What is the integral of tsin(9t) ?

The integral of tsin(9t) is -1/9 tcos(9t)+1/81 sin(9t)+C

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integral of tsin(9t)

\int t sin (9 t) d t

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

Solution steps

\int t sin (9 t) d t

Apply Integration By Parts

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

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

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

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

Simplify

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

Add a constant to the solution

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

(2.3) (4.4)

\frac{\partial}{\partial y} (4 y x)

x \to 3 lim (\frac{2}{x ^{2} - 9})

y = x, 4 x + y^{2} = 12

{\frac{5}{s ^{2} + 49}}

What is the integral of tsin(9t) ?
The integral of tsin(9t) is -1/9 tcos(9t)+1/81 sin(9t)+C