\[ \int \frac {300-120 x^2+12 x^4+2^{-\frac {x}{-5+x^2}} \left (-75+150 x-45 x^2-60 x^3+27 x^4+6 x^5-3 x^6+\left (-15 x+30 x^2-18 x^3+6 x^4-3 x^5\right ) \log (2)\right )}{100-200 x+60 x^2+80 x^3-36 x^4-8 x^5+4 x^6} \, dx \]
Optimal antiderivative \[ 18-\frac {3 x}{x^{2}-x}-\frac {3 x \,{\mathrm e}^{\frac {\ln \left (2\right )}{\frac {5}{x}-x}}}{4} \]
command
Int[(300 - 120*x^2 + 12*x^4 + (-75 + 150*x - 45*x^2 - 60*x^3 + 27*x^4 + 6*x^5 - 3*x^6 + (-15*x + 30*x^2 - 18*x^3 + 6*x^4 - 3*x^5)*Log[2])/2^(x/(-5 + x^2)))/(100 - 200*x + 60*x^2 + 80*x^3 - 36*x^4 - 8*x^5 + 4*x^6),x]
Rubi 4.17.3 under Mathematica 13.3.1 output
\[ \int \frac {300-120 x^2+12 x^4+2^{-\frac {x}{-5+x^2}} \left (-75+150 x-45 x^2-60 x^3+27 x^4+6 x^5-3 x^6+\left (-15 x+30 x^2-18 x^3+6 x^4-3 x^5\right ) \log (2)\right )}{100-200 x+60 x^2+80 x^3-36 x^4-8 x^5+4 x^6} \, dx \]
Rubi 4.16.1 under Mathematica 13.3.1 output
\[ -\frac {15 (x+5)}{8 (1-x) \left (5-x^2\right )}-\frac {15 (3 x+5)}{16 \left (5-x^2\right )}-\frac {3\ 2^{\frac {x}{5-x^2}-2} \left (x^3 \log (2)+x \log (32)\right )}{\left (5-x^2\right )^2 \left (\frac {2 x^2}{\left (5-x^2\right )^2}+\frac {1}{5-x^2}\right ) \log (2)}+\frac {93}{16 (1-x)}-\frac {3}{32} \left (25+13 \sqrt {5}\right ) \log \left (\sqrt {5}-x\right )+\frac {3}{16} \left (15+7 \sqrt {5}\right ) \log \left (\sqrt {5}-x\right )-\frac {3}{32} \left (5+\sqrt {5}\right ) \log \left (\sqrt {5}-x\right )-\frac {3}{32} \left (5-\sqrt {5}\right ) \log \left (x+\sqrt {5}\right )+\frac {3}{16} \left (15-7 \sqrt {5}\right ) \log \left (x+\sqrt {5}\right )-\frac {3}{32} \left (25-13 \sqrt {5}\right ) \log \left (x+\sqrt {5}\right ) \]