∫ e x ____________ 2−x+log(2) (−2x−x log(2))+e450+ x______2−x+log (2)+50 log2(x2) (−2x−x log(2)) x600 +e225+25 log2(x2) (600−600x+150x2+(600−300x) log(2)+150 log2(2)+e x ____________ 2−x+log(2) (4x+2x log(2))+(−200+200x−50x2+(−200+100x) log(2)−50 log2(2)) log(x2)) __________________________________________________________________________________________________________________________________________________________________________________________________________________x300 _______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ 4x−4x2+x3+(4x−2x2) log(2)+x log2(2)+e225+25 log2(x2)(−8x+8x2−2x3+(−8x+4x2) log(2)−2x log2(2)) _____________________________________________________________________________________x300+e450+50 log2(x2)(4x−4x2+x3+(4x−2x2) log(2)+x log2(2)) _____________________________________________________________________________

3.68.67 $\int \frac {e^{\frac {x}{2-x+\log (2)}} (-2 x-x \log (2))+\frac {e^{450+\frac {x}{2-x+\log (2)}+50 \log ^2(x^2)} (-2 x-x \log (2))}{x^{600}}+\frac {e^{225+25 \log ^2(x^2)} (600-600 x+150 x^2+(600-300 x) \log (2)+150 \log ^2(2)+e^{\frac {x}{2-x+\log (2)}} (4 x+2 x \log (2))+(-200+200 x-50 x^2+(-200+100 x) \log (2)-50 \log ^2(2)) \log (x^2))}{x^{300}}}{4 x-4 x^2+x^3+(4 x-2 x^2) \log (2)+x \log ^2(2)+\frac {e^{225+25 \log ^2(x^2)} (-8 x+8 x^2-2 x^3+(-8 x+4 x^2) \log (2)-2 x \log ^2(2))}{x^{300}}+\frac {e^{450+50 \log ^2(x^2)} (4 x-4 x^2+x^3+(4 x-2 x^2) \log (2)+x \log ^2(2))}{x^{600}}} \, dx$

Optimal. Leaf size=38 \[ -e^{\frac {x}{2-x+\log (2)}}+\frac {1}{2 \left (-1+e^{25 \left (3-\log \left (x^2\right )\right )^2}\right )} \]

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Rubi [F] time = 180.08, 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*} \text {\$Aborted} \end {gather*}

Veriﬁcation is not applicable to the result.

[In]

Int[(E^(x/(2 - x + Log[2]))*(-2*x - x*Log[2]) + (E^(450 + x/(2 - x + Log[2]) + 50*Log[x^2]^2)*(-2*x - x*Log[2]

))/x^600 + (E^(225 + 25*Log[x^2]^2)*(600 - 600*x + 150*x^2 + (600 - 300*x)*Log[2] + 150*Log[2]^2 + E^(x/(2 - x

+ Log[2]))*(4*x + 2*x*Log[2]) + (-200 + 200*x - 50*x^2 + (-200 + 100*x)*Log[2] - 50*Log[2]^2)*Log[x^2]))/x^30

0)/(4*x - 4*x^2 + x^3 + (4*x - 2*x^2)*Log[2] + x*Log[2]^2 + (E^(225 + 25*Log[x^2]^2)*(-8*x + 8*x^2 - 2*x^3 + (

-8*x + 4*x^2)*Log[2] - 2*x*Log[2]^2))/x^300 + (E^(450 + 50*Log[x^2]^2)*(4*x - 4*x^2 + x^3 + (4*x - 2*x^2)*Log[

2] + x*Log[2]^2))/x^600),x]

[Out]

$Aborted

Rubi steps

Aborted

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Mathematica [F] time = 180.08, size = 0, normalized size = 0.00 \begin {gather*} \text {\$Aborted} \end {gather*}

Veriﬁcation is not applicable to the result.

[In]

Integrate[(E^(x/(2 - x + Log[2]))*(-2*x - x*Log[2]) + (E^(450 + x/(2 - x + Log[2]) + 50*Log[x^2]^2)*(-2*x - x*

Log[2]))/x^600 + (E^(225 + 25*Log[x^2]^2)*(600 - 600*x + 150*x^2 + (600 - 300*x)*Log[2] + 150*Log[2]^2 + E^(x/

(2 - x + Log[2]))*(4*x + 2*x*Log[2]) + (-200 + 200*x - 50*x^2 + (-200 + 100*x)*Log[2] - 50*Log[2]^2)*Log[x^2])

)/x^300)/(4*x - 4*x^2 + x^3 + (4*x - 2*x^2)*Log[2] + x*Log[2]^2 + (E^(225 + 25*Log[x^2]^2)*(-8*x + 8*x^2 - 2*x

^3 + (-8*x + 4*x^2)*Log[2] - 2*x*Log[2]^2))/x^300 + (E^(450 + 50*Log[x^2]^2)*(4*x - 4*x^2 + x^3 + (4*x - 2*x^2

)*Log[2] + x*Log[2]^2))/x^600),x]

[Out]

