∫ 1_ 5ee 1 ___25 (3600x2+1200x3+100x4+e6(144+48x+4x2)+e3(1440x+480x2+40x3)) (−25+e 1 ___ 25(3600x2+1200x3+100x4+e6(144+48x+4x2)+e3(1440x+480x2+40x3)) (14400x− 2800x3 − 400x4 + e6(96 − 32x − 8x2) + e3(2880 + 480x − 720x2 − 120x3))) dx [6159]

3.62.59 \(\int \frac {1}{5} e^{e^{\frac {1}{25} (3600 x^2+1200 x^3+100 x^4+e^6 (144+48 x+4 x^2)+e^3 (1440 x+480 x^2+40 x^3))}} (-25+e^{\frac {1}{25} (3600 x^2+1200 x^3+100 x^4+e^6 (144+48 x+4 x^2)+e^3 (1440 x+480 x^2+40 x^3))} (14400 x-2800 x^3-400 x^4+e^6 (96-32 x-8 x^2)+e^3 (2880+480 x-720 x^2-120 x^3))) \, dx\) [6159]

Optimal. Leaf size=32 \[ 2+5 e^{e^{(6+x)^2 \left (\frac {2 e^3}{5}+2 x\right )^2}} (2-x) \]

[Out]

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

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Rubi [B] Leaf count is larger than twice the leaf count of optimal. \(139\) vs. \(2(32)=64\).
time = 0.57, antiderivative size = 139, normalized size of antiderivative = 4.34, number of steps used = 2, number of rules used = 2, integrand size = 164, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.012, Rules used = {12, 2326} \begin {gather*} \frac {5 \left (-50 x^4-350 x^3+e^6 \left (-x^2-4 x+12\right )+15 e^3 \left (-x^3-6 x^2+4 x+24\right )+1800 x\right ) \exp \left (\exp \left (\frac {4}{25} \left (25 x^4+300 x^3+900 x^2+e^6 \left (x^2+12 x+36\right )+10 e^3 \left (x^3+12 x^2+36 x\right )\right )\right )\right )}{50 x^3+450 x^2+15 e^3 \left (x^2+8 x+12\right )+900 x+e^6 (x+6)} \end {gather*}

Antiderivative was successfully veriﬁed.

[In]

Int[(E^E^((3600*x^2 + 1200*x^3 + 100*x^4 + E^6*(144 + 48*x + 4*x^2) + E^3*(1440*x + 480*x^2 + 40*x^3))/25)*(-2

5 + E^((3600*x^2 + 1200*x^3 + 100*x^4 + E^6*(144 + 48*x + 4*x^2) + E^3*(1440*x + 480*x^2 + 40*x^3))/25)*(14400

*x - 2800*x^3 - 400*x^4 + E^6*(96 - 32*x - 8*x^2) + E^3*(2880 + 480*x - 720*x^2 - 120*x^3))))/5,x]

[Out]

(5*E^E^((4*(900*x^2 + 300*x^3 + 25*x^4 + E^6*(36 + 12*x + x^2) + 10*E^3*(36*x + 12*x^2 + x^3)))/25)*(1800*x -

350*x^3 - 50*x^4 + E^6*(12 - 4*x - x^2) + 15*E^3*(24 + 4*x - 6*x^2 - x^3)))/(900*x + 450*x^2 + 50*x^3 + E^6*(6

+ x) + 15*E^3*(12 + 8*x + x^2))

Rule 12

Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] && !MatchQ[u, (b_)*(v_) /; FreeQ[b, x]]

Rule 2326

Int[(y_.)*(F_)^(u_)*((v_) + (w_)), x_Symbol] :> With[{z = v*(y/(Log[F]*D[u, x]))}, Simp[F^u*z, x] /; EqQ[D[z,

x], w*y]] /; FreeQ[F, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{5} \int \exp \left (\exp \left (\frac {1}{25} \left (3600 x^2+1200 x^3+100 x^4+e^6 \left (144+48 x+4 x^2\right )+e^3 \left (1440 x+480 x^2+40 x^3\right )\right )\right )\right ) \left (-25+\exp \left (\frac {1}{25} \left (3600 x^2+1200 x^3+100 x^4+e^6 \left (144+48 x+4 x^2\right )+e^3 \left (1440 x+480 x^2+40 x^3\right )\right )\right ) \left (14400 x-2800 x^3-400 x^4+e^6 \left (96-32 x-8 x^2\right )+e^3 \left (2880+480 x-720 x^2-120 x^3\right )\right )\right ) \, dx\\ &=\frac {5 \exp \left (\exp \left (\frac {4}{25} \left (900 x^2+300 x^3+25 x^4+e^6 \left (36+12 x+x^2\right )+10 e^3 \left (36 x+12 x^2+x^3\right )\right )\right )\right ) \left (1800 x-350 x^3-50 x^4+e^6 \left (12-4 x-x^2\right )+15 e^3 \left (24+4 x-6 x^2-x^3\right )\right )}{900 x+450 x^2+50 x^3+e^6 (6+x)+15 e^3 \left (12+8 x+x^2\right )}\\ \end {aligned} \end {gather*}

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Mathematica [A]
time = 0.10, size = 27, normalized size = 0.84 \begin {gather*} -5 e^{e^{\frac {4}{25} (6+x)^2 \left (e^3+5 x\right )^2}} (-2+x) \end {gather*}

Antiderivative was successfully veriﬁed.

