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

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

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

\int \frac{- 1}{1 - 2 x + x ^{2}} d x

\frac{1}{x - 1} + C

Solution steps

\int \frac{- 1}{1 - 2 x + x ^{2}} d x

Take the constant out:

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

= - \int \frac{1}{1 - 2 x + x ^{2}} d x

Complete the square

1 - 2 x + x^{2} : (x - 1)^{2}

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

Apply u-substitution

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

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

Apply the Power Rule

: - \frac{1}{u}

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

Substitute back

u = x - 1

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

Simplify

= \frac{1}{x - 1}

Add a constant to the solution

= \frac{1}{x - 1} + C

x \to 0 lim (e^{c s c (x)})

f (x) = \frac{4 x}{9 e ^{5 x}}

(5, - 2), (- 6, 4)

\int 4 x + 3 d x

2 x y d y = (y^{2} + 1) d x

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