}{4 \, {\left (x^{2} - 2 \, {\left (x - 2\right )} e^{\left (e^{5}\right )} - 4 \, x + e^{\left (2 \, e^{5}\right )} + 4\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-4*exp(x+1)*exp(exp(5))^3+(12*x-24)*exp(x+1)*exp(exp(5))^2+(-12*x^2+48*x-48)*exp(x+1)*exp(exp(5))+
(4*x^3-24*x^2+48*x-32)*exp(x+1))*exp(-exp(x+1)+log(5))^2+((-2*x*exp(x+1)+2)*exp(exp(5))^2+((4*x^2-8*x)*exp(x+1
)-2*x+8)*exp(exp(5))+(-2*x^3+8*x^2-8*x)*exp(x+1)-4*x+8)*exp(-exp(x+1)+log(5))+x*exp(exp(5))+2*x)/(2*exp(exp(5)
)^3+(12-6*x)*exp(exp(5))^2+(6*x^2-24*x+24)*exp(exp(5))-2*x^3+12*x^2-24*x+16),x, algorithm="fricas")

[Out]

1/4*(4*(x^2 - 2*(x - 2)*e^(e^5) - 4*x + e^(2*e^5) + 4)*e^(2*(e^(3*e^5)*log(5) - e^(x + 3*e^5 + 1))*e^(-3*e^5))
- 4*(x^2 - x*e^(e^5) - 2*x)*e^((e^(3*e^5)*log(5) - e^(x + 3*e^5 + 1))*e^(-3*e^5)) + 2*(x - 2)*e^(e^5) + 4*x -
e^(2*e^5) - 4)/(x^2 - 2*(x - 2)*e^(e^5) - 4*x + e^(2*e^5) + 4)

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {2 \, {\left ({\left (x^{3} - 4 \, x^{2} + 4 \, x\right )} e^{\left (x + 1\right )} + {\left (x e^{\left (x + 1\right )} - 1\right )} e^{\left (2 \, e^{5}\right )} - {\left (2 \, {\left (x^{2} - 2 \, x\right )} e^{\left (x + 1\right )} - x + 4\right )} e^{\left (e^{5}\right )} + 2 \, x - 4\right )} e^{\left (-e^{\left (x + 1\right )} + \log \relax (5)\right )} - 4 \, {\left (3 \, {\left (x - 2\right )} e^{\left (x + 2 \, e^{5} + 1\right )} - 3 \, {\left (x^{2} - 4 \, x + 4\right )} e^{\left (x + e^{5} + 1\right )} + {\left (x^{3} - 6 \, x^{2} + 12 \, x - 8\right )} e^{\left (x + 1\right )} - e^{\left (x + 3 \, e^{5} + 1\right )}\right )} e^{\left (-2 \, e^{\left (x + 1\right )} + 2 \, \log \relax (5)\right )} - x e^{\left (e^{5}\right )} - 2 \, x}{2 \, {\left (x^{3} - 6 \, x^{2} + 3 \, {\left (x - 2\right )} e^{\left (2 \, e^{5}\right )} - 3 \, {\left (x^{2} - 4 \, x + 4\right )} e^{\left (e^{5}\right )} + 12 \, x - e^{\left (3 \, e^{5}\right )} - 8\right )}}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-4*exp(x+1)*exp(exp(5))^3+(12*x-24)*exp(x+1)*exp(exp(5))^2+(-12*x^2+48*x-48)*exp(x+1)*exp(exp(5))+
(4*x^3-24*x^2+48*x-32)*exp(x+1))*exp(-exp(x+1)+log(5))^2+((-2*x*exp(x+1)+2)*exp(exp(5))^2+((4*x^2-8*x)*exp(x+1
)-2*x+8)*exp(exp(5))+(-2*x^3+8*x^2-8*x)*exp(x+1)-4*x+8)*exp(-exp(x+1)+log(5))+x*exp(exp(5))+2*x)/(2*exp(exp(5)
)^3+(12-6*x)*exp(exp(5))^2+(6*x^2-24*x+24)*exp(exp(5))-2*x^3+12*x^2-24*x+16),x, algorithm="giac")

[Out]

integrate(1/2*(2*((x^3 - 4*x^2 + 4*x)*e^(x + 1) + (x*e^(x + 1) - 1)*e^(2*e^5) - (2*(x^2 - 2*x)*e^(x + 1) - x +
4)*e^(e^5) + 2*x - 4)*e^(-e^(x + 1) + log(5)) - 4*(3*(x - 2)*e^(x + 2*e^5 + 1) - 3*(x^2 - 4*x + 4)*e^(x + e^5
+ 1) + (x^3 - 6*x^2 + 12*x - 8)*e^(x + 1) - e^(x + 3*e^5 + 1))*e^(-2*e^(x + 1) + 2*log(5)) - x*e^(e^5) - 2*x)
/(x^3 - 6*x^2 + 3*(x - 2)*e^(2*e^5) - 3*(x^2 - 4*x + 4)*e^(e^5) + 12*x - e^(3*e^5) - 8), x)

