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

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

\int \frac{1}{x x} d x

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y^{^{''}} - 3 y^{^{'}} + 4 y = x e^{x}

\frac{d}{d x} (1 (- 5 x + 3) (- 3 x + 2))