en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Calculus >

integral of (4+u)/u

Solution

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

Solution

4 ln ∣ u ∣ + u + C

Solution steps

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

Expand

\frac{4 + u}{u} : \frac{4}{u} + 1

= \int \frac{4}{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{4}{u} d u + \int 1 d u

\int \frac{4}{u} d u = 4 ln ∣ u ∣

\int 1 d u = u

= 4 ln ∣ u ∣ + u

Add a constant to the solution

= 4 ln ∣ u ∣ + u + C

Graph

Popular Examples

derivative of (9x^4+5^3)

derivative of y= 1/(x+\frac{1){x+1}}

derivative of (3x^{-4})

derivative of 8e^x+x

Frequently Asked Questions (FAQ)

What is the integral of (4+u)/u ?
The integral of (4+u)/u is 4ln|u|+u+C