What is the integral of (cos(pi/(x^4)))/(x^5) ?

The integral of (cos(pi/(x^4)))/(x^5) is -1/(4pi)sin(pi/(x^4))+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^4)))/(x^5)

\int \frac{cos ( \frac{π}{x ^{4}} )}{x ^{5}} d x

- \frac{1}{4 π} sin (\frac{π}{x ^{4}}) + C

Solution steps

\int \frac{cos ( \frac{π}{x ^{4}} )}{x ^{5}} d x

Apply u-substitution

: \int \frac{cos ( \frac{π}{u} )}{4 u ^{2}} d u

= \int \frac{cos ( \frac{π}{u} )}{4 u ^{2}} d u

Take the constant out:

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

= \frac{1}{4} \cdot \int \frac{cos ( \frac{π}{u} )}{u ^{2}} d u

Apply u-substitution

: \int - \frac{cos ( v )}{π} d v

= \frac{1}{4} \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}{4} (- \frac{1}{π} \cdot \int cos (v) d v)

Use the common integral:

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

= \frac{1}{4} (- \frac{1}{π} sin (v))

Substitute back

= \frac{1}{4} (- \frac{1}{π} sin (\frac{π}{x ^{4}}))

Simplify

\frac{1}{4} (- \frac{1}{π} sin (\frac{π}{x ^{4}})) : - \frac{1}{4 π} sin (\frac{π}{x ^{4}})

= - \frac{1}{4 π} sin (\frac{π}{x ^{4}})

Add a constant to the solution

= - \frac{1}{4 π} sin (\frac{π}{x ^{4}}) + C

\int \frac{1}{2 x - 1 + 1} d x

\int \frac{1}{( arctan ( y ) ) ( 1 + y ^{2} )} d y

\int (3 - cos (x))^{2} d x

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

\int sec^{2} (x) e^{2 t a n (x)} d x

What is the integral of (cos(pi/(x^4)))/(x^5) ?
The integral of (cos(pi/(x^4)))/(x^5) is -1/(4pi)sin(pi/(x^4))+C