∫ (50−10ex−10x) log2(−5+ex+x)+e 2x−2x2 ___________________ log (−5+ex+x) (−4x3+8x4−4x5+ex(−4x3+8x4−4x5)+(−20x2+64x3−52x4+8x5+ex(4x2−12x3+8x4)) log(−5+ex+x)+(−20x+34x2−6x3+ex(4x−6x2)) log2(−5+ex+x)) ___________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ (−125x2+25exx2+25x3) log2(−5+ex+x)+e 2x−2x2 ___________________ log (−5+ex+x) (50x3−60x4+10x5+ex(−10x3+10x4)) log2(−5+ex+x)+e 2(2x−2x2) ___________________ log (−5+ex+x) (−5x4+11x5−7x6+x7+ex(x4−2x5+x6)) log2(−5+ex+x) dx

Optimal. Leaf size=37 \[ \frac {2}{x \left (5-e^{\frac {2 (1-x) x}{\log \left (-5+e^x+x\right )}} \left (x-x^2\right )\right )} \]

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Rubi [F] time = 180.00, 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*}

Int[((50 - 10*E^x - 10*x)*Log[-5 + E^x + x]^2 + E^((2*x - 2*x^2)/Log[-5 + E^x + x])*(-4*x^3 + 8*x^4 - 4*x^5 +

E^x*(-4*x^3 + 8*x^4 - 4*x^5) + (-20*x^2 + 64*x^3 - 52*x^4 + 8*x^5 + E^x*(4*x^2 - 12*x^3 + 8*x^4))*Log[-5 + E^x

+ x] + (-20*x + 34*x^2 - 6*x^3 + E^x*(4*x - 6*x^2))*Log[-5 + E^x + x]^2))/((-125*x^2 + 25*E^x*x^2 + 25*x^3)*L

og[-5 + E^x + x]^2 + E^((2*x - 2*x^2)/Log[-5 + E^x + x])*(50*x^3 - 60*x^4 + 10*x^5 + E^x*(-10*x^3 + 10*x^4))*L

og[-5 + E^x + x]^2 + E^((2*(2*x - 2*x^2))/Log[-5 + E^x + x])*(-5*x^4 + 11*x^5 - 7*x^6 + x^7 + E^x*(x^4 - 2*x^5

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Mathematica [A] time = 0.51, size = 61, normalized size = 1.65 \begin {gather*} \frac {2 e^{\frac {2 x^2}{\log \left (-5+e^x+x\right )}}}{x \left (5 e^{\frac {2 x^2}{\log \left (-5+e^x+x\right )}}+e^{\frac {2 x}{\log \left (-5+e^x+x\right )}} (-1+x) x\right )} \end {gather*}

Integrate[((50 - 10*E^x - 10*x)*Log[-5 + E^x + x]^2 + E^((2*x - 2*x^2)/Log[-5 + E^x + x])*(-4*x^3 + 8*x^4 - 4*

x^5 + E^x*(-4*x^3 + 8*x^4 - 4*x^5) + (-20*x^2 + 64*x^3 - 52*x^4 + 8*x^5 + E^x*(4*x^2 - 12*x^3 + 8*x^4))*Log[-5

+ E^x + x] + (-20*x + 34*x^2 - 6*x^3 + E^x*(4*x - 6*x^2))*Log[-5 + E^x + x]^2))/((-125*x^2 + 25*E^x*x^2 + 25*

x^3)*Log[-5 + E^x + x]^2 + E^((2*x - 2*x^2)/Log[-5 + E^x + x])*(50*x^3 - 60*x^4 + 10*x^5 + E^x*(-10*x^3 + 10*x

^4))*Log[-5 + E^x + x]^2 + E^((2*(2*x - 2*x^2))/Log[-5 + E^x + x])*(-5*x^4 + 11*x^5 - 7*x^6 + x^7 + E^x*(x^4 -

