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

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

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

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

x^{2} - 4 x + 3 + C

Solution steps

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

Apply u-substitution

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

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

Apply the Power Rule

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

= \frac{1}{2} \cdot 2 u^{\frac{1}{2}}

Substitute back

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

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

Simplify

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

= x^{2} - 4 x + 3

Add a constant to the solution

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

f (x) = ln (e^{x} + x e^{x})

x \to 0 lim (\frac{x ^{2} - 1}{x - 1})

\int (2 x + 2) e^{- 2 x} d x

\int_{1}^{e} \frac{ln ( t )}{t} d t

n = 1 \sum \infty \frac{2 ^{n}}{3 ^{n}}

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