What is the integral of tsin(2t) ?

The integral of tsin(2t) is -1/2 tcos(2t)+1/4 sin(2t)+C

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integral of tsin(2t)

\int t sin (2 t) d t

- \frac{1}{2} t cos (2 t) + \frac{1}{4} sin (2 t) + C

Solution steps

\int t sin (2 t) d t

Apply Integration By Parts

: - \frac{1}{2} t cos (2 t) - \int - \frac{1}{2} cos (2 t) d t

= - \frac{1}{2} t cos (2 t) - \int - \frac{1}{2} cos (2 t) d t

\int - \frac{1}{2} cos (2 t) d t = - \frac{1}{4} sin (2 t)

= - \frac{1}{2} t cos (2 t) - (- \frac{1}{4} sin (2 t))

Simplify

= - \frac{1}{2} t cos (2 t) + \frac{1}{4} sin (2 t)

Add a constant to the solution

= - \frac{1}{2} t cos (2 t) + \frac{1}{4} sin (2 t) + C

x \to 0 + lim (x^{2} sin (\frac{1}{x}))

\frac{\partial}{\partial y} (4 y^{3} - 100 y)

y^{^{'}} = (1 + x) (1 + y^{2})

\int e^{(- 2 x)} d x

What is the integral of tsin(2t) ?
The integral of tsin(2t) is -1/2 tcos(2t)+1/4 sin(2t)+C