What is the integral of 2sin(x)+cos(x)-3 ?

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

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integral of 2sin(x)+cos(x)-3

\int 2 sin (x) + cos (x) - 3 d x

- 2 cos (x) + sin (x) - 3 x + C

Solution steps

\int 2 sin (x) + cos (x) - 3 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 2 sin (x) d x + \int cos (x) d x - \int 3 d x

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

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

\int 3 d x = 3 x

= - 2 cos (x) + sin (x) - 3 x

Add a constant to the solution

= - 2 cos (x) + sin (x) - 3 x + C

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