What is the integral of-cos(2y) ?

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

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integral of-cos(2y)

\int - cos (2 y) d y

- \frac{1}{2} sin (2 y) + C

Solution steps

\int - cos (2 y) d y

Take the constant out:

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

= - \int cos (2 y) d y

Apply u-substitution

: \int cos (u) \frac{1}{2} d u

= - \int cos (u) \frac{1}{2} d u

Take the constant out:

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

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

Use the common integral:

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

= - \frac{1}{2} sin (u)

Substitute back

u = 2 y

= - \frac{1}{2} sin (2 y)

Add a constant to the solution

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

4 x - \frac{3}{x ^{6}}

\int 2 x^{2} - 4 d x

\int \frac{4}{x + 4 + x} d x

x \to - 1 lim (4 x^{3} - 2 m)

x \to 0 - lim (\frac{x ^{2}}{2} - \frac{1}{x})