(2*E^((2*x^2)/Log[-5 + E^x + x]))/(x*(5*E^((2*x^2)/Log[-5 + E^x + x]) + E^((2*x)/Log[-5 + E^x + x])*(-1 + x)*x

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fricas [A] time = 0.63, size = 36, normalized size = 0.97 \begin {gather*} \frac {2}{{\left (x^{3} - x^{2}\right )} e^{\left (-\frac {2 \, {\left (x^{2} - x\right )}}{\log \left (x + e^{x} - 5\right )}\right )} + 5 \, x} \end {gather*}

integrate(((((-6*x^2+4*x)*exp(x)-6*x^3+34*x^2-20*x)*log(exp(x)+x-5)^2+((8*x^4-12*x^3+4*x^2)*exp(x)+8*x^5-52*x^

4+64*x^3-20*x^2)*log(exp(x)+x-5)+(-4*x^5+8*x^4-4*x^3)*exp(x)-4*x^5+8*x^4-4*x^3)*exp((-2*x^2+2*x)/log(exp(x)+x-

5))+(-10*exp(x)-10*x+50)*log(exp(x)+x-5)^2)/(((x^6-2*x^5+x^4)*exp(x)+x^7-7*x^6+11*x^5-5*x^4)*log(exp(x)+x-5)^2

*exp((-2*x^2+2*x)/log(exp(x)+x-5))^2+((10*x^4-10*x^3)*exp(x)+10*x^5-60*x^4+50*x^3)*log(exp(x)+x-5)^2*exp((-2*x

^2+2*x)/log(exp(x)+x-5))+(25*exp(x)*x^2+25*x^3-125*x^2)*log(exp(x)+x-5)^2),x, algorithm="fricas")

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

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

integrate(((((-6*x^2+4*x)*exp(x)-6*x^3+34*x^2-20*x)*log(exp(x)+x-5)^2+((8*x^4-12*x^3+4*x^2)*exp(x)+8*x^5-52*x^

4+64*x^3-20*x^2)*log(exp(x)+x-5)+(-4*x^5+8*x^4-4*x^3)*exp(x)-4*x^5+8*x^4-4*x^3)*exp((-2*x^2+2*x)/log(exp(x)+x-

5))+(-10*exp(x)-10*x+50)*log(exp(x)+x-5)^2)/(((x^6-2*x^5+x^4)*exp(x)+x^7-7*x^6+11*x^5-5*x^4)*log(exp(x)+x-5)^2

*exp((-2*x^2+2*x)/log(exp(x)+x-5))^2+((10*x^4-10*x^3)*exp(x)+10*x^5-60*x^4+50*x^3)*log(exp(x)+x-5)^2*exp((-2*x

^2+2*x)/log(exp(x)+x-5))+(25*exp(x)*x^2+25*x^3-125*x^2)*log(exp(x)+x-5)^2),x, algorithm="giac")

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

UT:Evaluation time: 5.85Unable to divide, perhaps due to rounding error%%%{8,[0,10,17]%%%}+%%%{-96,[0,10,16]%%

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method	result	size

risch	$\frac {2}{x \left (x^{2} {\mathrm e}^{-\frac {2 x \left (x -1\right )}{\ln \left ({\mathrm e}^{x}+x -5\right )}}-x \,{\mathrm e}^{-\frac {2 x \left (x -1\right )}{\ln \left ({\mathrm e}^{x}+x -5\right )}}+5\right )}$	$47$

int(((((-6*x^2+4*x)*exp(x)-6*x^3+34*x^2-20*x)*ln(exp(x)+x-5)^2+((8*x^4-12*x^3+4*x^2)*exp(x)+8*x^5-52*x^4+64*x^

3-20*x^2)*ln(exp(x)+x-5)+(-4*x^5+8*x^4-4*x^3)*exp(x)-4*x^5+8*x^4-4*x^3)*exp((-2*x^2+2*x)/ln(exp(x)+x-5))+(-10*

exp(x)-10*x+50)*ln(exp(x)+x-5)^2)/(((x^6-2*x^5+x^4)*exp(x)+x^7-7*x^6+11*x^5-5*x^4)*ln(exp(x)+x-5)^2*exp((-2*x^

