What is the integral of 4sin(x)+cos(x) ?

The integral of 4sin(x)+cos(x) is -4cos(x)+sin(x)+C

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integral of 4sin(x)+cos(x)

\int 4 sin (x) + cos (x) d x

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

Solution steps

\int 4 sin (x) + 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 4 sin (x) d x + \int cos (x) d x

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

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

= - 4 cos (x) + sin (x)

Add a constant to the solution

= - 4 cos (x) + sin (x) + C

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\int (y + z) d x

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