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

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

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integral of cos(1/2)x

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule

: \frac{x ^{2}}{2}

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

Simplify

cos (\frac{1}{2}) \frac{x ^{2}}{2} : \frac{1}{2} cos (\frac{1}{2}) x^{2}

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

Add a constant to the solution

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

t y^{^{'}} + 2 y = sin (t), y (\frac{π}{2}) = 5

\frac{\partial}{\partial x} (6 x - 4 y)

\int (8 + x^{2}) d x

\int \frac{1}{8 - 2 x ^{2}} d x

\int \frac{2 x}{x ^{2} + 6 x + 5} d x

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