Question

Помогите решить неопределенный интеграл

Answer 1

$\displaystyle \int \frac{ \sqrt{\ln (x) +5} }{x} dx= \left[\begin{array}{ccc}u=\ln x\\du= \frac{dx}{x} \\\end{array}\right] = \int \sqrt{u+5}\, du = \left[\begin{array}{ccc}t=u+5\\dt=du\end{array}\right] =\\\\\int \sqrt{t}\, dt=\int t^{1/2}dt= \frac{t^{3/2}}{3/2} +C= \frac{2}{3} t\sqrt[2]{t} +C= \frac{2}{3}(u+5) \sqrt{u+5} +C=\\\\= \frac{2}{3}(\ln x+5) \sqrt{\ln x +5}+C$