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

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

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integral of-cos(x/2)

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

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

Solution steps

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

Take the constant out:

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

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

Apply u-substitution

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

= - \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 \int cos (u) d u

Use the common integral:

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

= - 2 sin (u)

Substitute back

u = \frac{x}{2}

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

Add a constant to the solution

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

\frac{d}{d x} (x + \frac{7}{x})

\frac{d}{d x} ((x - 2 π)^{2})

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

\frac{d}{d x} (\frac{4 x}{3 x + 1})

x \to 5 lim ((3 + \frac{1}{x})^{3})