What is the integral of 3/((x-2)^2) ?

The integral of 3/((x-2)^2) is -3/(x-2)+C

integral of 3/((x-2)^2)

\int \frac{3}{( x - 2 ) ^{2}} d x

- \frac{3}{x - 2} + C

Solution steps

\int \frac{3}{( x - 2 ) ^{2}} d x

Take the constant out:

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

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

Apply u-substitution

= 3 \cdot \int \frac{1}{u ^{2}} d u

Apply the Power Rule

= 3 (- \frac{1}{u})

Substitute back

u = x - 2

= 3 (- \frac{1}{x - 2})

Simplify

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

= - \frac{3}{x - 2}

Add a constant to the solution

= - \frac{3}{x - 2} + C

s l o p e in t erce pt (12, - 16), (- 9, 8)

\frac{d}{d x} (\frac{cos ( x )}{1 + cot ( x )})

\int_{0}^{\frac{π}{4}} sin (3 x) d x

\frac{d}{d x} (\frac{2 ( - x ^{2} - 4 )}{( x ^{2} - 4 ) ^{2}})

x \to 0 lim (\frac{tan ( 4 x )}{3 x})