2+2*x)/ln(exp(x)+x-5))^2+((10*x^4-10*x^3)*exp(x)+10*x^5-60*x^4+50*x^3)*ln(exp(x)+x-5)^2*exp((-2*x^2+2*x)/ln(ex

p(x)+x-5))+(25*exp(x)*x^2+25*x^3-125*x^2)*ln(exp(x)+x-5)^2),x,method=_RETURNVERBOSE)

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

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maxima [A] time = 1.12, size = 58, normalized size = 1.57 \begin {gather*} \frac {2 \, e^{\left (\frac {2 \, x^{2}}{\log \left (x + e^{x} - 5\right )}\right )}}{5 \, x e^{\left (\frac {2 \, x^{2}}{\log \left (x + e^{x} - 5\right )}\right )} + {\left (x^{3} - x^{2}\right )} e^{\left (\frac {2 \, x}{\log \left (x + e^{x} - 5\right )}\right )}} \end {gather*}

integrate(((((-6*x^2+4*x)*exp(x)-6*x^3+34*x^2-20*x)*log(exp(x)+x-5)^2+((8*x^4-12*x^3+4*x^2)*exp(x)+8*x^5-52*x^

4+64*x^3-20*x^2)*log(exp(x)+x-5)+(-4*x^5+8*x^4-4*x^3)*exp(x)-4*x^5+8*x^4-4*x^3)*exp((-2*x^2+2*x)/log(exp(x)+x-

5))+(-10*exp(x)-10*x+50)*log(exp(x)+x-5)^2)/(((x^6-2*x^5+x^4)*exp(x)+x^7-7*x^6+11*x^5-5*x^4)*log(exp(x)+x-5)^2

*exp((-2*x^2+2*x)/log(exp(x)+x-5))^2+((10*x^4-10*x^3)*exp(x)+10*x^5-60*x^4+50*x^3)*log(exp(x)+x-5)^2*exp((-2*x

^2+2*x)/log(exp(x)+x-5))+(25*exp(x)*x^2+25*x^3-125*x^2)*log(exp(x)+x-5)^2),x, algorithm="maxima")

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

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mupad [F] time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int -\frac {{\ln \left (x+{\mathrm {e}}^x-5\right )}^2\,\left (10\,x+10\,{\mathrm {e}}^x-50\right )+{\mathrm {e}}^{\frac {2\,x-2\,x^2}{\ln \left (x+{\mathrm {e}}^x-5\right )}}\,\left ({\ln \left (x+{\mathrm {e}}^x-5\right )}^2\,\left (20\,x-{\mathrm {e}}^x\,\left (4\,x-6\,x^2\right )-34\,x^2+6\,x^3\right )+{\mathrm {e}}^x\,\left (4\,x^5-8\,x^4+4\,x^3\right )+4\,x^3-8\,x^4+4\,x^5-\ln \left (x+{\mathrm {e}}^x-5\right )\,\left ({\mathrm {e}}^x\,\left (8\,x^4-12\,x^3+4\,x^2\right )-20\,x^2+64\,x^3-52\,x^4+8\,x^5\right )\right )}{{\ln \left (x+{\mathrm {e}}^x-5\right )}^2\,\left (25\,x^2\,{\mathrm {e}}^x-125\,x^2+25\,x^3\right )-{\ln \left (x+{\mathrm {e}}^x-5\right )}^2\,{\mathrm {e}}^{\frac {2\,x-2\,x^2}{\ln \left (x+{\mathrm {e}}^x-5\right )}}\,\left ({\mathrm {e}}^x\,\left (10\,x^3-10\,x^4\right )-50\,x^3+60\,x^4-10\,x^5\right )+{\ln \left (x+{\mathrm {e}}^x-5\right )}^2\,{\mathrm {e}}^{\frac {2\,\left (2\,x-2\,x^2\right )}{\ln \left (x+{\mathrm {e}}^x-5\right )}}\,\left ({\mathrm {e}}^x\,\left (x^6-2\,x^5+x^4\right )-5\,x^4+11\,x^5-7\,x^6+x^7\right )} \,d x \end {gather*}

int(-(log(x + exp(x) - 5)^2*(10*x + 10*exp(x) - 50) + exp((2*x - 2*x^2)/log(x + exp(x) - 5))*(log(x + exp(x) -