[In]

Integrate[(E^E^((3600*x^2 + 1200*x^3 + 100*x^4 + E^6*(144 + 48*x + 4*x^2) + E^3*(1440*x + 480*x^2 + 40*x^3))/2

5)*(-25 + E^((3600*x^2 + 1200*x^3 + 100*x^4 + E^6*(144 + 48*x + 4*x^2) + E^3*(1440*x + 480*x^2 + 40*x^3))/25)*

(14400*x - 2800*x^3 - 400*x^4 + E^6*(96 - 32*x - 8*x^2) + E^3*(2880 + 480*x - 720*x^2 - 120*x^3))))/5,x]

[Out]

-5*E^E^((4*(6 + x)^2*(E^3 + 5*x)^2)/25)*(-2 + x)

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Maple [A]
time = 0.67, size = 30, normalized size = 0.94


method	result	size

risch	\(\frac {\left (-25 x +50\right ) {\mathrm e}^{{\mathrm e}^{\frac {4 \left (x +6\right )^{2} \left (10 x \,{\mathrm e}^{3}+25 x^{2}+{\mathrm e}^{6}\right )}{25}}}}{5}\)	\(30\)
norman	\(-5 x \,{\mathrm e}^{{\mathrm e}^{\frac {\left (4 x^{2}+48 x +144\right ) {\mathrm e}^{6}}{25}+\frac {\left (40 x^{3}+480 x^{2}+1440 x \right ) {\mathrm e}^{3}}{25}+4 x^{4}+48 x^{3}+144 x^{2}}}+10 \,{\mathrm e}^{{\mathrm e}^{\frac {\left (4 x^{2}+48 x +144\right ) {\mathrm e}^{6}}{25}+\frac {\left (40 x^{3}+480 x^{2}+1440 x \right ) {\mathrm e}^{3}}{25}+4 x^{4}+48 x^{3}+144 x^{2}}}\)	\(111\)

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int(1/5*(((-8*x^2-32*x+96)*exp(3)^2+(-120*x^3-720*x^2+480*x+2880)*exp(3)-400*x^4-2800*x^3+14400*x)*exp(1/25*(4

*x^2+48*x+144)*exp(3)^2+1/25*(40*x^3+480*x^2+1440*x)*exp(3)+4*x^4+48*x^3+144*x^2)-25)*exp(exp(1/25*(4*x^2+48*x

+144)*exp(3)^2+1/25*(40*x^3+480*x^2+1440*x)*exp(3)+4*x^4+48*x^3+144*x^2)),x,method=_RETURNVERBOSE)

[Out]

1/5*(-25*x+50)*exp(exp(4/25*(x+6)^2*(10*x*exp(3)+25*x^2+exp(6))))

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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 58 vs. \(2 (24) = 48\).
time = 0.45, size = 58, normalized size = 1.81 \begin {gather*} -5 \, {\left (x - 2\right )} e^{\left (e^{\left (4 \, x^{4} + \frac {8}{5} \, x^{3} e^{3} + 48 \, x^{3} + \frac {4}{25} \, x^{2} e^{6} + \frac {96}{5} \, x^{2} e^{3} + 144 \, x^{2} + \frac {48}{25} \, x e^{6} + \frac {288}{5} \, x e^{3} + \frac {144}{25} \, e^{6}\right )}\right )} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/5*(((-8*x^2-32*x+96)*exp(3)^2+(-120*x^3-720*x^2+480*x+2880)*exp(3)-400*x^4-2800*x^3+14400*x)*exp(1

/25*(4*x^2+48*x+144)*exp(3)^2+1/25*(40*x^3+480*x^2+1440*x)*exp(3)+4*x^4+48*x^3+144*x^2)-25)*exp(exp(1/25*(4*x^

2+48*x+144)*exp(3)^2+1/25*(40*x^3+480*x^2+1440*x)*exp(3)+4*x^4+48*x^3+144*x^2)),x, algorithm="maxima")

[Out]

-5*(x - 2)*e^(e^(4*x^4 + 8/5*x^3*e^3 + 48*x^3 + 4/25*x^2*e^6 + 96/5*x^2*e^3 + 144*x^2 + 48/25*x*e^6 + 288/5*x*

e^3 + 144/25*e^6))

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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 51 vs. \(2 (24) = 48\).
time = 0.39, size = 51, normalized size = 1.59 \begin {gather*} -5 \, {\left (x - 2\right )} e^{\left (e^{\left (4 \, x^{4} + 48 \, x^{3} + 144 \, x^{2} + \frac {4}{25} \, {\left (x^{2} + 12 \, x + 36\right )} e^{6} + \frac {8}{5} \, {\left (x^{3} + 12 \, x^{2} + 36 \, x\right )} e^{3}\right )}\right )} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/5*(((-8*x^2-32*x+96)*exp(3)^2+(-120*x^3-720*x^2+480*x+2880)*exp(3)-400*x^4-2800*x^3+14400*x)*exp(1

