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

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

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integral of cos(1/2 x)

\int cos (\frac{1}{2} x) d x

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

Solution steps

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

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

Add a constant to the solution

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

\frac{d}{d x} (\frac{x ^{5}}{5 !})

\frac{d}{d x} (x^{2} + cos (x))

n = 1 \sum \infty \frac{4 ^{n}}{4 ^{n}}

\frac{d}{d x} (4 x^{4} e^{x})

\int - x + tan (x) d x

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