What is the integral of (1-2x)/(sqrt(x^2-4)) ?

The integral of (1-2x)/(sqrt(x^2-4)) is ln(1/2 |sqrt(x^2-4)+x|)-2sqrt(x^2-4)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (1-2x)/(sqrt(x^2-4))

\int \frac{1 - 2 x}{x ^{2} - 4} d x

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

Solution steps

\int \frac{1 - 2 x}{x ^{2} - 4} d x

Expand

\frac{1 - 2 x}{x ^{2} - 4} : \frac{1}{x ^{2} - 4} - \frac{2 x}{x ^{2} - 4}

= \int \frac{1}{x ^{2} - 4} - \frac{2 x}{x ^{2} - 4} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int \frac{1}{x ^{2} - 4} d x - \int \frac{2 x}{x ^{2} - 4} d x

\int \frac{1}{x ^{2} - 4} d x = ln (\frac{1}{2} x^{2} - 4 + x)

\int \frac{2 x}{x ^{2} - 4} d x = 2 x^{2} - 4

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

Add a constant to the solution

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

\int tan^{4} (x) sec (x) d x

\int_{2}^{7} t^{2} ln (2 t) d t

\int \frac{tan ( x )}{sec ( x ) + tan ( x )} d x

\int sin^{2} (\frac{x}{5}) d x

\frac{d y}{d t} = y + 1 + 2 sin (t)

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