44.67 Problem number 5196

$$\int \frac{16x^5+4x^6+e^{\frac{3(-1+2x)}{x}}(-1296x-756x^2)+e^{\frac{4(-1+2x)}{x}}(1296+324x-108x^2)+e^{\frac{2(-1+2x)}{x}}(432x^2+540x^3+72x^4)+e^{\frac{-1+2x}{x}}(-48x^3-156x^4-32x^5)+(e^{\frac{4(-1+2x)}{x}}(-1728-432x+108x^2)+e^{\frac{3(-1+2x)}{x}}(1296x+756x^2+36x^3)+e^{\frac{2(-1+2x)}{x}}(-288x^2-360x^3-60x^4)+e^{\frac{-1+2x}{x}}(16x^3+52x^4+12x^5))\log (4+x)+(e^{\frac{4(-1+2x)}{x}}(864+216x-36x^2)+e^{\frac{3(-1+2x)}{x}}(-432x-252x^2-24x^3)+e^{\frac{2(-1+2x)}{x}}(48x^2+60x^3+12x^4)){\log }^2(4+x)+(e^{\frac{4(-1+2x)}{x}}(-192-48x+4x^2)+e^{\frac{3(-1+2x)}{x}}(48x+28x^2+4x^3)){\log }^3(4+x)+e^{\frac{4(-1+2x)}{x}}(16+4x){\log }^4(4+x)}{4x^2+x^3}dx$$

Optimal antiderivative $${({\mathrm{e}}^{2-\frac{1}{x}}(3-\ln (4+x))-x)}^4$$

command

integrate(((4*x+16)*exp((-1+2*x)/x)**4*ln(4+x)**4+((4*x**2-48*x-192)*exp((-1+2*x)/x)**4+(4*x**3+28*x**2+48*x)*exp((-1+2*x)/x)**3)*ln(4+x)**3+((-36*x**2+216*x+864)*exp((-1+2*x)/x)**4+(-24*x**3-252*x**2-432*x)*exp((-1+2*x)/x)**3+(12*x**4+60*x**3+48*x**2)*exp((-1+2*x)/x)**2)*ln(4+x)**2+((108*x**2-432*x-1728)*exp((-1+2*x)/x)**4+(36*x**3+756*x**2+1296*x)*exp((-1+2*x)/x)**3+(-60*x**4-360*x**3-288*x**2)*exp((-1+2*x)/x)**2+(12*x**5+52*x**4+16*x**3)*exp((-1+2*x)/x))*ln(4+x)+(-108*x**2+324*x+1296)*exp((-1+2*x)/x)**4+(-756*x**2-1296*x)*exp((-1+2*x)/x)**3+(72*x**4+540*x**3+432*x**2)*exp((-1+2*x)/x)**2+(-32*x**5-156*x**4-48*x**3)*exp((-1+2*x)/x)+4*x**6+16*x**5)/(x**3+4*x**2),x)

Sympy 1.10.1 under Python 3.10.4 output

$$\text{Timed out}$$

Sympy 1.8 under Python 3.8.8 output

$$x^4+(4x^3\log (x+4)-12x^3)e^{\frac{2x-1}{x}}+(6x^2\log {(x+4)}^2-36x^2\log (x+4)+54x^2)e^{\frac{2(2x-1)}{x}}+(4x\log {(x+4)}^3-36x\log {(x+4)}^2+108x\log (x+4)-108x)e^{\frac{3(2x-1)}{x}}+(\log {(x+4)}^4-12\log {(x+4)}^3+54\log {(x+4)}^2-108\log (x+4)+81)e^{\frac{4(2x-1)}{x}}$$