What is the integral of (sin(5/x))/(x^2) ?

The integral of (sin(5/x))/(x^2) is 1/5 cos(5/x)+C

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integral of (sin(5/x))/(x^2)

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

\frac{1}{5} cos (\frac{5}{x}) + C

Solution steps

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

Apply u-substitution

: \int - \frac{sin ( u )}{5} d u

= \int - \frac{sin ( u )}{5} d u

Take the constant out:

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

= - \frac{1}{5} \cdot \int sin (u) d u

Use the common integral:

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

= - \frac{1}{5} (- cos (u))

Substitute back

u = \frac{5}{x}

= - \frac{1}{5} (- cos (\frac{5}{x}))

Simplify

= \frac{1}{5} cos (\frac{5}{x})

Add a constant to the solution

= \frac{1}{5} cos (\frac{5}{x}) + C

\frac{\partial}{\partial x} (9 x y - 5 x^{2} y)

\frac{\partial}{\partial y} (2 x - 3 y)

\frac{d}{d x} ((2 tan^{2} (2 x) - 1)^{\frac{1}{2}})

\frac{d}{d u} (u^{2} + v^{2})

n = 1 \sum \infty \frac{( - 3 ) ^{n}}{7 ^{n + 1}}

What is the integral of (sin(5/x))/(x^2) ?
The integral of (sin(5/x))/(x^2) is 1/5 cos(5/x)+C