What is the integral of tsin(nt) ?

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

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integral of tsin(nt)

\int t sin (n t) d t

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

Solution steps

\int t sin (n t) d t

Apply Integration By Parts

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

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

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

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

Simplify

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

Add a constant to the solution

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

\frac{\partial}{\partial x} (cot (x))

\frac{5}{x}

\frac{d}{d x} (\frac{1}{( x - 6 ) ^{2}})

f (x) = x^{2} + 3 x + 4 π, at x = 2.5

\frac{\partial}{\partial y} (2 sin (x) + sin (x + y))

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