What is the integral of (5x+3)/(x^2+4) ?

The integral of (5x+3)/(x^2+4) is 5/2 ln|x^2+4|+3/2 arctan(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 (5x+3)/(x^2+4)

\int \frac{5 x + 3}{x ^{2} + 4} d x

\frac{5}{2} ln x^{2} + 4 + \frac{3}{2} arctan (\frac{x}{2}) + C

Solution steps

\int \frac{5 x + 3}{x ^{2} + 4} d x

Expand

\frac{5 x + 3}{x ^{2} + 4} : \frac{5 x}{x ^{2} + 4} + \frac{3}{x ^{2} + 4}

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

\int \frac{5 x}{x ^{2} + 4} d x = \frac{5}{2} ln x^{2} + 4

\int \frac{3}{x ^{2} + 4} d x = \frac{3}{2} arctan (\frac{x}{2})

= \frac{5}{2} ln x^{2} + 4 + \frac{3}{2} arctan (\frac{x}{2})

Add a constant to the solution

= \frac{5}{2} ln x^{2} + 4 + \frac{3}{2} arctan (\frac{x}{2}) + C

\int cos^{0} (x) d x

\frac{d}{d x} ((x - 2)^{3} e^{3 x})

\frac{\partial}{\partial z} (6 x y sin (z))

- \frac{4}{3} (x + 1), 2, 5, 0

\int 3 sec (x) (tan (x) - sec (x)) d x

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