Indefinite Integral of e raised to a negative fraction

MathMan09
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Homework Statement


Find the constant, c, that satisfies the following equation:


Homework Equations


The integral is from -infinity to infinity

1 = c \int e ^ -|x|/2 *dx

The Attempt at a Solution



c = 1/4

I have the solution given to me, but I do not understand how to get the steps to the answer.
 
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Find the integral of e^(-|x|/2) from 0 to infinity (where you can drop the absolute value). Compare that with the integral of the same function from -infinity to 0.
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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