$Aborted

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fricas [B] time = 0.54, size = 71, normalized size = 1.87 \begin {gather*} -\frac {2 \, e^{\left (25 \, \log \left (x^{2}\right )^{2} - \frac {x}{x - \log \relax (2) - 2} - 150 \, \log \left (x^{2}\right ) + 225\right )} - 2 \, e^{\left (-\frac {x}{x - \log \relax (2) - 2}\right )} - 1}{2 \, {\left (e^{\left (25 \, \log \left (x^{2}\right )^{2} - 150 \, \log \left (x^{2}\right ) + 225\right )} - 1\right )}} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-x*log(2)-2*x)*exp(x/(log(2)+2-x))*exp(25*log(x^2)^2-150*log(x^2)+225)^2+((-50*log(2)^2+(100*x-200

)*log(2)-50*x^2+200*x-200)*log(x^2)+(2*x*log(2)+4*x)*exp(x/(log(2)+2-x))+150*log(2)^2+(-300*x+600)*log(2)+150*

x^2-600*x+600)*exp(25*log(x^2)^2-150*log(x^2)+225)+(-x*log(2)-2*x)*exp(x/(log(2)+2-x)))/((x*log(2)^2+(-2*x^2+4

*x)*log(2)+x^3-4*x^2+4*x)*exp(25*log(x^2)^2-150*log(x^2)+225)^2+(-2*x*log(2)^2+(4*x^2-8*x)*log(2)-2*x^3+8*x^2-

8*x)*exp(25*log(x^2)^2-150*log(x^2)+225)+x*log(2)^2+(-2*x^2+4*x)*log(2)+x^3-4*x^2+4*x),x, algorithm="fricas")

[Out]

-1/2*(2*e^(25*log(x^2)^2 - x/(x - log(2) - 2) - 150*log(x^2) + 225) - 2*e^(-x/(x - log(2) - 2)) - 1)/(e^(25*lo

g(x^2)^2 - 150*log(x^2) + 225) - 1)

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

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-x*log(2)-2*x)*exp(x/(log(2)+2-x))*exp(25*log(x^2)^2-150*log(x^2)+225)^2+((-50*log(2)^2+(100*x-200

)*log(2)-50*x^2+200*x-200)*log(x^2)+(2*x*log(2)+4*x)*exp(x/(log(2)+2-x))+150*log(2)^2+(-300*x+600)*log(2)+150*

x^2-600*x+600)*exp(25*log(x^2)^2-150*log(x^2)+225)+(-x*log(2)-2*x)*exp(x/(log(2)+2-x)))/((x*log(2)^2+(-2*x^2+4

*x)*log(2)+x^3-4*x^2+4*x)*exp(25*log(x^2)^2-150*log(x^2)+225)^2+(-2*x*log(2)^2+(4*x^2-8*x)*log(2)-2*x^3+8*x^2-

8*x)*exp(25*log(x^2)^2-150*log(x^2)+225)+x*log(2)^2+(-2*x^2+4*x)*log(2)+x^3-4*x^2+4*x),x, algorithm="giac")

[Out]

Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,sageVARx):;OUTP

UT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Ch

eck [abs(sa

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maple [C] time = 1.40, size = 162, normalized size = 4.26


method	result	size

risch	$-{\mathrm e}^{\frac {x}{\ln \relax (2)+2-x}}+\frac {1}{\frac {2 x^{-100 i \pi \,\mathrm {csgn}\left (i x^{2}\right )} x^{100 i \pi \,\mathrm {csgn}\left (i x \right )} {\mathrm e}^{100 \ln \relax (x )^{2}+225} {\mathrm e}^{-\frac {25 \pi ^{2} \mathrm {csgn}\left (i x^{2}\right )^{6}}{4}} {\mathrm e}^{25 \pi ^{2} \mathrm {csgn}\left (i x^{2}\right )^{5} \mathrm {csgn}\left (i x \right )} {\mathrm e}^{-\frac {75 \pi ^{2} \mathrm {csgn}\left (i x^{2}\right )^{4} \mathrm {csgn}\left (i x \right )^{2}}{2}} {\mathrm e}^{25 \pi ^{2} \mathrm {csgn}\left (i x^{2}\right )^{3} \mathrm {csgn}\left (i x \right )^{3}} {\mathrm e}^{-\frac {25 \pi ^{2} \mathrm {csgn}\left (i x^{2}\right )^{2} \mathrm {csgn}\left (i x \right )^{4}}{4}}}{x^{300}}-2}$	$162$

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int(((-x*ln(2)-2*x)*exp(x/(ln(2)+2-x))*exp(25*ln(x^2)^2-150*ln(x^2)+225)^2+((-50*ln(2)^2+(100*x-200)*ln(2)-50*

x^2+200*x-200)*ln(x^2)+(2*x*ln(2)+4*x)*exp(x/(ln(2)+2-x))+150*ln(2)^2+(-300*x+600)*ln(2)+150*x^2-600*x+600)*ex

p(25*ln(x^2)^2-150*ln(x^2)+225)+(-x*ln(2)-2*x)*exp(x/(ln(2)+2-x)))/((x*ln(2)^2+(-2*x^2+4*x)*ln(2)+x^3-4*x^2+4*

x)*exp(25*ln(x^2)^2-150*ln(x^2)+225)^2+(-2*x*ln(2)^2+(4*x^2-8*x)*ln(2)-2*x^3+8*x^2-8*x)*exp(25*ln(x^2)^2-150*l

n(x^2)+225)+x*ln(2)^2+(-2*x^2+4*x)*ln(2)+x^3-4*x^2+4*x),x,method=_RETURNVERBOSE)

