What is the integral of cos(3y) ?

The integral of cos(3y) is 1/3 sin(3y)+C

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integral of cos(3y)

\int cos (3 y) d y

\frac{1}{3} sin (3 y) + C

Solution steps

\int cos (3 y) d y

Apply u-substitution

: \int cos (u) \frac{1}{3} d u

= \int cos (u) \frac{1}{3} d u

Take the constant out:

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

= \frac{1}{3} \cdot \int cos (u) d u

Use the common integral:

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

= \frac{1}{3} sin (u)

Substitute back

u = 3 y

= \frac{1}{3} sin (3 y)

Add a constant to the solution

= \frac{1}{3} sin (3 y) + C

x \to \infty lim ((cos (\frac{1}{x}))^{\frac{1}{x ^{2}}})

n = 3 \sum \infty \frac{n x ^{n}}{n + 2}

\frac{d x}{d t} - x = 5 t

\frac{\partial}{\partial x} (1 + ln (x y))

y^{^{''}} - 8 y^{^{'}} + 16 y = t^{- 2} e^{4 t}