Question-206543

Question Number 206543 by luciferit last updated on 18/Apr/24

Answered by lepuissantcedricjunior last updated on 18/Apr/24

\int \frac{3 + 2 \sqrt{x}}{4 + \sqrt{x}} d x = \int \frac{2 (4 + \sqrt{x}) - 5}{4 + \sqrt{x}} d x

= 2 x - {5 \int \frac{d x}{4 + \sqrt{x}} x = t^{2} \Leftrightarrow d x = 2 t d t}

= 2 x - {10 \int (1 - \frac{4}{4 + t}) d t}

= 2 x - 10 \sqrt{x} + 40 l n (4 + \sqrt{x}) + c