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

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

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

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

- \frac{3}{2 ( x - 1 ) ^{2}} + C

Solution steps

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

Apply u-substitution

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

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

Apply the Power Rule

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

= 3 (- \frac{1}{2 u ^{2}})

Substitute back

u = x - 1

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

Simplify

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

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

Add a constant to the solution

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

\frac{d}{d x} (arctan (\frac{x}{8}))

\int x^{3} (\frac{1}{x} + 6 x^{2}) d x

\int 7 x^{6} sin (x^{7}) d x

\int x x^{2} - 3 d x

\frac{1}{s + 2}

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