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Popular >

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

Popular Examples

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\int \frac{- 2 ( x - 9 )}{( x + 5 ) ( x - 2 )} d x

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\int e^{- 3 x} cos (5 x) d x

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\int \frac{1}{( 5 - 4 x - x ^{2} )} d x

integral of sin^3(y)cos^8(y)

\int sin^{3} (y) cos^{8} (y) d y

integral of (11}{x^2}sin^2(\frac{11)/x)

\int \frac{11}{x ^{2}} sin^{2} (\frac{11}{x}) d x

Frequently Asked Questions (FAQ)

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