What is the integral of (x+1)/(x^2+3x-10) ?

The integral of (x+1)/(x^2+3x-10) is 3/7 ln|x-2|+4/7 ln|x+5|+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)/(x^2+3x-10)

\int \frac{x + 1}{x ^{2} + 3 x - 10} d x

\frac{3}{7} ln ∣ x - 2 ∣ + \frac{4}{7} ln ∣ x + 5 ∣ + C

Solution steps

\int \frac{x + 1}{x ^{2} + 3 x - 10} d x

Take the partial fraction of

\frac{x + 1}{x ^{2} + 3 x - 10} : \frac{3}{7 ( x - 2 )} + \frac{4}{7 ( x + 5 )}

= \int \frac{3}{7 ( x - 2 )} + \frac{4}{7 ( x + 5 )} 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{3}{7 ( x - 2 )} d x + \int \frac{4}{7 ( x + 5 )} d x

\int \frac{3}{7 ( x - 2 )} d x = \frac{3}{7} ln ∣ x - 2 ∣

\int \frac{4}{7 ( x + 5 )} d x = \frac{4}{7} ln ∣ x + 5 ∣

= \frac{3}{7} ln ∣ x - 2 ∣ + \frac{4}{7} ln ∣ x + 5 ∣

Add a constant to the solution

= \frac{3}{7} ln ∣ x - 2 ∣ + \frac{4}{7} ln ∣ x + 5 ∣ + C

\int \frac{8}{( 1 - 7 t ) ^{9}} d t

\int 9 sin (5 x) d x

\int \frac{2}{n} sin (\frac{n x}{2}) d x

\int e^{x} ln (1 + x) d x

\int x^{2} 3 x + 4 d x

What is the integral of (x+1)/(x^2+3x-10) ?
The integral of (x+1)/(x^2+3x-10) is 3/7 ln|x-2|+4/7 ln|x+5|+C