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

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

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integral of 4x+4sin(x)

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

2 x^{2} - 4 cos (x) + C

Solution steps

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

\int 4 x d x = 2 x^{2}

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

= 2 x^{2} - 4 cos (x)

Add a constant to the solution

= 2 x^{2} - 4 cos (x) + C

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

\frac{d}{d x} (6 arcsin (x^{4}))

\frac{d y}{d x} = x + 5 y, y (0) = 3

x \to 0 lim (cos^{\frac{3}{x ^{2}}} (2 x))

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

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