What is the integral of 3e^x-2sin(x)+1 ?

The integral of 3e^x-2sin(x)+1 is 3e^x+2cos(x)+x+C

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integral of 3e^x-2sin(x)+1

\int 3 e^{x} - 2 sin (x) + 1 d x

3 e^{x} + 2 cos (x) + x + C

Solution steps

\int 3 e^{x} - 2 sin (x) + 1 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 e^{x} d x - \int 2 sin (x) d x + \int 1 d x

\int 3 e^{x} d x = 3 e^{x}

\int 2 sin (x) d x = - 2 cos (x)

\int 1 d x = x

= 3 e^{x} - (- 2 cos (x)) + x

Simplify

= 3 e^{x} + 2 cos (x) + x

Add a constant to the solution

= 3 e^{x} + 2 cos (x) + x + C

What is the integral of 3e^x-2sin(x)+1 ?
The integral of 3e^x-2sin(x)+1 is 3e^x+2cos(x)+x+C