The problem is i need to
study the convergence of A and B
and find the antiderivative of C
$$A=\int_0^\infty \frac{\sin(x) +x}{\sqrt x + x^3}dx$$ $$B=\int_0^\infty \frac{1}{\sqrt {e^x-1}(x^2+x^{1/3} )}dx$$
$$C=\int\frac{1}{x}\sqrt\frac{2-x}{2+x}dx$$
in C i try substitution $$U =\sqrt\frac{2-x}{2+x}$$
hi sami i look if the problem C u need to use substitution 5 time $$u=\dfrac{1}{x+2}$$ & then after that $$X=\sqrt{4u-1}$$ & $$w=X+1$$ &
....
but the final answer is $$\ln\left(\left|\sqrt{-\dfrac{x-2}{x+2}}-1\right|\right)-\ln\left(\sqrt{-\dfrac{x-2}{x+2}}+1\right)+2\arctan\left(\sqrt{-\dfrac{x-2}{x+2}}\right)+C$$