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

\int \frac{7 x + 3}{x ^{2} + 3 x - 4} d x

\int x sin (1 n x) d x

\int \frac{e ^{5 x}}{x} d x

\int \frac{1}{3 x ^{2} - 4} d x

\int \frac{3 x ^{2}}{5 x ^{3} - 7} d x

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