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

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

Popular >

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

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

- \frac{1}{( x - 1 ) ^{2}} + C

Solution steps

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

Take the constant out:

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

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

Apply u-substitution

: \int \frac{1}{u ^{3}} d u

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

Apply the Power Rule

: - \frac{1}{2 u ^{2}}

= 2 (- \frac{1}{2 u ^{2}})

Substitute back

u = x - 1

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

Simplify

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

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

Add a constant to the solution

= - \frac{1}{( x - 1 ) ^{2}} + C

x \to 0 + lim (\frac{1}{e ^{x} - 1} - \frac{1}{x})

y = 4 - x^{2}, y = 0

cos (3 t) - cos (7 t)

x^{3} + 3

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

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