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

The integral of-4cos(x)-x is -4sin(x)-(x^2)/2+C

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integral of-4cos(x)-x

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

- 4 sin (x) - \frac{x ^{2}}{2} + C

Solution steps

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

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

\int x d x = \frac{x ^{2}}{2}

= - 4 sin (x) - \frac{x ^{2}}{2}

Add a constant to the solution

= - 4 sin (x) - \frac{x ^{2}}{2} + C

\frac{d}{d x} ((5 x^{3} - 3 x + 4)^{20})

y^{^{'}} = 7 y^{5}

\int \frac{x}{4 + 2 x ^{2}} d x

\frac{d}{d x} (c f (x) + f (x) (c x))

\frac{d}{d x} (\frac{1}{2} ln (x^{2}))

What is the integral of-4cos(x)-x ?
The integral of-4cos(x)-x is -4sin(x)-(x^2)/2+C