5)^2*(20*x - exp(x)*(4*x - 6*x^2) - 34*x^2 + 6*x^3) + exp(x)*(4*x^3 - 8*x^4 + 4*x^5) + 4*x^3 - 8*x^4 + 4*x^5

- log(x + exp(x) - 5)*(exp(x)*(4*x^2 - 12*x^3 + 8*x^4) - 20*x^2 + 64*x^3 - 52*x^4 + 8*x^5)))/(log(x + exp(x) -

5)^2*(25*x^2*exp(x) - 125*x^2 + 25*x^3) - log(x + exp(x) - 5)^2*exp((2*x - 2*x^2)/log(x + exp(x) - 5))*(exp(x

)*(10*x^3 - 10*x^4) - 50*x^3 + 60*x^4 - 10*x^5) + log(x + exp(x) - 5)^2*exp((2*(2*x - 2*x^2))/log(x + exp(x) -

5))*(exp(x)*(x^4 - 2*x^5 + x^6) - 5*x^4 + 11*x^5 - 7*x^6 + x^7)),x)

int(-(log(x + exp(x) - 5)^2*(10*x + 10*exp(x) - 50) + exp((2*x - 2*x^2)/log(x + exp(x) - 5))*(log(x + exp(x) -

5)^2*(20*x - exp(x)*(4*x - 6*x^2) - 34*x^2 + 6*x^3) + exp(x)*(4*x^3 - 8*x^4 + 4*x^5) + 4*x^3 - 8*x^4 + 4*x^5

- log(x + exp(x) - 5)*(exp(x)*(4*x^2 - 12*x^3 + 8*x^4) - 20*x^2 + 64*x^3 - 52*x^4 + 8*x^5)))/(log(x + exp(x) -

5)^2*(25*x^2*exp(x) - 125*x^2 + 25*x^3) - log(x + exp(x) - 5)^2*exp((2*x - 2*x^2)/log(x + exp(x) - 5))*(exp(x

)*(10*x^3 - 10*x^4) - 50*x^3 + 60*x^4 - 10*x^5) + log(x + exp(x) - 5)^2*exp((2*(2*x - 2*x^2))/log(x + exp(x) -

5))*(exp(x)*(x^4 - 2*x^5 + x^6) - 5*x^4 + 11*x^5 - 7*x^6 + x^7)), x)

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

integrate(((((-6*x**2+4*x)*exp(x)-6*x**3+34*x**2-20*x)*ln(exp(x)+x-5)**2+((8*x**4-12*x**3+4*x**2)*exp(x)+8*x**

5-52*x**4+64*x**3-20*x**2)*ln(exp(x)+x-5)+(-4*x**5+8*x**4-4*x**3)*exp(x)-4*x**5+8*x**4-4*x**3)*exp((-2*x**2+2*

x)/ln(exp(x)+x-5))+(-10*exp(x)-10*x+50)*ln(exp(x)+x-5)**2)/(((x**6-2*x**5+x**4)*exp(x)+x**7-7*x**6+11*x**5-5*x

**4)*ln(exp(x)+x-5)**2*exp((-2*x**2+2*x)/ln(exp(x)+x-5))**2+((10*x**4-10*x**3)*exp(x)+10*x**5-60*x**4+50*x**3)

*ln(exp(x)+x-5)**2*exp((-2*x**2+2*x)/ln(exp(x)+x-5))+(25*exp(x)*x**2+25*x**3-125*x**2)*ln(exp(x)+x-5)**2),x)

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