Question

integerationof [√x-1/√x] dx is equal to :​

Answer 1

Step-by-step explanation:

y= ∫(√x + 1/√x)dx

∫xⁿdx =xⁿ+¹/(n+1) + c

Consider,

∫√xdx= ∫x¹/²dx =(x¹/² + ¹)/(1+1/2)=x³/²/(3/2)

∫√xdx=(2x³/²)/3 =(2x√x)/3 + c'

Also,

∫dx/√x = (x-¹/² +¹)/(-1/2 +1)

∫dx/√x = (x¹/²)/(1/2)=2√x

So, y= ∫√xdx + ∫dx/√x

y=(2x√x)/3 + 2√x +c