What is the integral of 1/(2*x^2-x-3) ?

The integral of 1/(2*x^2-x-3) is -1/5 ln|x+1|+1/5 ln|2x-3|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 1/(2*x^2-x-3)

\int \frac{1}{2 \cdot x ^{2} - x - 3} d x

- \frac{1}{5} ln ∣ x + 1 ∣ + \frac{1}{5} ln ∣ 2 x - 3 ∣ + C

Solution steps

\int \frac{1}{2 x ^{2} - x - 3} d x

Take the partial fraction of

\frac{1}{2 x ^{2} - x - 3} : - \frac{1}{5 ( x + 1 )} + \frac{2}{5 ( 2 x - 3 )}

= \int - \frac{1}{5 ( x + 1 )} + \frac{2}{5 ( 2 x - 3 )} 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}{5 ( x + 1 )} d x + \int \frac{2}{5 ( 2 x - 3 )} d x

\int \frac{1}{5 ( x + 1 )} d x = \frac{1}{5} ln ∣ x + 1 ∣

\int \frac{2}{5 ( 2 x - 3 )} d x = \frac{1}{5} ln ∣ 2 x - 3 ∣

= - \frac{1}{5} ln ∣ x + 1 ∣ + \frac{1}{5} ln ∣ 2 x - 3 ∣

Add a constant to the solution

= - \frac{1}{5} ln ∣ x + 1 ∣ + \frac{1}{5} ln ∣ 2 x - 3 ∣ + C

\frac{\partial}{\partial s} (e^{s t})

\int (2 sin (x) - 3 cos (x) + \frac{1}{2}) d x

\int csc^{2} (t) d t

\frac{2}{( s + 3 ) ^{2} - 9}

\int csc^{2} (5 y) d y

What is the integral of 1/(2*x^2-x-3) ?
The integral of 1/(2*x^2-x-3) is -1/5 ln|x+1|+1/5 ln|2x-3|+C