What is the integral of 4sin(x)+3cos(x)+5e^x ?

The integral of 4sin(x)+3cos(x)+5e^x is -4cos(x)+3sin(x)+5e^x+C

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integral of 4sin(x)+3cos(x)+5e^x

\int 4 sin (x) + 3 cos (x) + 5 e^{x} d x

- 4 cos (x) + 3 sin (x) + 5 e^{x} + C

Solution steps

\int 4 sin (x) + 3 cos (x) + 5 e^{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 4 sin (x) d x + \int 3 cos (x) d x + \int 5 e^{x} d x

\int 4 sin (x) d x = - 4 cos (x)

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

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

= - 4 cos (x) + 3 sin (x) + 5 e^{x}

Add a constant to the solution

= - 4 cos (x) + 3 sin (x) + 5 e^{x} + C

What is the integral of 4sin(x)+3cos(x)+5e^x ?
The integral of 4sin(x)+3cos(x)+5e^x is -4cos(x)+3sin(x)+5e^x+C