What is the integral of t^2sin(5t) ?

The integral of t^2sin(5t) is -1/5 t^2cos(5t)+2/125 (5tsin(5t)+cos(5t))+C

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integral of t^2sin(5t)

\int t^{2} sin (5 t) d t

- \frac{1}{5} t^{2} cos (5 t) + \frac{2}{125} (5 t sin (5 t) + cos (5 t)) + C

Solution steps

\int t^{2} sin (5 t) d t

Apply Integration By Parts

: - \frac{1}{5} t^{2} cos (5 t) - \int - \frac{2}{5} t cos (5 t) d t

= - \frac{1}{5} t^{2} cos (5 t) - \int - \frac{2}{5} t cos (5 t) d t

\int - \frac{2}{5} t cos (5 t) d t = - \frac{2}{125} (5 t sin (5 t) + cos (5 t))

= - \frac{1}{5} t^{2} cos (5 t) - (- \frac{2}{125} (5 t sin (5 t) + cos (5 t)))

Simplify

= - \frac{1}{5} t^{2} cos (5 t) + \frac{2}{125} (5 t sin (5 t) + cos (5 t))

Add a constant to the solution

= - \frac{1}{5} t^{2} cos (5 t) + \frac{2}{125} (5 t sin (5 t) + cos (5 t)) + C

\frac{d}{d n} ((1 + i)^{n} + (1 - i)^{n})

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

\int_{1}^{3} f (2 x) d x

t \to 0 lim (ln (t + 1))

y^{^{''}} + 6 y^{^{'}} + 8 y = cos (3 t)

What is the integral of t^2sin(5t) ?
The integral of t^2sin(5t) is -1/5 t^2cos(5t)+2/125 (5tsin(5t)+cos(5t))+C