What is x^3(1/x-sin(1/x)) ?

The solution to x^3(1/x-sin(1/x)) is x^2(-sin(1/x)x+1)

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simplify x^3(1/x-sin(1/x))

simplify

x^{3} (\frac{1}{x} - sin (\frac{1}{x}))

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

Solution steps

x^{3} (\frac{1}{x} - sin (\frac{1}{x}))

Join

\frac{1}{x} - sin (\frac{1}{x}) : \frac{- sin ( \frac{1}{x} ) x + 1}{x}

= x^{3} \frac{- sin ( \frac{1}{x} ) x + 1}{x}

Apply the fraction rule:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{x ^{3} ( - sin ( \frac{1}{x} ) x + 1 )}{x}

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

x^{3} = x x^{2}

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

Cancel the common factor:

x

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

\frac{x}{( x + 2 ) ( x + 3 )}

\frac{d}{d x} ((f (x, y)) (x + x^{2} - y^{2}))

\frac{ab}{( sc + b ) ( s d + a )}

(\frac{ln ( 6 x + 1 )}{x + 2} + \frac{6 ln ( 3 x + 6 )}{6 x + 1}) (3 x + 6)^{l n (6 x + 1)}

\frac{4 s}{( s - 2 ) ( s ^{2} + 4 )}

What is x^3(1/x-sin(1/x)) ?
The solution to x^3(1/x-sin(1/x)) is x^2(-sin(1/x)x+1)