What is the integral of xsin(3x) ?

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

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integral of xsin(3x)

\int x 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

y = 2 cos (x), y = 6 - 4 cos (x), 0 \leq x \leq 2 π

f (x) = 18 x^{2} - 14 x + 9

\frac{d}{d x} (ln (x^{2} + 2 x + 1))

- 2 x cos (x^{2}) - e^{- x - 2}

y = \frac{4 x ^{4} + 5}{x ^{2}}

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