What is the integral of 15cos(15x) ?

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

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integral of 15cos(15x)

\int 15 cos (15 x) d x

sin (15 x) + C

Solution steps

\int 15 cos (15 x) d x

Take the constant out:

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

= 15 \cdot \int cos (15 x) d x

Apply u-substitution

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

= 15 \cdot \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

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

Use the common integral:

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

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

Substitute back

u = 15 x

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

Simplify

15 \cdot \frac{1}{15} sin (15 x) : sin (15 x)

= sin (15 x)

Add a constant to the solution

= sin (15 x) + C

f (x) = 9 x - 10 x^{\frac{1}{4}}

\int \frac{1}{cos ( y )} d y

\int_{0}^{0.75} 2 x d x

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

x = y \frac{1}{3}, x = 0, y = 64