What's the integral of √x?

The integral of √x is (2/3)x^(3/2) + C, where C is the constant of integration.

To find the integral of √x, we can use the power rule of integration, which states that the integral of x^n is (1/(n+1))x^(n+1) + C, where C is the constant of integration. In this case, we have n = 1/2, so we add 1 to get n+1 = 3/2. Then we divide by n+1 to get 1/(n+1) = 2/3. Finally, we substitute x^(3/2) for x^n to get the integral of √x as (2/3)x^(3/2) + C.

To check our answer, we can differentiate (2/3)x^(3/2) + C using the power rule of differentiation, which states that the derivative of x^n is nx^(n-1). In this case, we have n = 3/2, so we multiply by n to get the derivative as (3/2)(2/3)x^(3/2-1) = x^(1/2). This is the same as √x, so our answer is correct.

In summary, the integral of √x is (2/3)x^(3/2) + C, where C is the constant of integration. We can use the power rule of integration to find this answer, and we can check our answer by differentiating it.