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maple [B]  time = 0.39, size = 81, normalized size = 2.61

method	result	size
risch	\(\frac {\left (1+\frac {{\mathrm e}^{{\mathrm e}^{5}}}{2}\right ) x -\frac {{\mathrm e}^{2 \,{\mathrm e}^{5}}}{4}-{\mathrm e}^{{\mathrm e}^{5}}-1}{{\mathrm e}^{2 \,{\mathrm e}^{5}}-2 x \,{\mathrm e}^{{\mathrm e}^{5}}+x^{2}+4 \,{\mathrm e}^{{\mathrm e}^{5}}-4 x +4}+25 \,{\mathrm e}^{-2 \,{\mathrm e}^{x +1}}+\frac {5 x \,{\mathrm e}^{-{\mathrm e}^{x +1}}}{{\mathrm e}^{{\mathrm e}^{5}}-x +2}\)	\(81\)
norman	\(\frac {25 x^{2} {\mathrm e}^{-2 \,{\mathrm e}^{x +1}}+\left (1+\frac {{\mathrm e}^{{\mathrm e}^{5}}}{2}\right ) x +25 \left ({\mathrm e}^{2 \,{\mathrm e}^{5}}+4 \,{\mathrm e}^{{\mathrm e}^{5}}+4\right ) {\mathrm e}^{-2 \,{\mathrm e}^{x +1}}+25 \left (-2 \,{\mathrm e}^{{\mathrm e}^{5}}-4\right ) x \,{\mathrm e}^{-2 \,{\mathrm e}^{x +1}}+\left ({\mathrm e}^{{\mathrm e}^{5}}+2\right ) x \,{\mathrm e}^{-{\mathrm e}^{x +1}+\ln \relax (5)}-x^{2} {\mathrm e}^{-{\mathrm e}^{x +1}+\ln \relax (5)}-\frac {{\mathrm e}^{2 \,{\mathrm e}^{5}}}{4}-{\mathrm e}^{{\mathrm e}^{5}}-1}{\left ({\mathrm e}^{{\mathrm e}^{5}}-x +2\right )^{2}}\)	\(129\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((-4*exp(x+1)*exp(exp(5))^3+(12*x-24)*exp(x+1)*exp(exp(5))^2+(-12*x^2+48*x-48)*exp(x+1)*exp(exp(5))+(4*x^3
-24*x^2+48*x-32)*exp(x+1))*exp(-exp(x+1)+ln(5))^2+((-2*x*exp(x+1)+2)*exp(exp(5))^2+((4*x^2-8*x)*exp(x+1)-2*x+8
)*exp(exp(5))+(-2*x^3+8*x^2-8*x)*exp(x+1)-4*x+8)*exp(-exp(x+1)+ln(5))+x*exp(exp(5))+2*x)/(2*exp(exp(5))^3+(12-
6*x)*exp(exp(5))^2+(6*x^2-24*x+24)*exp(exp(5))-2*x^3+12*x^2-24*x+16),x,method=_RETURNVERBOSE)

[Out]

((1+1/2*exp(exp(5)))*x-1/4*exp(2*exp(5))-exp(exp(5))-1)/(exp(2*exp(5))-2*x*exp(exp(5))+x^2+4*exp(exp(5))-4*x+4
)+25*exp(-2*exp(x+1))+5*x/(exp(exp(5))-x+2)*exp(-exp(x+1))

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maxima [B]  time = 0.51, size = 114, normalized size = 3.68 \begin {gather*} -\frac {5 \, {\left (x e^{\left (e^{\left (x + 1\right )}\right )} - 5 \, x + 5 \, e^{\left (e^{5}\right )} + 10\right )} e^{\left (-2 \, e^{\left (x + 1\right )}\right )}}{x - e^{\left (e^{5}\right )} - 2} + \frac {{\left (2 \, x - e^{\left (e^{5}\right )} - 2\right )} e^{\left (e^{5}\right )}}{4 \, {\left (x^{2} - 2 \, x {\left (e^{\left (e^{5}\right )} + 2\right )} + e^{\left (2 \, e^{5}\right )} + 4 \, e^{\left (e^{5}\right )} + 4\right )}} + \frac {2 \, x - e^{\left (e^{5}\right )} - 2}{2 \, {\left (x^{2} - 2 \, x {\left (e^{\left (e^{5}\right )} + 2\right )} + e^{\left (2 \, e^{5}\right )} + 4 \, e^{\left (e^{5}\right )} + 4\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-4*exp(x+1)*exp(exp(5))^3+(12*x-24)*exp(x+1)*exp(exp(5))^2+(-12*x^2+48*x-48)*exp(x+1)*exp(exp(5))+
(4*x^3-24*x^2+48*x-32)*exp(x+1))*exp(-exp(x+1)+log(5))^2+((-2*x*exp(x+1)+2)*exp(exp(5))^2+((4*x^2-8*x)*exp(x+1
)-2*x+8)*exp(exp(5))+(-2*x^3+8*x^2-8*x)*exp(x+1)-4*x+8)*exp(-exp(x+1)+log(5))+x*exp(exp(5))+2*x)/(2*exp(exp(5)
)^3+(12-6*x)*exp(exp(5))^2+(6*x^2-24*x+24)*exp(exp(5))-2*x^3+12*x^2-24*x+16),x, algorithm="maxima")

