What is the integral of ((x-2))/((x^2-4x+3)^3) ?

The integral of ((x-2))/((x^2-4x+3)^3) is -1/(4(x^2-4x+3)^2)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of ((x-2))/((x^2-4x+3)^3)

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

- \frac{1}{4 ( x ^{2} - 4 x + 3 ) ^{2}} + C

Solution steps

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

Apply u-substitution

: \int \frac{1}{2 u ^{3}} d u

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

Take the constant out:

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

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

Apply the Power Rule

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

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

Substitute back

u = x^{2} - 4 x + 3

= \frac{1}{2} (- \frac{1}{2 ( x ^{2} - 4 x + 3 ) ^{2}})

Simplify

\frac{1}{2} (- \frac{1}{2 ( x ^{2} - 4 x + 3 ) ^{2}}) : - \frac{1}{4 ( x ^{2} - 4 x + 3 ) ^{2}}

= - \frac{1}{4 ( x ^{2} - 4 x + 3 ) ^{2}}

Add a constant to the solution

= - \frac{1}{4 ( x ^{2} - 4 x + 3 ) ^{2}} + C

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

\frac{12}{s}

\int_{0}^{3} x - 1 d x

f (x) = \frac{1}{x}

\int_{- 2}^{3} \frac{11}{x ^{4}} d x

What is the integral of ((x-2))/((x^2-4x+3)^3) ?
The integral of ((x-2))/((x^2-4x+3)^3) is -1/(4(x^2-4x+3)^2)+C