What is the integral from e^2 to e^6 of 5t^{-1} ?

The integral from e^2 to e^6 of 5t^{-1} is 20

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integral from e^2 to e^6 of 5t^{-1}

\int_{e^{2}}^{e^{6}} 5 t^{- 1} d t

20

Solution steps

\int_{e^{2}}^{e^{6}} 5 t^{- 1} d t

Take the constant out:

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

= 5 \cdot \int_{e^{2}}^{e^{6}} t^{- 1} d t

Use the common integral:

\int t^{- 1} d t = ln (∣ t ∣)

= 5 [ln ∣ t ∣]_{e^{2}}^{e^{6}}

Compute the boundaries:

4

= 5 \cdot 4

Simplify

= 20

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What is the integral from e^2 to e^6 of 5t^{-1} ?
The integral from e^2 to e^6 of 5t^{-1} is 20