What is the integral of (10cos(pi/x))/(x^2) ?

The integral of (10cos(pi/x))/(x^2) is -(10)/pi sin(pi/x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (10cos(pi/x))/(x^2)

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

- \frac{10}{π} sin (\frac{π}{x}) + C

Solution steps

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

Take the constant out:

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

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

Apply u-substitution

: \int - \frac{cos ( u )}{π} d u

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

Take the constant out:

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

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

Use the common integral:

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

= 10 (- \frac{1}{π} sin (u))

Substitute back

u = \frac{π}{x}

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

Simplify

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

= - \frac{10}{π} sin (\frac{π}{x})

Add a constant to the solution

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

\int t cos (π) t d t

\int \frac{x}{9 - 6 x ^{2}} d x

\int (\frac{5}{4} x^{4} - \frac{x ^{2}}{2} - 4) d x

\int ln (3 x - 7) d x

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

What is the integral of (10cos(pi/x))/(x^2) ?
The integral of (10cos(pi/x))/(x^2) is -(10)/pi sin(pi/x)+C