en

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

Solution

\int 1 + \frac{2}{x} d x

Solution

x + 2 ln ∣ x ∣ + C

Solution steps

\int 1 + \frac{2}{x} 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 1 d x + \int \frac{2}{x} d x

\int 1 d x = x

\int \frac{2}{x} d x = 2 ln ∣ x ∣

= x + 2 ln ∣ x ∣

Add a constant to the solution

= x + 2 ln ∣ x ∣ + C

Popular Examples

derivative of cos(sin(5x^2))

\frac{d}{d x} (cos (sin (5 x^{2})))

derivative of (x^3-1/(x^3+1))

\frac{d}{d x} (\frac{x ^{3} - 1}{x ^{3} + 1})

y^{''}+y=cos(t)

y^{^{''}} + y = cos (t)

tangent of f(x)=x^3-3x^2+2x-2,\at x=2 tangent of

f (x) = x^{3} - 3 x^{2} + 2 x - 2, at x = 2

integral of 2x^2+2x

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

Frequently Asked Questions (FAQ)

What is the integral of 1+2/x ?
The integral of 1+2/x is x+2ln|x|+C