What is the integral of cos(cx) ?

The integral of cos(cx) is 1/c sin(cx)+C

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integral of cos(cx)

\int cos (c x) d x

\frac{1}{c} sin (c x) + C

Solution steps

\int cos (c x) d x

Apply u-substitution

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

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

Take the constant out:

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

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

Use the common integral:

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

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

Substitute back

u = c x

= \frac{1}{c} sin (c x)

Add a constant to the solution

= \frac{1}{c} sin (c x) + C

\frac{d}{d x} (sin (\frac{π}{3}))

\int \frac{x ^{2} - 324}{x} d x

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

x^{4} + 5 y^{4} x^{5} + 4 y^{^{'}} = 0, y (0) = 1

\int \frac{4 x ^{4} - 5 x ^{2}}{( x + 3 ) ( x - 2 )} d x