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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

\frac{x}{2 - x} + ln ∣ 2 - x ∣ + \frac{1}{2 - x} + C

Solution steps

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

Expand

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

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

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

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

= \frac{x}{2 - x} + ln ∣ 2 - x ∣ + \frac{1}{2 - x}

Add a constant to the solution

= \frac{x}{2 - x} + ln ∣ 2 - x ∣ + \frac{1}{2 - x} + C

\int_{0}^{4} (e^{- 2 x} + 1) d x

\frac{d}{d x} (y^{x})

f (x) = 7 x + 6

\int \frac{1}{2 tan ( x )} d x

\frac{s ^{2} + 3 s + 5}{s ^{3} ( s + 2 )}

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