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

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

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

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

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

Solution steps

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

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

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

= sin (x) - 2 cos (x)

Add a constant to the solution

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

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