\[ \int \frac {3 x^3+4^{25 x} \left (-2 x^2-25 x^3 \log (4)\right )+e^{2 \log ^2(x)} \left (x-25\ 4^{25 x} x \log (4)+\left (-4^{1+25 x}+4 x\right ) \log (x)\right )+e^{\log ^2(x)} \left (4 x^2+4^{25 x} \left (-2 x-50 x^2 \log (4)\right )+\left (-4^{1+25 x} x+4 x^2\right ) \log (x)\right )}{x} \, dx \]
Optimal antiderivative \[ -\left (x -{\mathrm e}^{50 x \ln \left (2\right )}\right ) \left (x +{\mathrm e}^{\ln \left (x \right )^{2}}\right ) \left (-x -{\mathrm e}^{\ln \left (x \right )^{2}}\right ) \]
command
Integrate[(3*x^3 + 4^(25*x)*(-2*x^2 - 25*x^3*Log[4]) + E^(2*Log[x]^2)*(x - 25*4^(25*x)*x*Log[4] + (-4^(1 + 25*x) + 4*x)*Log[x]) + E^Log[x]^2*(4*x^2 + 4^(25*x)*(-2*x - 50*x^2*Log[4]) + (-(4^(1 + 25*x)*x) + 4*x^2)*Log[x]))/x,x]
Mathematica 13.1 output
\[ \int \frac {3 x^3+4^{25 x} \left (-2 x^2-25 x^3 \log (4)\right )+e^{2 \log ^2(x)} \left (x-25\ 4^{25 x} x \log (4)+\left (-4^{1+25 x}+4 x\right ) \log (x)\right )+e^{\log ^2(x)} \left (4 x^2+4^{25 x} \left (-2 x-50 x^2 \log (4)\right )+\left (-4^{1+25 x} x+4 x^2\right ) \log (x)\right )}{x} \, dx \]
Mathematica 12.3 output
\[ -\left (\left (2^{50 x}-x\right ) \left (e^{\log ^2(x)}+x\right )^2\right ) \]