∫ e144x2−e4x2 x2−288x3−2e2x2 x3+143x4+(288x−288x2) log(x)+144 log2(x) ___________________________________________________________________________________________________ 9e4x2+18e2x2x+9x2 (288x2−2e6x2 x2−288x3−6e4x2 x3−288x4+286x5+e2x2 (288x−864x3−582x4+2304x5−1152x6)+(288x−288x2+e2x2 (288+288x−576x2−2304x3+2304x4)) log(x)+(−288x−1152e2x2 x2) log2(x))_______________________________________________________________________________________________________________________________________________________________________________________

Optimal. Leaf size=36 \[ e^{-\frac {x^2}{9}+\frac {16 \left (-x+x^2-\log (x)\right )^2}{\left (e^{2 x^2}+x\right )^2}} \]

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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[(E^((144*x^2 - E^(4*x^2)*x^2 - 288*x^3 - 2*E^(2*x^2)*x^3 + 143*x^4 + (288*x - 288*x^2)*Log[x] + 144*Log[x]

^2)/(9*E^(4*x^2) + 18*E^(2*x^2)*x + 9*x^2))*(288*x^2 - 2*E^(6*x^2)*x^2 - 288*x^3 - 6*E^(4*x^2)*x^3 - 288*x^4 +

286*x^5 + E^(2*x^2)*(288*x - 864*x^3 - 582*x^4 + 2304*x^5 - 1152*x^6) + (288*x - 288*x^2 + E^(2*x^2)*(288 + 2

88*x - 576*x^2 - 2304*x^3 + 2304*x^4))*Log[x] + (-288*x - 1152*E^(2*x^2)*x^2)*Log[x]^2))/(9*E^(6*x^2)*x + 27*E

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Mathematica [B] time = 0.73, size = 77, normalized size = 2.14 \begin {gather*} e^{\frac {x^2 \left (144-e^{4 x^2}-288 x-2 e^{2 x^2} x+143 x^2\right )+144 \log ^2(x)}{9 \left (e^{2 x^2}+x\right )^2}} x^{-\frac {32 (-1+x) x}{\left (e^{2 x^2}+x\right )^2}} \end {gather*}

Integrate[(E^((144*x^2 - E^(4*x^2)*x^2 - 288*x^3 - 2*E^(2*x^2)*x^3 + 143*x^4 + (288*x - 288*x^2)*Log[x] + 144*

Log[x]^2)/(9*E^(4*x^2) + 18*E^(2*x^2)*x + 9*x^2))*(288*x^2 - 2*E^(6*x^2)*x^2 - 288*x^3 - 6*E^(4*x^2)*x^3 - 288

*x^4 + 286*x^5 + E^(2*x^2)*(288*x - 864*x^3 - 582*x^4 + 2304*x^5 - 1152*x^6) + (288*x - 288*x^2 + E^(2*x^2)*(2

88 + 288*x - 576*x^2 - 2304*x^3 + 2304*x^4))*Log[x] + (-288*x - 1152*E^(2*x^2)*x^2)*Log[x]^2))/(9*E^(6*x^2)*x

E^((x^2*(144 - E^(4*x^2) - 288*x - 2*E^(2*x^2)*x + 143*x^2) + 144*Log[x]^2)/(9*(E^(2*x^2) + x)^2))/x^((32*(-1

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fricas [B] time = 0.62, size = 79, normalized size = 2.19 \begin {gather*} e^{\left (\frac {143 \, x^{4} - 2 \, x^{3} e^{\left (2 \, x^{2}\right )} - 288 \, x^{3} - x^{2} e^{\left (4 \, x^{2}\right )} + 144 \, x^{2} - 288 \, {\left (x^{2} - x\right )} \log \relax (x) + 144 \, \log \relax (x)^{2}}{9 \, {\left (x^{2} + 2 \, x e^{\left (2 \, x^{2}\right )} + e^{\left (4 \, x^{2}\right )}\right )}}\right )} \end {gather*}

integrate(((-1152*x^2*exp(x^2)^2-288*x)*log(x)^2+((2304*x^4-2304*x^3-576*x^2+288*x+288)*exp(x^2)^2-288*x^2+288

