What is the integral of-5x+10-e^{-x} ?

The integral of-5x+10-e^{-x} is -(5x^2)/2+10x+e^{-x}+C

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integral of-5x+10-e^{-x}

\int - 5 x + 10 - e^{- x} d x

- \frac{5 x ^{2}}{2} + 10 x + e^{- x} + C

Solution steps

\int - 5 x + 10 - e^{- 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 5 x d x + \int 10 d x - \int e^{- x} d x

\int 5 x d x = \frac{5 x ^{2}}{2}

\int 10 d x = 10 x

\int e^{- x} d x = - e^{- x}

= - \frac{5 x ^{2}}{2} + 10 x - (- e^{- x})

Simplify

= - \frac{5 x ^{2}}{2} + 10 x + e^{- x}

Add a constant to the solution

= - \frac{5 x ^{2}}{2} + 10 x + e^{- x} + C

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What is the integral of-5x+10-e^{-x} ?
The integral of-5x+10-e^{-x} is -(5x^2)/2+10x+e^{-x}+C