What is the integral of x^{-2}sin(1/x) ?

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

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integral of x^{-2}sin(1/x)

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

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

Solution steps

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

Simplify

x^{- 2} sin (\frac{1}{x}) : \frac{sin ( \frac{1}{x} )}{x ^{2}}

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

\frac{d P}{d t} = P t, P (1) = 2

\frac{d ^{2}}{d x ^{2}} ((- 5 x + 6)^{5})

t \cdot y^{^{'}} + y = 2 t

y^{^{''}} + y^{^{'}} + 3 y = 0

x y^{^{'}} + (x + 1) y = x

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