What is the integral of 1/((8-x)^2) ?

The integral of 1/((8-x)^2) is 1/(8-x)+C

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integral of 1/((8-x)^2)

\int \frac{1}{( 8 - x ) ^{2}} d x

\frac{1}{8 - x} + C

Solution steps

\int \frac{1}{( 8 - x ) ^{2}} d x

Apply u-substitution

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

Apply the Power Rule

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

Substitute back

u = 8 - x

= - (- \frac{1}{8 - x})

Simplify

= \frac{1}{8 - x}

Add a constant to the solution

= \frac{1}{8 - x} + C