Question

How do you integrate by substitution `int 1/(2sqrt(x))dx`?

Answer 1

There is no need to use substitution.

Explanation:

`int 1/(2sqrtx) dx = 1/2 int x^-(1/2) dx`

Now use the power rule for integrals.

`= 1/2 2*x^(1/2) +C`

`= x^(1/2) +C`

IF someone insisted that I must do a substitution, I would let `u = x` so `du = dx` and integrate `1/(2sqrtu) du` exactly as above.