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Popular Calculus >

integral of (t+1)/t

Solution

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

Solution

t + ln ∣ t ∣ + C

Solution steps

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

Expand

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

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

\int 1 d t = t

\int \frac{1}{t} d t = ln ∣ t ∣

= t + ln ∣ t ∣

Add a constant to the solution

= t + ln ∣ t ∣ + C

Graph

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Frequently Asked Questions (FAQ)

What is the integral of (t+1)/t ?
The integral of (t+1)/t is t+ln|t|+C