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

The integral of (sin(2x))/x is \Si(2x)+C

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integral of (sin(2x))/x

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

Si (2 x) + C

Solution steps

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

Apply u-substitution

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

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

Use the nonelementary integral:

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

= Si (u)

Substitute back

u = 2 x

= Si (2 x)

Add a constant to the solution

= Si (2 x) + C

- \frac{2}{x ^{3}} + \frac{3}{x ^{2}} - 4 x

x \to 0 lim (\frac{( cos ( 4 x ) - cos ( 6 x ) )}{cos ( 2 x ) sin ^{2} ( 5 x )})

y^{^{'}} + y \cdot sin (x) = sin (x)

e^{- x} x - 2 e^{- x}

(cos (x^{2}))^{^{'}}