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

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

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

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

Solution steps

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

Take the partial fraction of

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

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

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

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

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

Add a constant to the solution

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

\int x^{2} + 3 x - 10 d x

\int e^{(- 3 x^{2} - 1)} 6 x d x

\int e^{(3 - s) t} d t

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

\int \frac{1}{( sin ( x ) )} d x

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