What is the integral of (-3x+7)/(x^2+x-2) ?

The integral of (-3x+7)/(x^2+x-2) is 4/3 ln|x-1|-13/3 ln|x+2|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (-3x+7)/(x^2+x-2)

\int \frac{- 3 x + 7}{x ^{2} + x - 2} d x

\frac{4}{3} ln ∣ x - 1 ∣ - \frac{13}{3} ln ∣ x + 2 ∣ + C

Solution steps

\int \frac{- 3 x + 7}{x ^{2} + x - 2} d x

Take the partial fraction of

\frac{- 3 x + 7}{x ^{2} + x - 2} : \frac{4}{3 ( x - 1 )} - \frac{13}{3 ( x + 2 )}

= \int \frac{4}{3 ( x - 1 )} - \frac{13}{3 ( x + 2 )} 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{4}{3 ( x - 1 )} d x - \int \frac{13}{3 ( x + 2 )} d x

\int \frac{4}{3 ( x - 1 )} d x = \frac{4}{3} ln ∣ x - 1 ∣

\int \frac{13}{3 ( x + 2 )} d x = \frac{13}{3} ln ∣ x + 2 ∣

= \frac{4}{3} ln ∣ x - 1 ∣ - \frac{13}{3} ln ∣ x + 2 ∣

Add a constant to the solution

= \frac{4}{3} ln ∣ x - 1 ∣ - \frac{13}{3} ln ∣ x + 2 ∣ + C

\int \frac{y ^{4} + 4 y ^{2} - 1}{y ^{3} + 4 y} d y

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

\int \frac{7 x ^{2}}{( 121 + x ^{2} ) ^{2}} d x

\int \frac{cos ( x ) sin ( x )}{1 + cos ^{4} ( x )} d x

\int \frac{2}{cos ( θ ) - 1} d θ

What is the integral of (-3x+7)/(x^2+x-2) ?
The integral of (-3x+7)/(x^2+x-2) is 4/3 ln|x-1|-13/3 ln|x+2|+C