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

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

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integral of x*sin(3x)

\int x \cdot sin (3 x) d x

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

Solution steps

\int x sin (3 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

x cos (π) x, x = 0

f (- 1) = x^{2} + 2 - 1

f (x) = \frac{1}{2 x + 3}

\int (x^{3} + 2 x)^{5} (6 x^{2} + 4) d x

\frac{d}{d x} (ln (\frac{x}{2 e}))

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