What is the integral of 5e^{-2x}+4 ?

The integral of 5e^{-2x}+4 is -5/2 e^{-2x}+4x+C

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integral of 5e^{-2x}+4

\int 5 e^{- 2 x} + 4 d x

- \frac{5}{2} e^{- 2 x} + 4 x + C

Solution steps

\int 5 e^{- 2 x} + 4 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^{- 2 x} d x + \int 4 d x

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

\int 4 d x = 4 x

= - \frac{5}{2} e^{- 2 x} + 4 x

Add a constant to the solution

= - \frac{5}{2} e^{- 2 x} + 4 x + C

6 \frac{d y}{d x} - y^{2} = 0

2 cos (t)

2 x^{2} y^{^{''}} + 5 x y^{^{'}} + y = x^{2} - x

\frac{s}{( s ^{2} + 2 s + 2 )}

y^{^{'}} - \frac{1}{t} y = 0

What is the integral of 5e^{-2x}+4 ?
The integral of 5e^{-2x}+4 is -5/2 e^{-2x}+4x+C