What is the integral of xsin(3ax) ?

The integral of xsin(3ax) is -1/(3a)xcos(3ax)+1/(9a^2)sin(3ax)+C

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integral of xsin(3ax)

\int x sin (3 a x) d x

- \frac{1}{3 a} x cos (3 a x) + \frac{1}{9 a ^{2}} sin (3 a x) + C

Solution steps

\int x sin (3 a x) d x

Apply Integration By Parts

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

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

\int - \frac{1}{3 a} cos (3 a x) d x = - \frac{1}{9 a ^{2}} sin (3 a x)

= - \frac{1}{3 a} x cos (3 a x) - (- \frac{1}{9 a ^{2}} sin (3 a x))

Simplify

= - \frac{1}{3 a} x cos (3 a x) + \frac{1}{9 a ^{2}} sin (3 a x)

Add a constant to the solution

= - \frac{1}{3 a} x cos (3 a x) + \frac{1}{9 a ^{2}} sin (3 a x) + C

\frac{\partial}{\partial x} (x ln (z^{4} + x^{3}))

f (x) = (\frac{x + 3}{x - 3})^{2}, at x = 4

\frac{d}{d x} (ln (\frac{( 1 - x )}{1 + x}))

\int_{1}^{9} π (x - 1)^{2} d x

s \to 0 lim (\frac{3}{s \cdot ( s + 2 )})

What is the integral of xsin(3ax) ?
The integral of xsin(3ax) is -1/(3a)xcos(3ax)+1/(9a^2)sin(3ax)+C