What is the integral of xsin(kx) ?

The integral of xsin(kx) is -1/k xcos(kx)+1/(k^2)sin(kx)+C

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integral of xsin(kx)

\int x sin (k x) d x

- \frac{1}{k} x cos (k x) + \frac{1}{k ^{2}} sin (k x) + C

Solution steps

\int x sin (k x) d x

Apply Integration By Parts

: - \frac{1}{k} x cos (k x) - \int - \frac{1}{k} cos (k x) d x

= - \frac{1}{k} x cos (k x) - \int - \frac{1}{k} cos (k x) d x

\int - \frac{1}{k} cos (k x) d x = - \frac{1}{k ^{2}} sin (k x)

= - \frac{1}{k} x cos (k x) - (- \frac{1}{k ^{2}} sin (k x))

Simplify

= - \frac{1}{k} x cos (k x) + \frac{1}{k ^{2}} sin (k x)

Add a constant to the solution

= - \frac{1}{k} x cos (k x) + \frac{1}{k ^{2}} sin (k x) + C

2 x e^{x^{2}}

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

\frac{d y}{d x}, y = \frac{9}{x}

x \to - 1 lim (\frac{1}{x ^{2} + 2 x + 1})

4^{s i n (x)}

What is the integral of xsin(kx) ?
The integral of xsin(kx) is -1/k xcos(kx)+1/(k^2)sin(kx)+C