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

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.
Since is constant with respect to , move out of the integral.
The integral of with respect to is .
Let . Then . Rewrite using and .
Let . Find .
Differentiate .
By the Sum Rule, the derivative of with respect to is .
Differentiate using the Power Rule which states that is where .
Since is constant with respect to , the derivative of with respect to is .
Add and .
Rewrite the problem using and .
The integral of with respect to is .
Simplify.
Replace all occurrences of with .
Evaluate integral of 1/(x(x-1)) with respect to x

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