What is the integral of (sin(8/x))/(x^2) ?

The integral of (sin(8/x))/(x^2) is 1/8 cos(8/x)+C

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integral of (sin(8/x))/(x^2)

\int \frac{sin ( \frac{8}{x} )}{x ^{2}} d x

\frac{1}{8} cos (\frac{8}{x}) + C

Solution steps

\int \frac{sin ( \frac{8}{x} )}{x ^{2}} d x

Apply u-substitution

: \int - \frac{sin ( u )}{8} d u

= \int - \frac{sin ( u )}{8} d u

Take the constant out:

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

= - \frac{1}{8} \cdot \int sin (u) d u

Use the common integral:

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

= - \frac{1}{8} (- cos (u))

Substitute back

u = \frac{8}{x}

= - \frac{1}{8} (- cos (\frac{8}{x}))

Simplify

= \frac{1}{8} cos (\frac{8}{x})

Add a constant to the solution

= \frac{1}{8} cos (\frac{8}{x}) + C

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

\int_{- π}^{π} cos^{2} (n x) d x

e^{x^{2}}, 0

\int_{- 1}^{0} x^{3} + 1 d x

18 x - 3 x

What is the integral of (sin(8/x))/(x^2) ?
The integral of (sin(8/x))/(x^2) is 1/8 cos(8/x)+C