en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Calculus >

integral of (6+u)/u

Solution

\int \frac{6 + u}{u} d u

Solution

6 ln ∣ u ∣ + u + C

Solution steps

\int \frac{6 + u}{u} d u

Expand

\frac{6 + u}{u} : \frac{6}{u} + 1

= \int \frac{6}{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{6}{u} d u + \int 1 d u

\int \frac{6}{u} d u = 6 ln ∣ u ∣

\int 1 d u = u

= 6 ln ∣ u ∣ + u

Add a constant to the solution

= 6 ln ∣ u ∣ + u + C

Graph

Popular Examples

derivative of-2sin(2t)

derivative of (x^2/3)

integral of (e^{3x})/(sqrt(4-4e^{6x))}

area-4x^2+6.25x+8,2.5x+7

Frequently Asked Questions (FAQ)

What is the integral of (6+u)/u ?
The integral of (6+u)/u is 6ln|u|+u+C