What is the integral of-sin(1/2 x) ?

The integral of-sin(1/2 x) is 2cos(1/2 x)+C

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integral of-sin(1/2 x)

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

2 cos (\frac{1}{2} x) + C

Solution steps

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

Take the constant out:

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

= - \int sin (\frac{1}{2} x) d x

Apply u-substitution

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

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

Use the common integral:

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

= - 2 (- cos (u))

Substitute back

u = \frac{1}{2} x

= - 2 (- cos (\frac{1}{2} x))

Simplify

= 2 cos (\frac{1}{2} x)

Add a constant to the solution

= 2 cos (\frac{1}{2} x) + C

f (x) = 6 cos (x)

\int \frac{tan ^{2} ( x )}{cos ^{2} ( x )} d x

f (x) = 3 x^{3}, (- 1, - 3)

\frac{d}{d x} (x e - x)

\frac{d}{d x} (e^{π})

What is the integral of-sin(1/2 x) ?
The integral of-sin(1/2 x) is 2cos(1/2 x)+C