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

The integral of sin(3x)x is -1/3 xcos(3x)+1/9 sin(3x)+C

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integral of sin(3x)x

\int sin (3 x) x d x

- \frac{1}{3} x cos (3 x) + \frac{1}{9} sin (3 x) + C

Solution steps

\int sin (3 x) x d x

Apply Integration By Parts

: - \frac{1}{3} x cos (3 x) - \int - \frac{1}{3} cos (3 x) d x

= - \frac{1}{3} x cos (3 x) - \int - \frac{1}{3} cos (3 x) d x

\int - \frac{1}{3} cos (3 x) d x = - \frac{1}{9} sin (3 x)

= - \frac{1}{3} x cos (3 x) - (- \frac{1}{9} sin (3 x))

Simplify

= - \frac{1}{3} x cos (3 x) + \frac{1}{9} sin (3 x)

Add a constant to the solution

= - \frac{1}{3} x cos (3 x) + \frac{1}{9} sin (3 x) + C

\int 3 csc^{2} (2 x) d x

\int 9 x - 7 d x

\int 3^{- 2 x + 1} d x

\int \frac{5}{16 - 9 x ^{2}} d x

\frac{2}{3 x ^{2}}

What is the integral of sin(3x)x ?
The integral of sin(3x)x is -1/3 xcos(3x)+1/9 sin(3x)+C