Antiderivative of 1

The antiderivative of 1 is equal to x+C, where C is a constant. In this post, we will learn how to find the antiderivative of 1.

How to Find Antiderivative of 1

The antiderivative of 1 is a function whose derivative will be equal to 1. To calculate it, we need to integrate the constant function 1. In other words, the anti-derivative of 1 will be equal to

∫ 1 dx

where

• 1 is the integrand
• dx denotes that the integration is with respect to the variable x.

Now, ∫ 1 dx

= 1 ∫ dx using the rule of the integration of a function multiplied by a constant.

= 1⋅x + C as we know that the integration of dx is x.

= x+C.

So the anti-derivative of 1 is equal to x+C where C is a constant.

Checking:

Now, we verify that the derivative of x+C is equal to 1.

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

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

= 1 + 0, by the power rule of derivatives: d/dx(xⁿ) = nx^n-1, and the derivative of a constant is zero.

= 1, hence verified.

Also Read:

Anti-Derivative of x

Derivative of e^sinx

Derivative of e^tanx

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