Question

verifique que: ∫ (1/√(1 - x²))dx = arc senx + k

Answer 1

∫ (1/√(1 - x²))dx

2 - caso da substituição trigonometrica

a = 1
x= a.sen&
x = sen&
dx = cos&d&

∫ (1/√(1 - x²))dx

= ∫ (1/√(1 - sen²&))cos&d&

= ∫ (1/√(cos²&))cos&d&

= ∫ (1/cos&).cos&d&

= ∫d&

=& + k

buscando & em x = sen&
aplicando a inversa do angulo

x = sen&
&= arc senx
logo

= arc senx +k

∫ (1/√(1 - x²))dx = arc senx + k