What is the integral of acos(wt) ?

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

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integral of acos(wt)

\int a cos (wt) d t

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

Solution steps

\int a cos (wt) d t

Take the constant out:

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

= a \cdot \int cos (wt) d t

Apply u-substitution

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

= a \cdot \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

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

Use the common integral:

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

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

Substitute back

u = wt

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

Add a constant to the solution

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

\frac{d}{d x} ((x - 3)^{3} (x + 4) (x^{2} + 1))

y = x - x^{3}

\int (cos (x))^{5} d x

\frac{\partial}{\partial y} (\frac{x - y}{x + z})

\frac{d y}{d x} = 7 x y