What is the integral of 5e^{-4x+8}-5 ?

The integral of 5e^{-4x+8}-5 is -5/4 e^{-4x+8}-5x+C

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integral of 5e^{-4x+8}-5

\int 5 e^{- 4 x + 8} - 5 d x

- \frac{5}{4} e^{- 4 x + 8} - 5 x + C

Solution steps

\int 5 e^{- 4 x + 8} - 5 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 e^{- 4 x + 8} d x - \int 5 d x

\int 5 e^{- 4 x + 8} d x = - \frac{5}{4} e^{- 4 x + 8}

\int 5 d x = 5 x

= - \frac{5}{4} e^{- 4 x + 8} - 5 x

Add a constant to the solution

= - \frac{5}{4} e^{- 4 x + 8} - 5 x + C

\int y e^{- 2 y} d y

\frac{d}{d t} (\frac{1}{2} t^{2} + t)

f (x) = 3^{- 6 x + 6}

\int_{0}^{2} \frac{2 x}{( x ^{2} + 1 ) ^{3}} d x

\frac{d}{d x} (3 x^{2} - 6 x + 1)

What is the integral of 5e^{-4x+8}-5 ?
The integral of 5e^{-4x+8}-5 is -5/4 e^{-4x+8}-5x+C