What is the integral of 1/(x^2)*cos(1/x) ?

The integral of 1/(x^2)*cos(1/x) is -sin(1/x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 1/(x^2)*cos(1/x)

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

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

Solution steps

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

Apply u-substitution

: \int - cos (u) d u

= \int - cos (u) d u

Take the constant out:

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

= - \int cos (u) d u

Use the common integral:

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

= - sin (u)

Substitute back

u = \frac{1}{x}

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

Add a constant to the solution

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

\int (x \cdot 2^{x}) d x

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

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

\int - x^{3} + 2 x^{2} + x - 2 d x

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

What is the integral of 1/(x^2)*cos(1/x) ?
The integral of 1/(x^2)*cos(1/x) is -sin(1/x)+C