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Am i doing something wrong, or are there other rules for integration that i am unaware of?

## Homework Statement

The two forms: the integral of x^(-1/2) dx and the integral of 1/(x^(1/2) dx.

## Homework Equations

The formula for solving the most basic integrals is x^(n+1)/(n+1) plus a constant.

## The Attempt at a Solution

In the fraction (inverse) form: the integral of 1/(x^(1/2) dx, i would solve it like this 1/(x^(1/2+1)/(1/2)+1; which gives me 1/(x^(3/2)/(3/2) = 2/((3x^(1/2)) + C.

However, in the form of x^(-1/2), i solve it by x^ ((-1/2) +1)/(-1/2)+1 = 2(x^(1/2).

Why is this the case?