What is the integral of ((x-5)^2)/(x-5) ?

The integral of ((x-5)^2)/(x-5) is (x^2)/2-5x+C

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integral of ((x-5)^2)/(x-5)

\int \frac{( x - 5 ) ^{2}}{x - 5} d x

\frac{x ^{2}}{2} - 5 x + C

Solution steps

\int \frac{( x - 5 ) ^{2}}{x - 5} d x

Cancel the common factor:

x - 5

= \int x - 5 d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int x d x - \int 5 d x

\int x d x = \frac{x ^{2}}{2}

\int 5 d x = 5 x

= \frac{x ^{2}}{2} - 5 x

Add a constant to the solution

= \frac{x ^{2}}{2} - 5 x + C

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What is the integral of ((x-5)^2)/(x-5) ?
The integral of ((x-5)^2)/(x-5) is (x^2)/2-5x+C