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

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

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

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

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

Solution steps

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

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

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

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

Add a constant to the solution

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

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