What is the integral of xsin(9x) ?

The integral of xsin(9x) is -1/9 xcos(9x)+1/81 sin(9x)+C

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integral of xsin(9x)

\int x sin (9 x) d x

- \frac{1}{9} x cos (9 x) + \frac{1}{81} sin (9 x) + C

Solution steps

\int x sin (9 x) d x

Apply Integration By Parts

: - \frac{1}{9} x cos (9 x) - \int - \frac{1}{9} cos (9 x) d x

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

\int - \frac{1}{9} cos (9 x) d x = - \frac{1}{81} sin (9 x)

= - \frac{1}{9} x cos (9 x) - (- \frac{1}{81} sin (9 x))

Simplify

= - \frac{1}{9} x cos (9 x) + \frac{1}{81} sin (9 x)

Add a constant to the solution

= - \frac{1}{9} x cos (9 x) + \frac{1}{81} sin (9 x) + C

3 y^{^{''}} = 8 e^{- 4 t}

\int cot^{4} (2 x) d x

\frac{x}{1 - ln ( x - 4 )}

f (x) = 2 x^{2} - 3

x - sin (x)

What is the integral of xsin(9x) ?
The integral of xsin(9x) is -1/9 xcos(9x)+1/81 sin(9x)+C