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

Let's integrate:

\int(\sqrt{x})dx

Use the integration formula for

\sqrt{x}

\int(x^{n})dx = \frac{x^{(n + 1)}}{n + 1}

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

ℹ

\frac{1}{2} + 1

\frac{1 + 2}{2}

‖

\frac{1}{2} + 1

\frac{1 + 2}{2}

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

ℹ

1 + 2

3

‖

1 + 2

3

\frac{x^{\frac{3}{2}}}{\frac{3}{2}}

\frac{x^{\frac{3}{2}} \cdot 2}{3}

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

\frac{2 x^{\frac{3}{2}}}{3} + C

▷Result: $\frac{2 x^{\frac{3}{2}}}{3} + C$ , with C being any constant