Integral of √x

\int \sqrt{x}\,dx = \frac{2}{3}x^{\frac{3}{2}} + C.

Differentiate it: the derivative of \frac{2}{3}x^{\frac{3}{2}} is \sqrt{x}. CalcViz checks every antiderivative this way before showing it.

\int \sqrt{x}\,dx = \frac{2}{3}x^{\frac{3}{2}} + C

Rewrite as x^(1/2) and apply the power rule: add one to the exponent, divide by the new exponent.

Power rule
∫uⁿ du = uⁿ⁺¹/(n+1).
$\int \sqrt{x}\,dx = \frac{2}{3}x^{\frac{3}{2}}$

Constant C = 0.0

Every choice of C gives a valid antiderivative, since shifting up or down doesn’t change the slope.

Questions students ask

What is the integral of √x?

$\int \sqrt{x}\,dx = \frac{2}{3}x^{\frac{3}{2}} + C$ .

How do you integrate √x?

Rewrite as x^(1/2) and apply the power rule: add one to the exponent, divide by the new exponent.

How can I check the answer?

Differentiate it: the derivative of $\frac{2}{3}x^{\frac{3}{2}}$ is $\sqrt{x}$ . CalcViz checks every antiderivative this way before showing it.