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Popular Calculus >

integral of (1-t)/t

Solution

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

Solution

ln ∣ t ∣ - t + C

Solution steps

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

Expand

\frac{1 - t}{t} : \frac{1}{t} - 1

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

\int \frac{1}{t} d t = ln ∣ t ∣

\int 1 d t = t

= ln ∣ t ∣ - t

Add a constant to the solution

= ln ∣ t ∣ - t + C

Graph

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Frequently Asked Questions (FAQ)

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