What is the integral of 3arccos(x/2) ?

The integral of 3arccos(x/2) is 3(xarccos(x/2)-sqrt(4-x^2))+C

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integral of 3arccos(x/2)

\int 3 arccos (\frac{x}{2}) d x

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

Solution steps

\int 3 arccos (\frac{x}{2}) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 3 \cdot \int arccos (\frac{x}{2}) d x

Apply Integration By Parts

: x arccos (\frac{x}{2}) - \int - \frac{x}{4 - x ^{2}} d x

= 3 (x arccos (\frac{x}{2}) - \int - \frac{x}{4 - x ^{2}} d x)

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

= 3 (x arccos (\frac{x}{2}) - 4 - x^{2})

Add a constant to the solution

= 3 (x arccos (\frac{x}{2}) - 4 - x^{2}) + C

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

f (x) = 7 x^{4} + 5 x - 3, (1, 9)

y^{^{'}} = (x + y + 2)^{2}

\frac{d}{d x} (2 x^{2} + 3 x + 4)

\frac{d y}{d x} = sin (y) cos (x)

What is the integral of 3arccos(x/2) ?
The integral of 3arccos(x/2) is 3(xarccos(x/2)-sqrt(4-x^2))+C