*x)*log(x)-2*x^2*exp(x^2)^6-6*x^3*exp(x^2)^4+(-1152*x^6+2304*x^5-582*x^4-864*x^3+288*x)*exp(x^2)^2+286*x^5-288

*x^4-288*x^3+288*x^2)*exp((144*log(x)^2+(-288*x^2+288*x)*log(x)-x^2*exp(x^2)^4-2*x^3*exp(x^2)^2+143*x^4-288*x^

3+144*x^2)/(9*exp(x^2)^4+18*x*exp(x^2)^2+9*x^2))/(9*x*exp(x^2)^6+27*x^2*exp(x^2)^4+27*x^3*exp(x^2)^2+9*x^4),x,

e^(1/9*(143*x^4 - 2*x^3*e^(2*x^2) - 288*x^3 - x^2*e^(4*x^2) + 144*x^2 - 288*(x^2 - x)*log(x) + 144*log(x)^2)/(

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

integrate(((-1152*x^2*exp(x^2)^2-288*x)*log(x)^2+((2304*x^4-2304*x^3-576*x^2+288*x+288)*exp(x^2)^2-288*x^2+288

*x)*log(x)-2*x^2*exp(x^2)^6-6*x^3*exp(x^2)^4+(-1152*x^6+2304*x^5-582*x^4-864*x^3+288*x)*exp(x^2)^2+286*x^5-288

*x^4-288*x^3+288*x^2)*exp((144*log(x)^2+(-288*x^2+288*x)*log(x)-x^2*exp(x^2)^4-2*x^3*exp(x^2)^2+143*x^4-288*x^

3+144*x^2)/(9*exp(x^2)^4+18*x*exp(x^2)^2+9*x^2))/(9*x*exp(x^2)^6+27*x^2*exp(x^2)^4+27*x^3*exp(x^2)^2+9*x^4),x,

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method	result	size

risch	${\mathrm e}^{\frac {-2 x^{3} {\mathrm e}^{2 x^{2}}+143 x^{4}-288 x^{2} \ln \relax (x )-x^{2} {\mathrm e}^{4 x^{2}}-288 x^{3}+144 \ln \relax (x )^{2}+288 x \ln \relax (x )+144 x^{2}}{9 \,{\mathrm e}^{4 x^{2}}+18 x \,{\mathrm e}^{2 x^{2}}+9 x^{2}}}$	$81$

int(((-1152*x^2*exp(x^2)^2-288*x)*ln(x)^2+((2304*x^4-2304*x^3-576*x^2+288*x+288)*exp(x^2)^2-288*x^2+288*x)*ln(

x)-2*x^2*exp(x^2)^6-6*x^3*exp(x^2)^4+(-1152*x^6+2304*x^5-582*x^4-864*x^3+288*x)*exp(x^2)^2+286*x^5-288*x^4-288

*x^3+288*x^2)*exp((144*ln(x)^2+(-288*x^2+288*x)*ln(x)-x^2*exp(x^2)^4-2*x^3*exp(x^2)^2+143*x^4-288*x^3+144*x^2)

/(9*exp(x^2)^4+18*x*exp(x^2)^2+9*x^2))/(9*x*exp(x^2)^6+27*x^2*exp(x^2)^4+27*x^3*exp(x^2)^2+9*x^4),x,method=_RE

exp(1/9*(-2*x^3*exp(2*x^2)+143*x^4-288*x^2*ln(x)-x^2*exp(4*x^2)-288*x^3+144*ln(x)^2+288*x*ln(x)+144*x^2)/(2*x*

