Calculus • Step-by-Step

Integral of √x dx with Steps

Integrate the square root of x step by step. Rewrite √x as x^(1/2) and apply the power rule to obtain (2/3)x^(3/2) + C.

Problem Statement

\int \sqrt{x} \, dx

Final Result

F(x) = \frac{2 \cdot x^{\frac{3}{2}}}{3} + C

Formula Required: Power Rule with Fractional Exponents

1/2 + 1 = 3/2. Dividing by 3/2 is multiplying by 2/3.

\int x^{1/2} \, dx = \frac{x^{3/2}}{3/2} + C = \frac{2}{3}x^{3/2} + C

2 Steps

Set up the indefinite integral with respect to variable $x$.

\int \left( \sqrt{x} \right) \, dx

Apply the Power Rule for Integration to find the antiderivative.

F(x) = \frac{2 \cdot x^{\frac{3}{2}}}{3}

Interactive Calculator

Enter any equation like 2x + 8 = 20 or x² - 5x + 6 = 0 to get step-by-step solutions.

Convert √x to x^(1/2). Add 1 to the power: 1/2 + 1 = 3/2. Divide by 3/2: (2/3)x^(3/2) + C.