What is the integral of (sin(x)-5cos(x)) ?

The integral of (sin(x)-5cos(x)) is -cos(x)-5sin(x)+C

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integral of (sin(x)-5cos(x))

\int (sin (x) - 5 cos (x)) d x

- cos (x) - 5 sin (x) + C

Solution steps

\int sin (x) - 5 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 5 cos (x) d x

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

\int 5 cos (x) d x = 5 sin (x)

= - cos (x) - 5 sin (x)

Add a constant to the solution

= - cos (x) - 5 sin (x) + C

x \to 1 lim (\frac{x}{x ^{2} + 1})

\frac{\partial}{\partial x} (e^{- 2 x^{2} - 5 y^{2}})

\int x y e^{x} d x

\int (ln (x + 1 + x^{2}))^{'} d x

\frac{\partial}{\partial u} (u^{\frac{1}{3}} \cdot v^{\frac{2}{3}})

What is the integral of (sin(x)-5cos(x)) ?
The integral of (sin(x)-5cos(x)) is -cos(x)-5sin(x)+C