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

The integral of x^{-1}sin(x) is \Si(x)+C

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

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

Si (x) + C

Solution steps

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

Simplify

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

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

Use the nonelementary integral:

\int \frac{sin ( x )}{x} d x = Si (x)

= Si (x)

Add a constant to the solution

= Si (x) + C

x \to 0 lim (\frac{1 - cos ( 5 x )}{x})

\int sin (π x) sin (nπ x) d x

\frac{d}{d x} (x^{3} \cdot ln (x))

y = y

\frac{k x}{a ^{2} + x ^{2}}