What is the integral of cos(wnt) ?

The integral of cos(wnt) is 1/(wn)sin(wnt)+C

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integral of cos(wnt)

\int cos (w n t) d t

\frac{1}{w n} sin (w n t) + C

Solution steps

\int cos (w n t) d t

Apply u-substitution

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

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

Take the constant out:

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

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

Use the common integral:

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

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

Substitute back

u = w n t

= \frac{1}{w n} sin (w n t)

Add a constant to the solution

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

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- \frac{2 x}{y}

\int_{1}^{2} \frac{5}{x ^{3} + 4 x} d x

x \to 0 + lim (\frac{1}{x ^{3}})

(arcsin (3 x))^{^{'}}