What is the integral of 1/(u^2-10u+25) ?

The integral of 1/(u^2-10u+25) is -1/(u-5)+C

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integral of 1/(u^2-10u+25)

\int \frac{1}{u ^{2} - 10 u + 25} d u

- \frac{1}{u - 5} + C

Solution steps

\int \frac{1}{u ^{2} - 10 u + 25} d u

Take the partial fraction of

\frac{1}{u ^{2} - 10 u + 25} : \frac{1}{( u - 5 ) ^{2}}

= \int \frac{1}{( u - 5 ) ^{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 - 5

= - \frac{1}{u - 5}

Add a constant to the solution

= - \frac{1}{u - 5} + C

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What is the integral of 1/(u^2-10u+25) ?
The integral of 1/(u^2-10u+25) is -1/(u-5)+C