# Find the Antiderivative 1/(e^u)

Write as a function.
The function can be found by finding the indefinite integral of the derivative .
Set up the integral to solve.
Factor .
Simplify the expression.
Negate the exponent of and move it out of the denominator.
Simplify.
Multiply the exponents in .
Apply the power rule and multiply exponents, .
Move to the left of .
Rewrite as .
Multiply by .
Let . Then , so . Rewrite using and .
Let . Find .
Differentiate .
Since is constant with respect to , the derivative of with respect to is .
Differentiate using the Power Rule which states that is where .
Multiply by .
Rewrite the problem using and .
Since is constant with respect to , move out of the integral.
The integral of with respect to is .
Simplify.
Replace all occurrences of with .
The answer is the antiderivative of the function .
Find the Antiderivative 1/(e^u)

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