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

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

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integral of (sin(ax))/x

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

Si (a x) + C

Solution steps

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

Apply u-substitution

= \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 = a x

= Si (a x)

Add a constant to the solution

= Si (a x) + C

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