What is the integral of 3cos(x)+e^{-x}+4 ?

The integral of 3cos(x)+e^{-x}+4 is 3sin(x)-e^{-x}+4x+C

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integral of 3cos(x)+e^{-x}+4

\int 3 cos (x) + e^{- x} + 4 d x

3 sin (x) - e^{- x} + 4 x + C

Solution steps

\int 3 cos (x) + e^{- 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 3 cos (x) d x + \int e^{- x} d x + \int 4 d x

\int 3 cos (x) d x = 3 sin (x)

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

\int 4 d x = 4 x

= 3 sin (x) - e^{- x} + 4 x

Add a constant to the solution

= 3 sin (x) - e^{- x} + 4 x + C

What is the integral of 3cos(x)+e^{-x}+4 ?
The integral of 3cos(x)+e^{-x}+4 is 3sin(x)-e^{-x}+4x+C