The antiderivative of x is equal to x^{2}/2+C, where C is a constant. In this post, we will learn how to find the antiderivative of x.

## How to Find Antiderivative of x

The antiderivative of x is a function whose derivative will be equal to x. To calculate it, we need to integrate the function x. That is, calculate ∫ x dx.

Now, ∫ x dx

= ∫ x^{1} dx

= x^{1+1}/(1+1) + C by the power rule of integration: ∫ x^{n} dx = x^{n+1}/(n+1)

= x^{2}/2+C.

So the anti-derivative of x is equal to x^{2}/2+C where C is a constant.

**Checking:**

Now, we check that the derivative of x^{2}/2+C is equal to x.

$\dfrac{d}{dx}$(x^{2}/2+C)

= $\dfrac{d}{dx}$(x^{2}/2)+ $\dfrac{d}{dx}$(C)

= 2x/2 + 0 as the derivative of x^{n} is nx^{n-1}, and the derivative of a constant is zero.

= x, hence checked.

**Also Read:**

## FAQs

### Q1: What is the antiderivative of x?

Answer: The antiderivative of x is x^{2}/2+constant.