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# Given the derivative of a function, how would you find the original function?

I am trying to teach myself calculus, so I am asking this question. For example, given that the derivative of a function is 2x, you could use the d/dx [x^n] = (n)(x^{(n-1)}) to guess that the original function was x^{2}, but what would you do if you were told that x^{2} itself was the derivative of another function? Please help me. Note that I am NOT someone asking for homework help, my homework from school is not calculus.

## Discussions

It is called the anti-derivative, also known as an indefinite integral. So:

The integral of (x

^{n})= (x^{n+1})/(n+1))So in the case of x

^{2}. You would have, (x^{2+1})/(2+1) which is (x^{3})/3 + C. I added a (C) because C is any integer, and when the derivative is taken of an integer, it would = 0. So then when you check, the derivative of (x^{3})/3 , it would equal x^{2}.This concept does get more challenging, when you have definite integrals, radicals, or when you need to integrate through substitution.