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maxima [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \frac {2}{9} \, \int \frac {{\left (143 \, x^{5} - 144 \, x^{4} - 3 \, x^{3} e^{\left (4 \, x^{2}\right )} - 144 \, x^{3} - x^{2} e^{\left (6 \, x^{2}\right )} - 144 \, {\left (4 \, x^{2} e^{\left (2 \, x^{2}\right )} + x\right )} \log \relax (x)^{2} + 144 \, x^{2} - 3 \, {\left (192 \, x^{6} - 384 \, x^{5} + 97 \, x^{4} + 144 \, x^{3} - 48 \, x\right )} e^{\left (2 \, x^{2}\right )} - 144 \, {\left (x^{2} - {\left (8 \, x^{4} - 8 \, x^{3} - 2 \, x^{2} + x + 1\right )} e^{\left (2 \, x^{2}\right )} - x\right )} \log \relax (x)\right )} e^{\left (\frac {143 \, x^{4} - 2 \, x^{3} e^{\left (2 \, x^{2}\right )} - 288 \, x^{3} - x^{2} e^{\left (4 \, x^{2}\right )} + 144 \, x^{2} - 288 \, {\left (x^{2} - x\right )} \log \relax (x) + 144 \, \log \relax (x)^{2}}{9 \, {\left (x^{2} + 2 \, x e^{\left (2 \, x^{2}\right )} + e^{\left (4 \, x^{2}\right )}\right )}}\right )}}{x^{4} + 3 \, x^{3} e^{\left (2 \, x^{2}\right )} + 3 \, x^{2} e^{\left (4 \, x^{2}\right )} + x e^{\left (6 \, x^{2}\right )}}\,{d x} \end {gather*}

integrate(((-1152*x^2*exp(x^2)^2-288*x)*log(x)^2+((2304*x^4-2304*x^3-576*x^2+288*x+288)*exp(x^2)^2-288*x^2+288

*x)*log(x)-2*x^2*exp(x^2)^6-6*x^3*exp(x^2)^4+(-1152*x^6+2304*x^5-582*x^4-864*x^3+288*x)*exp(x^2)^2+286*x^5-288

*x^4-288*x^3+288*x^2)*exp((144*log(x)^2+(-288*x^2+288*x)*log(x)-x^2*exp(x^2)^4-2*x^3*exp(x^2)^2+143*x^4-288*x^

3+144*x^2)/(9*exp(x^2)^4+18*x*exp(x^2)^2+9*x^2))/(9*x*exp(x^2)^6+27*x^2*exp(x^2)^4+27*x^3*exp(x^2)^2+9*x^4),x,

2/9*integrate((143*x^5 - 144*x^4 - 3*x^3*e^(4*x^2) - 144*x^3 - x^2*e^(6*x^2) - 144*(4*x^2*e^(2*x^2) + x)*log(x

)^2 + 144*x^2 - 3*(192*x^6 - 384*x^5 + 97*x^4 + 144*x^3 - 48*x)*e^(2*x^2) - 144*(x^2 - (8*x^4 - 8*x^3 - 2*x^2

+ x + 1)*e^(2*x^2) - x)*log(x))*e^(1/9*(143*x^4 - 2*x^3*e^(2*x^2) - 288*x^3 - x^2*e^(4*x^2) + 144*x^2 - 288*(x

^2 - x)*log(x) + 144*log(x)^2)/(x^2 + 2*x*e^(2*x^2) + e^(4*x^2)))/(x^4 + 3*x^3*e^(2*x^2) + 3*x^2*e^(4*x^2) + x

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mupad [B] time = 4.15, size = 232, normalized size = 6.44 \begin {gather*} x^{\frac {32\,\left (x-x^2\right )}{{\mathrm {e}}^{4\,x^2}+2\,x\,{\mathrm {e}}^{2\,x^2}+x^2}}\,{\mathrm {e}}^{\frac {144\,x^2}{9\,{\mathrm {e}}^{4\,x^2}+18\,x\,{\mathrm {e}}^{2\,x^2}+9\,x^2}}\,{\mathrm {e}}^{\frac {143\,x^4}{9\,{\mathrm {e}}^{4\,x^2}+18\,x\,{\mathrm {e}}^{2\,x^2}+9\,x^2}}\,{\mathrm {e}}^{-\frac {288\,x^3}{9\,{\mathrm {e}}^{4\,x^2}+18\,x\,{\mathrm {e}}^{2\,x^2}+9\,x^2}}\,{\mathrm {e}}^{\frac {144\,{\ln \relax (x)}^2}{9\,{\mathrm {e}}^{4\,x^2}+18\,x\,{\mathrm {e}}^{2\,x^2}+9\,x^2}}\,{\mathrm {e}}^{-\frac {x^2\,{\mathrm {e}}^{4\,x^2}}{9\,{\mathrm {e}}^{4\,x^2}+18\,x\,{\mathrm {e}}^{2\,x^2}+9\,x^2}}\,{\mathrm {e}}^{-\frac {2\,x^3\,{\mathrm {e}}^{2\,x^2}}{9\,{\mathrm {e}}^{4\,x^2}+18\,x\,{\mathrm {e}}^{2\,x^2}+9\,x^2}} \end {gather*}

