What is the integral of ((x-2))/(sqrt(x^2-6x)) ?

The integral of ((x-2))/(sqrt(x^2-6x)) is sqrt(x^2-6x)+ln(1/3 |sqrt(x^2-6x)+x-3|)+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))/(sqrt(x^2-6x))

\int \frac{( x - 2 )}{x ^{2} - 6 x} d x

x^{2} - 6 x + ln (\frac{1}{3} x^{2} - 6 x + x - 3) + C

Solution steps

\int \frac{x - 2}{x ^{2} - 6 x} d x

Expand

\frac{x - 2}{x ^{2} - 6 x} : \frac{x}{x ^{2} - 6 x} - \frac{2}{x ^{2} - 6 x}

= \int \frac{x}{x ^{2} - 6 x} - \frac{2}{x ^{2} - 6 x} 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{x}{x ^{2} - 6 x} d x - \int \frac{2}{x ^{2} - 6 x} d x

\int \frac{x}{x ^{2} - 6 x} d x = x^{2} - 6 x + 3 ln (\frac{1}{3} x^{2} - 6 x + x - 3)

\int \frac{2}{x ^{2} - 6 x} d x = 2 ln (\frac{1}{3} x^{2} - 6 x + x - 3)

= x^{2} - 6 x + 3 ln (\frac{1}{3} x^{2} - 6 x + x - 3) - 2 ln (\frac{1}{3} x^{2} - 6 x + x - 3)

Simplify

= x^{2} - 6 x + ln (\frac{1}{3} x^{2} - 6 x + x - 3)

Add a constant to the solution

= x^{2} - 6 x + ln (\frac{1}{3} x^{2} - 6 x + x - 3) + C

\int \frac{4}{64 - 16 x ^{2}} d x

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

\int \frac{x ^{3} + x ^{2} + 2 x + 3}{x ^{4} + 5 x ^{2} + 6} d x

\int \frac{2 x + 1}{x ^{2} - 4 x + 5} d x

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

What is the integral of ((x-2))/(sqrt(x^2-6x)) ?
The integral of ((x-2))/(sqrt(x^2-6x)) is sqrt(x^2-6x)+ln(1/3 |sqrt(x^2-6x)+x-3|)+C