What is the integral of t*sin(2t) ?

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

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integral of t*sin(2t)

\int t \cdot 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

(8 (5 x)^{4} + 5)^{3}

\frac{d}{d x} (\frac{1}{x ^{4}} - \frac{3}{x ^{2}} + x^{3})

\int \frac{1}{2 x ^{2} + 3} d x

f (x) = x^{2} - 6 x + 9, (- 2, 25)

v \to 3 lim (\frac{v + 1 - 2}{v - 3})

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