Eli5 how do we know that the integration of x^n is x^(n+1)/n+1
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The integration of x^n involves finding the antiderivative, or the function whose derivative is x^n.
To derive the formula for the antiderivative of x^n, we use the power rule of differentiation. This rule states that the derivative of x^n is n*x^(n-1).
Using this rule, we can work backwards and say that the antiderivative of x^n must be x^(n+1)/(n+1), since the derivative of this function is (n+1)*x^(n)/(n+1) = x^n.
Therefore, we know that the integration of x^n is x^(n+1)/(n+1).
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