22.38 Problem number 6680

$$\int e^{-7+x^2-{25}^{\frac{4x}{e^2}}{\left(x^2\right)}^{\frac{4x}{e^2}}}(e^2(1+2x^2)+{25}^{\frac{4x}{e^2}}{\left(x^2\right)}^{\frac{4x}{e^2}}(-8x-4x\log \left(25x^2\right)))dx$$

Optimal antiderivative $$x{\mathrm{e}}^{-{\mathrm{e}}^{4x\ln \left(25x^2\right){\mathrm{e}}^{-2}}+x^2-5}$$

command

Integrate[E^(-7 + x^2 - 25^((4*x)/E^2)*(x^2)^((4*x)/E^2))*(E^2*(1 + 2*x^2) + 25^((4*x)/E^2)*(x^2)^((4*x)/E^2)*(-8*x - 4*x*Log[25*x^2])),x]

Mathematica 13.1 output

$$\int e^{-7+x^2-{25}^{\frac{4x}{e^2}}{\left(x^2\right)}^{\frac{4x}{e^2}}}(e^2(1+2x^2)+{25}^{\frac{4x}{e^2}}{\left(x^2\right)}^{\frac{4x}{e^2}}(-8x-4x\log \left(25x^2\right)))dx$$

Mathematica 12.3 output

$$e^{-5+x^2-{25}^{\frac{4x}{e^2}}{\left(x^2\right)}^{\frac{4x}{e^2}}}x$$