## ∫x^r dx =

### [x^(r+1) / (r +1) ] + C

Assuming that r is not equal to -1, the antiderivative of x^r with respect to x is:

∫x^r dx = (x^(r+1)) / (r+1) + C

Where C is the constant of integration.

This result follows from the Power Rule of Integration, which states that the antiderivative of x^n with respect to x is (x^(n+1))/(n+1) + C, where C is the constant of integration.

It is important to note that this result only holds for values of r not equal to -1, as in the case where r = -1, the antiderivative of x^r is ln|x| + C instead.

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