What is the integral of cos(5t) ?

The integral of cos(5t) is 1/5 sin(5t)+C

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integral of cos(5t)

\int cos (5 t) d t

\frac{1}{5} sin (5 t) + C

Solution steps

\int cos (5 t) d t

Apply u-substitution

: \int cos (u) \frac{1}{5} d u

= \int cos (u) \frac{1}{5} d u

Take the constant out:

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

= \frac{1}{5} \cdot \int cos (u) d u

Use the common integral:

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

= \frac{1}{5} sin (u)

Substitute back

u = 5 t

= \frac{1}{5} sin (5 t)

Add a constant to the solution

= \frac{1}{5} sin (5 t) + C

x \to 1 - lim (4 x)

y^{^{'}} = 0.05 ln (\frac{2000}{y}) y

\frac{s}{s + 8}

\frac{\partial}{\partial x} ((x + y) \cdot e^{x + 2 y})

4 - (x - 2)^{2}, 5 - (x - 4)^{2}, 2, 4