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

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

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integral of 4sin(x)+4

\int 4 sin (x) + 4 d x

- 4 cos (x) + 4 x + C

Solution steps

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

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

\int 4 d x = 4 x

= - 4 cos (x) + 4 x

Add a constant to the solution

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

\frac{d y}{d x} = \frac{1}{4} y

x \to - 5 - lim (\frac{6}{x ^{2} - 25})

f (x) = sin (x^{2} + 2)

\frac{d ^{2}}{d x ^{2}} (e^{2 x^{2}})

\frac{d y}{d x}, e^{9 x} = sin (x + 8 y)