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

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

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integral of 3sin(t)+2cos(t)+2

\int 3 sin (t) + 2 cos (t) + 2 d t

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

Solution steps

\int 3 sin (t) + 2 cos (t) + 2 d t

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 sin (t) d t + \int 2 cos (t) d t + \int 2 d t

\int 3 sin (t) d t = - 3 cos (t)

\int 2 cos (t) d t = 2 sin (t)

\int 2 d t = 2 t

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

Add a constant to the solution

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

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