en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Calculus >

integral of (2+u)/u

Solution

\int \frac{2 + u}{u} d u

Solution

2 ln ∣ u ∣ + u + C

Solution steps

\int \frac{2 + u}{u} d u

Expand

\frac{2 + u}{u} : \frac{2}{u} + 1

= \int \frac{2}{u} + 1 d u

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{2}{u} d u + \int 1 d u

\int \frac{2}{u} d u = 2 ln ∣ u ∣

\int 1 d u = u

= 2 ln ∣ u ∣ + u

Add a constant to the solution

= 2 ln ∣ u ∣ + u + C

Graph

Popular Examples

derivative of y=x^3(3-x^2)

(\partial)/(\partial x)(sin(pi(4x-2y)))

slope of y=3x^2,\at x=1

integral of (sec^5(x))

slope ofintercept (-4,5),(5,-22)

Frequently Asked Questions (FAQ)

What is the integral of (2+u)/u ?
The integral of (2+u)/u is 2ln|u|+u+C