22.53 Problem number 9713

$$\int \frac{42+144x+108x^2+32^{2+\frac{4x}{3}}{\left(\frac{1}{x^2}\right)}^{2x/3}{x}^4+2^{2x/3}{\left(\frac{1}{x^2}\right)}^{x/3}(51x^2+70x^3+x^3\log \left(\frac{4}{x^2}\right))}{48+144x+108x^2+32^{2+\frac{4x}{3}}{\left(\frac{1}{x^2}\right)}^{2x/3}{x}^4+2^{2x/3}{\left(\frac{1}{x^2}\right)}^{x/3}(48x^2+72x^3)}dx$$

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

command

Integrate[(42 + 144*x + 108*x^2 + 3*2^(2 + (4*x)/3)*(x^(-2))^((2*x)/3)*x^4 + 2^((2*x)/3)*(x^(-2))^(x/3)*(51*x^2 + 70*x^3 + x^3*Log[4/x^2]))/(48 + 144*x + 108*x^2 + 3*2^(2 + (4*x)/3)*(x^(-2))^((2*x)/3)*x^4 + 2^((2*x)/3)*(x^(-2))^(x/3)*(48*x^2 + 72*x^3)),x]

Mathematica 13.1 output

$$\int \frac{42+144x+108x^2+32^{2+\frac{4x}{3}}{\left(\frac{1}{x^2}\right)}^{2x/3}{x}^4+2^{2x/3}{\left(\frac{1}{x^2}\right)}^{x/3}(51x^2+70x^3+x^3\log \left(\frac{4}{x^2}\right))}{48+144x+108x^2+32^{2+\frac{4x}{3}}{\left(\frac{1}{x^2}\right)}^{2x/3}{x}^4+2^{2x/3}{\left(\frac{1}{x^2}\right)}^{x/3}(48x^2+72x^3)}dx$$

Mathematica 12.3 output

$$\frac{1}{4}x(4-\frac{1}{2+2^{2x/3}{\left(\frac{1}{x^2}\right)}^{-1+\frac{x}{3}}+3x})$$