/25*(4*x^2+48*x+144)*exp(3)^2+1/25*(40*x^3+480*x^2+1440*x)*exp(3)+4*x^4+48*x^3+144*x^2)-25)*exp(exp(1/25*(4*x^

2+48*x+144)*exp(3)^2+1/25*(40*x^3+480*x^2+1440*x)*exp(3)+4*x^4+48*x^3+144*x^2)),x, algorithm="fricas")

[Out]

-5*(x - 2)*e^(e^(4*x^4 + 48*x^3 + 144*x^2 + 4/25*(x^2 + 12*x + 36)*e^6 + 8/5*(x^3 + 12*x^2 + 36*x)*e^3))

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Sympy [F(-2)]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: SystemError} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/5*(((-8*x**2-32*x+96)*exp(3)**2+(-120*x**3-720*x**2+480*x+2880)*exp(3)-400*x**4-2800*x**3+14400*x)

*exp(1/25*(4*x**2+48*x+144)*exp(3)**2+1/25*(40*x**3+480*x**2+1440*x)*exp(3)+4*x**4+48*x**3+144*x**2)-25)*exp(e

xp(1/25*(4*x**2+48*x+144)*exp(3)**2+1/25*(40*x**3+480*x**2+1440*x)*exp(3)+4*x**4+48*x**3+144*x**2)),x)

[Out]

Exception raised: SystemError >> excessive stack use: stack is 3003 deep

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Giac [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/5*(((-8*x^2-32*x+96)*exp(3)^2+(-120*x^3-720*x^2+480*x+2880)*exp(3)-400*x^4-2800*x^3+14400*x)*exp(1

/25*(4*x^2+48*x+144)*exp(3)^2+1/25*(40*x^3+480*x^2+1440*x)*exp(3)+4*x^4+48*x^3+144*x^2)-25)*exp(exp(1/25*(4*x^

2+48*x+144)*exp(3)^2+1/25*(40*x^3+480*x^2+1440*x)*exp(3)+4*x^4+48*x^3+144*x^2)),x, algorithm="giac")

[Out]

integrate(-1/5*(8*(50*x^4 + 350*x^3 + (x^2 + 4*x - 12)*e^6 + 15*(x^3 + 6*x^2 - 4*x - 24)*e^3 - 1800*x)*e^(4*x^

4 + 48*x^3 + 144*x^2 + 4/25*(x^2 + 12*x + 36)*e^6 + 8/5*(x^3 + 12*x^2 + 36*x)*e^3) + 25)*e^(e^(4*x^4 + 48*x^3

+ 144*x^2 + 4/25*(x^2 + 12*x + 36)*e^6 + 8/5*(x^3 + 12*x^2 + 36*x)*e^3)), x)

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Mupad [B]
time = 4.51, size = 66, normalized size = 2.06 \begin {gather*} -5\,{\mathrm {e}}^{{\mathrm {e}}^{\frac {8\,x^3\,{\mathrm {e}}^3}{5}}\,{\mathrm {e}}^{\frac {4\,x^2\,{\mathrm {e}}^6}{25}}\,{\mathrm {e}}^{\frac {96\,x^2\,{\mathrm {e}}^3}{5}}\,{\mathrm {e}}^{\frac {144\,{\mathrm {e}}^6}{25}}\,{\mathrm {e}}^{4\,x^4}\,{\mathrm {e}}^{48\,x^3}\,{\mathrm {e}}^{144\,x^2}\,{\mathrm {e}}^{\frac {48\,x\,{\mathrm {e}}^6}{25}}\,{\mathrm {e}}^{\frac {288\,x\,{\mathrm {e}}^3}{5}}}\,\left (x-2\right ) \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp(exp((exp(6)*(48*x + 4*x^2 + 144))/25 + (exp(3)*(1440*x + 480*x^2 + 40*x^3))/25 + 144*x^2 + 48*x^3 +

4*x^4))*(exp((exp(6)*(48*x + 4*x^2 + 144))/25 + (exp(3)*(1440*x + 480*x^2 + 40*x^3))/25 + 144*x^2 + 48*x^3 + 4

*x^4)*(exp(6)*(32*x + 8*x^2 - 96) - 14400*x - exp(3)*(480*x - 720*x^2 - 120*x^3 + 2880) + 2800*x^3 + 400*x^4)

+ 25))/5,x)

[Out]

-5*exp(exp((8*x^3*exp(3))/5)*exp((4*x^2*exp(6))/25)*exp((96*x^2*exp(3))/5)*exp((144*exp(6))/25)*exp(4*x^4)*exp

(48*x^3)*exp(144*x^2)*exp((48*x*exp(6))/25)*exp((288*x*exp(3))/5))*(x - 2)

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