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

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

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integral of-2cos(x/2)

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

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

Solution steps

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

Take the constant out:

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

= - 2 \cdot \int cos (\frac{x}{2}) d x

Apply u-substitution

: \int cos (u) \cdot 2 d u

= - 2 \cdot \int cos (u) \cdot 2 d u

Take the constant out:

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

= - 2 \cdot 2 \cdot \int cos (u) d u

Use the common integral:

\int cos (u) d u = sin (u)

= - 2 \cdot 2 sin (u)

Substitute back

u = \frac{x}{2}

= - 2 \cdot 2 sin (\frac{x}{2})

Simplify

= - 4 sin (\frac{x}{2})

Add a constant to the solution

= - 4 sin (\frac{x}{2}) + C

x \to 2 lim (x^{2} + 3 x)

\int 9 x^{- 2} d x

\frac{d}{d x} (\frac{x - 2}{x + 2})

y = x e^{a x}

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