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

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

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

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

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

Solution steps

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

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

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

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

Add a constant to the solution

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

\int \frac{x + 3}{( x - 1 ) ( x ^{2} + 1 )} d x

\frac{d}{d x} (ln (3 x + 4))

x \to 6 + lim (x 6 - x)

x \to 0 lim ((x) sin (\frac{1}{x}))

x \to - 7 lim (\frac{x ^{2} - 3}{7 - x})

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