int(-(exp((144*log(x)^2 + log(x)*(288*x - 288*x^2) - 2*x^3*exp(2*x^2) - x^2*exp(4*x^2) + 144*x^2 - 288*x^3 + 1

43*x^4)/(9*exp(4*x^2) + 18*x*exp(2*x^2) + 9*x^2))*(exp(2*x^2)*(864*x^3 - 288*x + 582*x^4 - 2304*x^5 + 1152*x^6

) - log(x)*(288*x + exp(2*x^2)*(288*x - 576*x^2 - 2304*x^3 + 2304*x^4 + 288) - 288*x^2) + log(x)^2*(288*x + 11

52*x^2*exp(2*x^2)) + 6*x^3*exp(4*x^2) + 2*x^2*exp(6*x^2) - 288*x^2 + 288*x^3 + 288*x^4 - 286*x^5))/(9*x*exp(6*

x^2) + 27*x^3*exp(2*x^2) + 27*x^2*exp(4*x^2) + 9*x^4),x)

x^((32*(x - x^2))/(exp(4*x^2) + 2*x*exp(2*x^2) + x^2))*exp((144*x^2)/(9*exp(4*x^2) + 18*x*exp(2*x^2) + 9*x^2))

*exp((143*x^4)/(9*exp(4*x^2) + 18*x*exp(2*x^2) + 9*x^2))*exp(-(288*x^3)/(9*exp(4*x^2) + 18*x*exp(2*x^2) + 9*x^

2))*exp((144*log(x)^2)/(9*exp(4*x^2) + 18*x*exp(2*x^2) + 9*x^2))*exp(-(x^2*exp(4*x^2))/(9*exp(4*x^2) + 18*x*ex

p(2*x^2) + 9*x^2))*exp(-(2*x^3*exp(2*x^2))/(9*exp(4*x^2) + 18*x*exp(2*x^2) + 9*x^2))

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sympy [B] time = 2.78, size = 80, normalized size = 2.22 \begin {gather*} e^{\frac {143 x^{4} - 2 x^{3} e^{2 x^{2}} - 288 x^{3} - x^{2} e^{4 x^{2}} + 144 x^{2} + \left (- 288 x^{2} + 288 x\right ) \log {\relax (x )} + 144 \log {\relax (x )}^{2}}{9 x^{2} + 18 x e^{2 x^{2}} + 9 e^{4 x^{2}}}} \end {gather*}

integrate(((-1152*x**2*exp(x**2)**2-288*x)*ln(x)**2+((2304*x**4-2304*x**3-576*x**2+288*x+288)*exp(x**2)**2-288

*x**2+288*x)*ln(x)-2*x**2*exp(x**2)**6-6*x**3*exp(x**2)**4+(-1152*x**6+2304*x**5-582*x**4-864*x**3+288*x)*exp(

x**2)**2+286*x**5-288*x**4-288*x**3+288*x**2)*exp((144*ln(x)**2+(-288*x**2+288*x)*ln(x)-x**2*exp(x**2)**4-2*x*

*3*exp(x**2)**2+143*x**4-288*x**3+144*x**2)/(9*exp(x**2)**4+18*x*exp(x**2)**2+9*x**2))/(9*x*exp(x**2)**6+27*x*

exp((143*x**4 - 2*x**3*exp(2*x**2) - 288*x**3 - x**2*exp(4*x**2) + 144*x**2 + (-288*x**2 + 288*x)*log(x) + 144

*log(x)**2)/(9*x**2 + 18*x*exp(2*x**2) + 9*exp(4*x**2)))

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