What is the integral of tsin(pit) ?

The integral of tsin(pit) is -1/pi tcos(pit)+1/(pi^2)sin(pit)+C

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integral of tsin(pit)

\int t sin (π t) d t

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

Solution steps

\int t sin (π t) d t

Apply Integration By Parts

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

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

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

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

Simplify

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

Add a constant to the solution

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

y = (1 - 3 x)^{10}, (0, 1)

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What is the integral of tsin(pit) ?
The integral of tsin(pit) is -1/pi tcos(pit)+1/(pi^2)sin(pit)+C