Eli5 how do we know that the integration of x^n is x^(n+1)/n+1

Question

Eli5 how do we know that the integration of x^n is x^(n+1)/n+1

In: 0

Answer 1

Because that’s the definition.

X^1 = X

X^2 = X^(2-1) •X
-> divide both sides with X and you get what you asked for. You can prove it through induction if you want, but that wouldn’t be ELI5

You could also ask why nX-X=(n-1)X