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

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

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integral of-cos(2x)

\int - cos (2 x) d x

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

Solution steps

\int - cos (2 x) d x

Take the constant out:

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

= - \int cos (2 x) d x

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 x

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

Add a constant to the solution

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

\frac{x ^{2}}{2 - x ^{2}}

\int_{1}^{9} \frac{x - 2}{x} d x

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

\int_{0}^{2} x 7 - x^{2} d x

(11, 6), (16, y)