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

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

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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

(12, - 16), (- 9, 8)

\int (tan (x) (6 cos (x) - 6 sec (x))) d x

y^{^{''}} - y^{^{'}} - 6 y = - 4 e^{2} t, y (0) = 0, y^{^{'}} (0) = 0

\int \frac{x ^{2}}{( x - 1 ) ( x ^{2} + 4 x + 5 )} d x

\frac{d y}{d x} = \frac{5 x}{3 y}