What is the integral of cos(wt) ?

The integral of cos(wt) is 1/w sin(wt)+C

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integral of cos(wt)

\int cos (wt) d t

\frac{1}{w} sin (wt) + C

Solution steps

\int cos (wt) d t

Apply u-substitution

: \int \frac{cos ( u )}{w} d u

= \int \frac{cos ( u )}{w} d u

Take the constant out:

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

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

Use the common integral:

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

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

Substitute back

u = wt

= \frac{1}{w} sin (wt)

Add a constant to the solution

= \frac{1}{w} sin (wt) + C

x \to - 5 lim (\frac{3 x ^{2} + 15 x}{2 x ^{2} - 50})

y = (arctan (9 x))^{2}

\int 3 y^{3} d y

\frac{d}{d x} ((f (x) (5 x))^{2} - 2)

x \to 4 lim (\frac{7 x + 6}{3 x - 2})