What is the integral of 3t^{-1} ?

The integral of 3t^{-1} is 3ln|t|+C

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integral of 3t^{-1}

\int 3 t^{- 1} d t

3 ln ∣ t ∣ + C

Solution steps

\int 3 t^{- 1} d t

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 3 \cdot \int t^{- 1} d t

Use the common integral:

\int t^{- 1} d t = ln (∣ t ∣)

= 3 ln ∣ t ∣

Add a constant to the solution

= 3 ln ∣ t ∣ + C