What is the integral of tsin(5t) ?

The integral of tsin(5t) is -1/5 tcos(5t)+1/25 sin(5t)+C

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integral of tsin(5t)

\int t sin (5 t) d t

- \frac{1}{5} t cos (5 t) + \frac{1}{25} sin (5 t) + C

Solution steps

\int t sin (5 t) d t

Apply Integration By Parts

: - \frac{1}{5} t cos (5 t) - \int - \frac{1}{5} cos (5 t) d t

= - \frac{1}{5} t cos (5 t) - \int - \frac{1}{5} cos (5 t) d t

\int - \frac{1}{5} cos (5 t) d t = - \frac{1}{25} sin (5 t)

= - \frac{1}{5} t cos (5 t) - (- \frac{1}{25} sin (5 t))

Simplify

= - \frac{1}{5} t cos (5 t) + \frac{1}{25} sin (5 t)

Add a constant to the solution

= - \frac{1}{5} t cos (5 t) + \frac{1}{25} sin (5 t) + C

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\int \frac{3}{4 - x ^{2}} d x

What is the integral of tsin(5t) ?
The integral of tsin(5t) is -1/5 tcos(5t)+1/25 sin(5t)+C