What is the integral of 34+(44)/(e^{0.2x)} ?

The integral of 34+(44)/(e^{0.2x)} is 34x+44(x/(e^{0.2x)}+5(-0.2e^{-0.2x}x-e^{-0.2x}))+C

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integral of 34+(44)/(e^{0.2x)}

\int 34 + \frac{44}{e ^{0.2 x}} d x

34 x + 44 (\frac{x}{e ^{0.2 x}} + 5 (- 0.2 e^{- 0.2 x} x - e^{- 0.2 x})) + C

Solution steps

\int 34 + \frac{44}{e ^{0.2 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

= \int 34 d x + \int \frac{44}{e ^{0.2 x}} d x

\int 34 d x = 34 x

\int \frac{44}{e ^{0.2 x}} d x = 44 (\frac{x}{e ^{0.2 x}} + 5 (- 0.2 e^{- 0.2 x} x - e^{- 0.2 x}))

= 34 x + 44 (\frac{x}{e ^{0.2 x}} + 5 (- 0.2 e^{- 0.2 x} x - e^{- 0.2 x}))

Add a constant to the solution

= 34 x + 44 (\frac{x}{e ^{0.2 x}} + 5 (- 0.2 e^{- 0.2 x} x - e^{- 0.2 x})) + C

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What is the integral of 34+(44)/(e^{0.2x)} ?
The integral of 34+(44)/(e^{0.2x)} is 34x+44(x/(e^{0.2x)}+5(-0.2e^{-0.2x}x-e^{-0.2x}))+C