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

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

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

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

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

Solution steps

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

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 q + \int \frac{44}{e ^{0.2 q}} d q

\int 34 d q = 34 q

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

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

Add a constant to the solution

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

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