What is the integral of-4cos(x/2)+5 ?

The integral of-4cos(x/2)+5 is -8sin(x/2)+5x+C

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integral of-4cos(x/2)+5

\int - 4 cos (\frac{x}{2}) + 5 d x

- 8 sin (\frac{x}{2}) + 5 x + C

Solution steps

\int - 4 cos (\frac{x}{2}) + 5 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 (\frac{x}{2}) d x + \int 5 d x

\int 4 cos (\frac{x}{2}) d x = 8 sin (\frac{x}{2})

\int 5 d x = 5 x

= - 8 sin (\frac{x}{2}) + 5 x

Add a constant to the solution

= - 8 sin (\frac{x}{2}) + 5 x + C

(x + 1) y^{^{'}} + (x + 2) y = 2 x e^{- 2}

\int 49 x^{2} + 1764 d x

\int \frac{x \cdot e ^{2 x}}{( 1 + 2 x ) ^{2}} d x

\frac{\partial}{\partial y} (cos (x y^{2}))

x \to - 2 lim (x - 1)

What is the integral of-4cos(x/2)+5 ?
The integral of-4cos(x/2)+5 is -8sin(x/2)+5x+C