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

\frac{\partial}{\partial x} (5 \cdot (y + 3)^{3} \cdot (x - 4))

f (x) = (x^{2} + 2)^{2}

f (x) = (8 x^{3} + 3 x^{2})^{3}

\frac{\partial}{\partial x} (2 x y - 2 x^{2} y)

x \to \infty lim (ln (5 x))

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