What is the integral of (sin(3x))/(3x) ?

The integral of (sin(3x))/(3x) is 1/3 \Si(3x)+C

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integral of (sin(3x))/(3x)

\int \frac{sin ( 3 x )}{3 x} d x

\frac{1}{3} Si (3 x) + C

Solution steps

\int \frac{sin ( 3 x )}{3 x} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{3} \cdot \int \frac{sin ( 3 x )}{x} d x

Apply u-substitution

= \frac{1}{3} \cdot \int \frac{sin ( u )}{u} d u

Use the nonelementary integral:

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

= \frac{1}{3} Si (u)

Substitute back

u = 3 x

= \frac{1}{3} Si (3 x)

Add a constant to the solution

= \frac{1}{3} Si (3 x) + C

What is the integral of (sin(3x))/(3x) ?
The integral of (sin(3x))/(3x) is 1/3 \Si(3x)+C