What is the integral of 3.4(1-e^{-2.1x}) ?

The integral of 3.4(1-e^{-2.1x}) is 3.4(x+0.47619…e^{-2.1x})+C

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integral of 3.4(1-e^{-2.1x})

\int 3.4 (1 - e^{- 2.1 x}) d x

3.4 (x + 0.47619 \dots e^{- 2.1 x}) + C

Solution steps

\int 3.4 (1 - e^{- 2.1 x}) d x

Take the constant out:

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

= 3.4 \cdot \int 1 - e^{- 2.1 x} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= 3.4 (\int 1 d x - \int e^{- 2.1 x} d x)

\int 1 d x = x

\int e^{- 2.1 x} d x = - 0.47619 \dots e^{- 2.1 x}

= 3.4 (x - (- 0.47619 \dots e^{- 2.1 x}))

Simplify

= 3.4 (x + 0.47619 \dots e^{- 2.1 x})

Add a constant to the solution

= 3.4 (x + 0.47619 \dots e^{- 2.1 x}) + C

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What is the integral of 3.4(1-e^{-2.1x}) ?
The integral of 3.4(1-e^{-2.1x}) is 3.4(x+0.47619…e^{-2.1x})+C