What is the integral of 3/((x-1)^2) ?

The integral of 3/((x-1)^2) is -3/(x-1)+C

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integral of 3/((x-1)^2)

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

- \frac{3}{x - 1} + C

Solution steps

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

Apply u-substitution

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

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

Apply the Power Rule

: - \frac{1}{u}

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

Substitute back

u = x - 1

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

Simplify

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

= - \frac{3}{x - 1}

Add a constant to the solution

= - \frac{3}{x - 1} + C

y = x^{2} - x^{4} (1)

\frac{d}{d x} (2 x^{3} + \frac{2}{x ^{3}})

\frac{d y}{d x} = 0.0019 y (1000 - y)

y^{\frac{1}{2}} \frac{d y}{d x} + y^{\frac{3}{2}} = 1, y (0) = 4

y = x^{2} - 8 x