[Out]

-5*(x*e^(e^(x + 1)) - 5*x + 5*e^(e^5) + 10)*e^(-2*e^(x + 1))/(x - e^(e^5) - 2) + 1/4*(2*x - e^(e^5) - 2)*e^(e^
5)/(x^2 - 2*x*(e^(e^5) + 2) + e^(2*e^5) + 4*e^(e^5) + 4) + 1/2*(2*x - e^(e^5) - 2)/(x^2 - 2*x*(e^(e^5) + 2) +
e^(2*e^5) + 4*e^(e^5) + 4)

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mupad [B]  time = 3.72, size = 79, normalized size = 2.55 \begin {gather*} 25\,{\mathrm {e}}^{-2\,\mathrm {e}\,{\mathrm {e}}^x}+\frac {x\,\left ({\mathrm {e}}^{{\mathrm {e}}^5}+2\right )-\frac {{\left ({\mathrm {e}}^{{\mathrm {e}}^5}+2\right )}^2}{2}}{2\,x^2+\left (-4\,{\mathrm {e}}^{{\mathrm {e}}^5}-8\right )\,x+2\,{\mathrm {e}}^{2\,{\mathrm {e}}^5}+8\,{\mathrm {e}}^{{\mathrm {e}}^5}+8}+\frac {5\,x\,{\mathrm {e}}^{-\mathrm {e}\,{\mathrm {e}}^x}}{{\mathrm {e}}^{{\mathrm {e}}^5}-x+2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((2*x - exp(log(5) - exp(x + 1))*(4*x + exp(x + 1)*(8*x - 8*x^2 + 2*x^3) + exp(exp(5))*(2*x + exp(x + 1)*(8
*x - 4*x^2) - 8) + exp(2*exp(5))*(2*x*exp(x + 1) - 2) - 8) + x*exp(exp(5)) + exp(2*log(5) - 2*exp(x + 1))*(exp
(x + 1)*(48*x - 24*x^2 + 4*x^3 - 32) - 4*exp(3*exp(5))*exp(x + 1) - exp(x + 1)*exp(exp(5))*(12*x^2 - 48*x + 48
) + exp(2*exp(5))*exp(x + 1)*(12*x - 24)))/(2*exp(3*exp(5)) - 24*x + exp(exp(5))*(6*x^2 - 24*x + 24) - exp(2*e
xp(5))*(6*x - 12) + 12*x^2 - 2*x^3 + 16),x)

[Out]

25*exp(-2*exp(1)*exp(x)) + (x*(exp(exp(5)) + 2) - (exp(exp(5)) + 2)^2/2)/(2*exp(2*exp(5)) + 8*exp(exp(5)) - x*
(4*exp(exp(5)) + 8) + 2*x^2 + 8) + (5*x*exp(-exp(1)*exp(x)))/(exp(exp(5)) - x + 2)

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sympy [B]  time = 0.60, size = 90, normalized size = 2.90 \begin {gather*} \frac {- 5 x e^{- e^{x + 1}} + \left (25 x - 25 e^{e^{5}} - 50\right ) e^{- 2 e^{x + 1}}}{x - e^{e^{5}} - 2} + \frac {\left (- e^{e^{5}} - 2\right ) \left (- 2 x + 2 + e^{e^{5}}\right )}{4 x^{2} + x \left (- 8 e^{e^{5}} - 16\right ) + 16 + 16 e^{e^{5}} + 4 e^{2 e^{5}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-4*exp(x+1)*exp(exp(5))**3+(12*x-24)*exp(x+1)*exp(exp(5))**2+(-12*x**2+48*x-48)*exp(x+1)*exp(exp(5
))+(4*x**3-24*x**2+48*x-32)*exp(x+1))*exp(-exp(x+1)+ln(5))**2+((-2*x*exp(x+1)+2)*exp(exp(5))**2+((4*x**2-8*x)*
exp(x+1)-2*x+8)*exp(exp(5))+(-2*x**3+8*x**2-8*x)*exp(x+1)-4*x+8)*exp(-exp(x+1)+ln(5))+x*exp(exp(5))+2*x)/(2*ex
p(exp(5))**3+(12-6*x)*exp(exp(5))**2+(6*x**2-24*x+24)*exp(exp(5))-2*x**3+12*x**2-24*x+16),x)

[Out]

(-5*x*exp(-exp(x + 1)) + (25*x - 25*exp(exp(5)) - 50)*exp(-2*exp(x + 1)))/(x - exp(exp(5)) - 2) + (-exp(exp(5)
) - 2)*(-2*x + 2 + exp(exp(5)))/(4*x**2 + x*(-8*exp(exp(5)) - 16) + 16 + 16*exp(exp(5)) + 4*exp(2*exp(5)))

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