Antiderivative of x

The antiderivative of x is equal to x²/2+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

= ∫ x¹ dx

= x¹⁺¹/(1+1) + C by the power rule of integration: ∫ xⁿ dx = xⁿ⁺¹/(n+1)

= x²/2+C.

So the anti-derivative of x is equal to x²/2+C where C is a constant.

Checking:

Now, we check that the derivative of x²/2+C is equal to x.

$\dfrac{d}{dx}$(x²/2+C)

= $\dfrac{d}{dx}$(x²/2)+ $\dfrac{d}{dx}$(C)

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

= x, hence checked.

Also Read:

Derivative of e^sinx

Derivative of e^cosx

Derivative of e^tanx

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