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

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{- 6 x}{x ^{2} + 1}

\frac{d}{d x} (\frac{e ^{2 x - y}}{x ^{3}})

f (x) = \frac{1}{( 1 - x ) ^{2}}

f (x) = 4 x^{3} - 18 x^{2}

y^{^{'}} = 4 y (3 - y)