What is the integral of (5-4x)e^{6-5x} ?

The integral of (5-4x)e^{6-5x} is 4/5 e^{-5x+6}x-21/25 e^{-5x+6}+C

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integral of (5-4x)e^{6-5x}

\int (5 - 4 x) e^{6 - 5 x} d x

\frac{4}{5} e^{- 5 x + 6} x - \frac{21}{25} e^{- 5 x + 6} + C

Solution steps

\int (5 - 4 x) e^{6 - 5 x} d x

Expand

(5 - 4 x) e^{6 - 5 x} : 5 e^{6 - 5 x} - 4 e^{6 - 5 x} x

= \int 5 e^{6 - 5 x} - 4 e^{6 - 5 x} 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 e^{6 - 5 x} d x - \int 4 e^{6 - 5 x} x d x

\int 5 e^{6 - 5 x} d x = - e^{6 - 5 x}

\int 4 e^{6 - 5 x} x d x = 4 (- \frac{1}{5} e^{6 - 5 x} x - \frac{1}{25} e^{6 - 5 x})

= - e^{6 - 5 x} - 4 (- \frac{1}{5} e^{6 - 5 x} x - \frac{1}{25} e^{6 - 5 x})

Simplify

- e^{6 - 5 x} - 4 (- \frac{1}{5} e^{6 - 5 x} x - \frac{1}{25} e^{6 - 5 x}) : \frac{4}{5} e^{- 5 x + 6} x - \frac{21}{25} e^{- 5 x + 6}

= \frac{4}{5} e^{- 5 x + 6} x - \frac{21}{25} e^{- 5 x + 6}

Add a constant to the solution

= \frac{4}{5} e^{- 5 x + 6} x - \frac{21}{25} e^{- 5 x + 6} + C

What is the integral of (5-4x)e^{6-5x} ?
The integral of (5-4x)e^{6-5x} is 4/5 e^{-5x+6}x-21/25 e^{-5x+6}+C