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

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

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

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

cos (\frac{1}{x}) + C

Solution steps

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

Apply u-substitution

: \int - sin (u) d u

= \int - sin (u) d u

Take the constant out:

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

= - \int sin (u) d u

Use the common integral:

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

= - (- cos (u))

Substitute back

u = \frac{1}{x}

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

Simplify

= cos (\frac{1}{x})

Add a constant to the solution

= cos (\frac{1}{x}) + C

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