# Evaluate integral of 1/(x-x^2) with respect to x

Factor out of .
Raise to the power of .
Factor out of .
Factor out of .
Factor out of .
Write the fraction using partial fraction decomposition.
Replace each of the partial fraction coefficients in with the values found for and .
Split the single integral into multiple integrals.
The integral of with respect to is .
Let . Then , so . Rewrite using and .
Let . Find .
Rewrite.
Divide by .
Rewrite the problem using and .
Move the negative in front of the fraction.
Since is constant with respect to , move out of the integral.
The integral of with respect to is .
Simplify.
Replace all occurrences of with .
Evaluate integral of 1/(x-x^2) with respect to x

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