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

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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

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} (- \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

in v erse l a pl a ce \frac{12}{s}

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

t a y l or f (x) = \frac{1}{x}

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

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