What is the integral of (cos(pi/(x^{15)}))/(x^{16)} ?

The integral of (cos(pi/(x^{15)}))/(x^{16)} is -1/(15pi)sin(pi/(x^{15)})+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (cos(pi/(x^{15)}))/(x^{16)}

\int \frac{cos ( \frac{π}{x ^{15}} )}{x ^{16}} d x

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

Solution steps

\int \frac{cos ( \frac{π}{x ^{15}} )}{x ^{16}} d x

Apply u-substitution

: \int \frac{cos ( \frac{π}{u} )}{15 u ^{2}} d u

= \int \frac{cos ( \frac{π}{u} )}{15 u ^{2}} 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 \frac{cos ( \frac{π}{u} )}{u ^{2}} d u

Apply u-substitution

: \int - \frac{cos ( v )}{π} d v

= \frac{1}{15} \cdot \int - \frac{cos ( v )}{π} d v

Take the constant out:

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

= \frac{1}{15} (- \frac{1}{π} \cdot \int cos (v) d v)

Use the common integral:

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

= \frac{1}{15} (- \frac{1}{π} sin (v))

Substitute back

= \frac{1}{15} (- \frac{1}{π} sin (\frac{π}{x ^{15}}))

Simplify

\frac{1}{15} (- \frac{1}{π} sin (\frac{π}{x ^{15}})) : - \frac{1}{15 π} sin (\frac{π}{x ^{15}})

= - \frac{1}{15 π} sin (\frac{π}{x ^{15}})

Add a constant to the solution

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

6 x e^{x}

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

\int \frac{x ^{\frac{3}{2}}}{x} d x

\int e^{- s t} t d t

f (x) = 2 x^{3} - x^{2} + 9, at x = 2

What is the integral of (cos(pi/(x^{15)}))/(x^{16)} ?
The integral of (cos(pi/(x^{15)}))/(x^{16)} is -1/(15pi)sin(pi/(x^{15)})+C