integrate 1/sqrt(x) — step-by-step solution

Let's integrate:

\int(\frac{1}{\sqrt{x}})dx

We attempt to reverse an integration: starting from

\frac{1}{\sqrt{x}}

and

{(a^{n})}^{'} = n a^{(n - 1)}

, we differentiate using ^(m+1)

Let's differentiate:

{(x^{(- \frac{1}{2} + 1)})}^{'}

{(x^{(\frac{- 1 + 2}{2})})}^{'}

{(\sqrt{x})}^{'}

\frac{1}{2 \sqrt{x}}

The computed derivative matches the original math expression up to a constant factor. Therefore, the integral is:

2 \cdot \frac{1}{x^{- \frac{1}{2}}}

2 \sqrt{x}

Indefinite integrals are defined up to an additive constant C, so this yields:

2 \sqrt{x} + C

▷Answer: $2 \sqrt{x} + C$ , with C being any constant