What is the integral of 1/(u^2-2u+1) ?

The integral of 1/(u^2-2u+1) is -1/(u-1)+C

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integral of 1/(u^2-2u+1)

\int \frac{1}{u ^{2} - 2 u + 1} d u

- \frac{1}{u - 1} + C

Solution steps

\int \frac{1}{u ^{2} - 2 u + 1} d u

Complete the square

u^{2} - 2 u + 1 : (u - 1)^{2}

= \int \frac{1}{( u - 1 ) ^{2}} d u

Apply u-substitution

: \int \frac{1}{v ^{2}} d v

= \int \frac{1}{v ^{2}} d v

Apply the Power Rule

: - \frac{1}{v}

= - \frac{1}{v}

Substitute back

v = u - 1

= - \frac{1}{u - 1}

Add a constant to the solution

= - \frac{1}{u - 1} + C

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What is the integral of 1/(u^2-2u+1) ?
The integral of 1/(u^2-2u+1) is -1/(u-1)+C