What is the integral of cos(15x) ?

The integral of cos(15x) is 1/15 sin(15x)+C

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integral of cos(15x)

\int cos (15 x) d x

\frac{1}{15} sin (15 x) + C

Solution steps

\int cos (15 x) d x

Apply u-substitution

: \int cos (u) \frac{1}{15} d u

= \int cos (u) \frac{1}{15} d u

Take the constant out:

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

= \frac{1}{15} \cdot \int cos (u) d u

Use the common integral:

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

= \frac{1}{15} sin (u)

Substitute back

u = 15 x

= \frac{1}{15} sin (15 x)

Add a constant to the solution

= \frac{1}{15} sin (15 x) + C

\frac{d}{d x} (ln (\frac{1}{1 - x ^{2}}))

x \to - 5 - lim (3)

y^{^{'}} = 6 - y

x \to 3 - lim (\frac{x ^{2}}{9 - x ^{2}})

\int_{0}^{\frac{π}{4}} cos (2 x) d x