What is the integral of 7/((x-3)(x-3)) ?

The integral of 7/((x-3)(x-3)) is -7/(x-3)+C

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integral of 7/((x-3)(x-3))

\int \frac{7}{( x - 3 ) ( x - 3 )} d x

- \frac{7}{x - 3} + C

Solution steps

\int \frac{7}{( x - 3 ) ( x - 3 )} d x

Take the constant out:

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

= 7 \cdot \int \frac{1}{( x - 3 ) ( x - 3 )} d x

Take the partial fraction of

\frac{1}{( x - 3 ) ( x - 3 )} : \frac{1}{( x - 3 ) ^{2}}

= 7 \cdot \int \frac{1}{( x - 3 ) ^{2}} d x

Apply u-substitution

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

= 7 \cdot \int \frac{1}{u ^{2}} d u

Apply the Power Rule

: - \frac{1}{u}

= 7 (- \frac{1}{u})

Substitute back

u = x - 3

= 7 (- \frac{1}{x - 3})

Simplify

7 (- \frac{1}{x - 3}) : - \frac{7}{x - 3}

= - \frac{7}{x - 3}

Add a constant to the solution

= - \frac{7}{x - 3} + C

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What is the integral of 7/((x-3)(x-3)) ?
The integral of 7/((x-3)(x-3)) is -7/(x-3)+C