What is the integral of x^{-2}sin(x) ?

The integral of x^{-2}sin(x) is -(sin(x))/x+\Ci(x)+C

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integral of x^{-2}sin(x)

\int x^{- 2} sin (x) d x

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

Solution steps

\int x^{- 2} sin (x) d x

Simplify

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

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

Apply Integration By Parts

: - \frac{sin ( x )}{x} - \int - \frac{cos ( x )}{x} d x

= - \frac{sin ( x )}{x} - \int - \frac{cos ( x )}{x} d x

\int - \frac{cos ( x )}{x} d x = - Ci (x)

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

Simplify

= - \frac{sin ( x )}{x} + Ci (x)

Add a constant to the solution

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

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What is the integral of x^{-2}sin(x) ?
The integral of x^{-2}sin(x) is -(sin(x))/x+\Ci(x)+C