en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Calculus >

integral of (t+2)/t

Solution

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

Solution

t + 2 ln ∣ t ∣ + C

Solution steps

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

Expand

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

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

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

\int 1 d t = t

\int \frac{2}{t} d t = 2 ln ∣ t ∣

= t + 2 ln ∣ t ∣

Add a constant to the solution

= t + 2 ln ∣ t ∣ + C

Graph

Popular Examples

integral of (x-2)/(x^2-4x+5)

integral of (2-x^{15})

integral of sqrt(x-1/4)

integral of sqrt(t^2)

integral of (3x^2)/((x^3+1)^3)

Frequently Asked Questions (FAQ)

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