What is the integral of 4sin(x/2)+8 ?

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

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integral of 4sin(x/2)+8

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

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

Solution steps

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

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

\int 8 d x = 8 x

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

Add a constant to the solution

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

f (x) = x^{2} + 6, (1, 7)

\int csc^{6} (x) d x

\frac{( 1 - v )}{( 1 + v )}

\frac{d y}{d x} = \frac{1}{3} x (y - 2)^{2}

n = 0 \sum \infty 9

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