Задача 43661 ...

vk279388637

2020-01-25 09:45:10

∫ arcsin(x/4) dx

sova

2020-01-25 10:23:51

По частям
u=arcsin(x/4)
dv=dx ⇒ v=x


[m]du=\frac{1}{\sqrt{1-(\frac{x}{4})^2}}\cdot(\frac{x}{4})`dx=\frac{dx}{2\sqrt{4-x^2}}[/m]

[m]=x\cdot arcsin\frac{x}{4}-\int \frac{dx}{2\sqrt{4-x^2}}=x\cdot arcsin\frac{x}{4}-\frac{1}{2}\cdot arcsin\frac{x}{4}+C[/m]