What is the integral of (cos(pi/(x^{10)}))/(x^{11)} ?

The integral of (cos(pi/(x^{10)}))/(x^{11)} is -1/(10pi)sin(pi/(x^{10)})+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^{10)}))/(x^{11)}

\int \frac{cos ( \frac{π}{x ^{10}} )}{x ^{11}} d x

- \frac{1}{10 π} sin (\frac{π}{x ^{10}}) + C

Solution steps

\int \frac{cos ( \frac{π}{x ^{10}} )}{x ^{11}} d x

Apply u-substitution

: \int \frac{cos ( \frac{π}{u} )}{10 u ^{2}} d u

= \int \frac{cos ( \frac{π}{u} )}{10 u ^{2}} d u

Take the constant out:

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

= \frac{1}{10} \cdot \int \frac{cos ( \frac{π}{u} )}{u ^{2}} d u

Apply u-substitution

: \int - \frac{cos ( v )}{π} d v

= \frac{1}{10} \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}{10} (- \frac{1}{π} \cdot \int cos (v) d v)

Use the common integral:

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

= \frac{1}{10} (- \frac{1}{π} sin (v))

Substitute back

= \frac{1}{10} (- \frac{1}{π} sin (\frac{π}{x ^{10}}))

Simplify

\frac{1}{10} (- \frac{1}{π} sin (\frac{π}{x ^{10}})) : - \frac{1}{10 π} sin (\frac{π}{x ^{10}})

= - \frac{1}{10 π} sin (\frac{π}{x ^{10}})

Add a constant to the solution

= - \frac{1}{10 π} sin (\frac{π}{x ^{10}}) + C

\frac{d}{d x} (\frac{x + 1}{2 x - 1})

f (x) = x 3 - x^{2}

\int 3 x - 3 d x

x \to 3 lim (\frac{2 x - 5}{3 x + 4})

x^{12} e^{x}

What is the integral of (cos(pi/(x^{10)}))/(x^{11)} ?
The integral of (cos(pi/(x^{10)}))/(x^{11)} is -1/(10pi)sin(pi/(x^{10)})+C