Задача 70887 ...

643e8fb6dc8af77c5440385d

19.04.2023 13:43:52

Решить интеграл:
∫sqrt(x+4)/sqrt(x)

5f3ea7e3faf909182968ddd9

19.04.2023 14:35:58

★

[m]\frac{x+4}{x}=t^2[/m] ⇒ [m]x+4=xt^2[/m]

[m]xt^2-x=4[/m]

[m]x=\frac{4}{t^2-1}[/m]

[m]dx=(\frac{4}{t^2-1})`dt[/m]

[m]dx=-\frac{8t}{(t^2-1)^2}dt[/m]


[m] ∫ \sqrt{\frac{x+4}{x}} dx= ∫ t\cdot (-\frac{8t}{(t^2-1)^2})dt=-8 ∫t \cdot \frac{t}{(t^2-1)^2}dt

=[/m]