What is the integral of (4/x+x/4) ?

The integral of (4/x+x/4) is 4ln|x|+(x^2)/8+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (4/x+x/4)

\int (\frac{4}{x} + \frac{x}{4}) d x

4 ln ∣ x ∣ + \frac{x ^{2}}{8} + C

Solution steps

\int \frac{4}{x} + \frac{x}{4} 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}{x} d x + \int \frac{x}{4} d x

\int \frac{4}{x} d x = 4 ln ∣ x ∣

\int \frac{x}{4} d x = \frac{x ^{2}}{8}

= 4 ln ∣ x ∣ + \frac{x ^{2}}{8}

Add a constant to the solution

= 4 ln ∣ x ∣ + \frac{x ^{2}}{8} + C

11 x e^{x}

\frac{\partial}{\partial y} (5 x y)

\frac{d}{d x} (\frac{sin ( 2 x )}{sin ( 3 x )})

ln (x) \frac{d y}{d x} = \frac{y}{x}

\frac{\partial}{\partial y} (e^{x} + x cos (y))

What is the integral of (4/x+x/4) ?
The integral of (4/x+x/4) is 4ln|x|+(x^2)/8+C