[Out]

-exp(x/(ln(2)+2-x))+1/2/(1/x^300*(x^(-50*I*Pi*csgn(I*x^2)))^2*x^(100*I*Pi*csgn(I*x))*exp(100*ln(x)^2+225)*exp(

-25/4*Pi^2*csgn(I*x^2)^6)*exp(25*Pi^2*csgn(I*x^2)^5*csgn(I*x))*exp(-75/2*Pi^2*csgn(I*x^2)^4*csgn(I*x)^2)*exp(2

5*Pi^2*csgn(I*x^2)^3*csgn(I*x)^3)*exp(-25/4*Pi^2*csgn(I*x^2)^2*csgn(I*x)^4)-1)

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maxima [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-x*log(2)-2*x)*exp(x/(log(2)+2-x))*exp(25*log(x^2)^2-150*log(x^2)+225)^2+((-50*log(2)^2+(100*x-200

)*log(2)-50*x^2+200*x-200)*log(x^2)+(2*x*log(2)+4*x)*exp(x/(log(2)+2-x))+150*log(2)^2+(-300*x+600)*log(2)+150*

x^2-600*x+600)*exp(25*log(x^2)^2-150*log(x^2)+225)+(-x*log(2)-2*x)*exp(x/(log(2)+2-x)))/((x*log(2)^2+(-2*x^2+4

*x)*log(2)+x^3-4*x^2+4*x)*exp(25*log(x^2)^2-150*log(x^2)+225)^2+(-2*x*log(2)^2+(4*x^2-8*x)*log(2)-2*x^3+8*x^2-

8*x)*exp(25*log(x^2)^2-150*log(x^2)+225)+x*log(2)^2+(-2*x^2+4*x)*log(2)+x^3-4*x^2+4*x),x, algorithm="maxima")

[Out]

Timed out

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mupad [F(-1)] time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \text {Hanged} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp(x/(log(2) - x + 2))*(2*x + x*log(2)) - exp(25*log(x^2)^2 - 150*log(x^2) + 225)*(exp(x/(log(2) - x +

2))*(4*x + 2*x*log(2)) - log(2)*(300*x - 600) - 600*x - log(x^2)*(50*log(2)^2 - log(2)*(100*x - 200) - 200*x +

50*x^2 + 200) + 150*log(2)^2 + 150*x^2 + 600) + exp(x/(log(2) - x + 2))*exp(50*log(x^2)^2 - 300*log(x^2) + 45

0)*(2*x + x*log(2)))/(4*x + log(2)*(4*x - 2*x^2) - exp(25*log(x^2)^2 - 150*log(x^2) + 225)*(8*x + log(2)*(8*x

- 4*x^2) + 2*x*log(2)^2 - 8*x^2 + 2*x^3) + x*log(2)^2 - 4*x^2 + x^3 + exp(50*log(x^2)^2 - 300*log(x^2) + 450)*

(4*x + log(2)*(4*x - 2*x^2) + x*log(2)^2 - 4*x^2 + x^3)),x)

[Out]

\text{Hanged}

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sympy [A] time = 1.20, size = 31, normalized size = 0.82 \begin {gather*} \frac {x^{300}}{- 2 x^{300} + 2 e^{25 \log {\left (x^{2} \right )}^{2} + 225}} - e^{\frac {x}{- x + \log {\relax (2 )} + 2}} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-x*ln(2)-2*x)*exp(x/(ln(2)+2-x))*exp(25*ln(x**2)**2-150*ln(x**2)+225)**2+((-50*ln(2)**2+(100*x-200

)*ln(2)-50*x**2+200*x-200)*ln(x**2)+(2*x*ln(2)+4*x)*exp(x/(ln(2)+2-x))+150*ln(2)**2+(-300*x+600)*ln(2)+150*x**

2-600*x+600)*exp(25*ln(x**2)**2-150*ln(x**2)+225)+(-x*ln(2)-2*x)*exp(x/(ln(2)+2-x)))/((x*ln(2)**2+(-2*x**2+4*x

)*ln(2)+x**3-4*x**2+4*x)*exp(25*ln(x**2)**2-150*ln(x**2)+225)**2+(-2*x*ln(2)**2+(4*x**2-8*x)*ln(2)-2*x**3+8*x*

*2-8*x)*exp(25*ln(x**2)**2-150*ln(x**2)+225)+x*ln(2)**2+(-2*x**2+4*x)*ln(2)+x**3-4*x**2+4*x),x)

[Out]

x**300/(-2*x**300 + 2*exp(25*log(x**2)**2 + 225)) - exp(x/(-x + log(2) + 2))

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