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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

- sin (\frac{2}{x}) + C

Solution steps

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

Take the constant out:

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

= 2 \cdot \int \frac{1}{x ^{2}} cos (\frac{2}{x}) d x

Apply u-substitution

: \int - \frac{cos ( u )}{2} d u

= 2 \cdot \int - \frac{cos ( u )}{2} d u

Take the constant out:

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

= 2 (- \frac{1}{2} \cdot \int cos (u) d u)

Use the common integral:

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

= 2 (- \frac{1}{2} sin (u))

Substitute back

u = \frac{2}{x}

= 2 (- \frac{1}{2} sin (\frac{2}{x}))

Simplify

2 (- \frac{1}{2} sin (\frac{2}{x})) : - sin (\frac{2}{x})

= - sin (\frac{2}{x})

Add a constant to the solution

= - sin (\frac{2}{x}) + C

\frac{t ^{2}}{2}

\int 2 x x^{2} + 5 d x

\int \frac{3 x}{( 1 - 4 x ^{2} ) ^{2}} d x

x \to - 4 lim (2 x^{7} + 8 x^{4} - 1)

\int (y e^{y^{2}}) d y

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