What is the integral of xsin(1/4 x) ?

The integral of xsin(1/4 x) is -4xcos(1/4 x)+16sin(1/4 x)+C

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integral of xsin(1/4 x)

\int x sin (\frac{1}{4} x) d x

- 4 x cos (\frac{1}{4} x) + 16 sin (\frac{1}{4} x) + C

Solution steps

\int x sin (\frac{1}{4} x) d x

Apply Integration By Parts

: - 4 x cos (\frac{1}{4} x) - \int - 4 cos (\frac{1}{4} x) d x

= - 4 x cos (\frac{1}{4} x) - \int - 4 cos (\frac{1}{4} x) d x

\int - 4 cos (\frac{1}{4} x) d x = - 16 sin (\frac{1}{4} x)

= - 4 x cos (\frac{1}{4} x) - (- 16 sin (\frac{1}{4} x))

Simplify

= - 4 x cos (\frac{1}{4} x) + 16 sin (\frac{1}{4} x)

Add a constant to the solution

= - 4 x cos (\frac{1}{4} x) + 16 sin (\frac{1}{4} x) + C

\frac{\partial}{\partial s} (3 s^{2} + t^{2})

\frac{d y}{d x} = x - y, y (0) = 2

x \to 0 lim (ln (\frac{1}{x ^{2}}))

\frac{\partial}{\partial z} (y^{2} z)

What is the integral of xsin(1/4 x) ?
The integral of xsin(1/4 x) is -4xcos(1/4 x)+16sin(1/4 x)+C