44.6 Problem number 284

\[ \int \frac {e^{\frac {x}{4+2 x+2 \log \left (x^2\right )}} \left (-16+8 x+20 x^2+6 x^3+\left (-16+17 x+11 x^2\right ) \log \left (x^2\right )+(-4+6 x) \log ^2\left (x^2\right )\right )}{8 x^3-8 x^4-6 x^5+4 x^6+2 x^7+\left (8 x^3-12 x^4+4 x^6\right ) \log \left (x^2\right )+\left (2 x^3-4 x^4+2 x^5\right ) \log ^2\left (x^2\right )} \, dx \]

Optimal antiderivative \[ \frac {{\mathrm e}^{\frac {x}{2 \ln \left (x^{2}\right )+2 x +4}}}{\left (-x^{2}+x \right ) x} \]

command

integrate(((6*x-4)*ln(x**2)**2+(11*x**2+17*x-16)*ln(x**2)+6*x**3+20*x**2+8*x-16)*exp(x/(2*ln(x**2)+2*x+4))/((2*x**5-4*x**4+2*x**3)*ln(x**2)**2+(4*x**6-12*x**4+8*x**3)*ln(x**2)+2*x**7+4*x**6-6*x**5-8*x**4+8*x**3),x)

Sympy 1.10.1 under Python 3.10.4 output

\[ \text {Exception raised: TypeError} \]

Sympy 1.8 under Python 3.8.8 output

\[ - \frac {e^{\frac {x}{2 x + 2 \log {\left (x^{2} \right )} + 4}}}{x^{3} - x^{2}} \]