What is the integral of xsin(4x) ?

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

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integral of xsin(4x)

\int x sin (4 x) d x

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

Solution steps

\int x sin (4 x) d x

Apply Integration By Parts

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

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

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

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

Simplify

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

Add a constant to the solution

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

\frac{\partial}{\partial x} ((\frac{y}{x}) \cdot ln (x))

x \to 0 lim (\frac{x}{x - 4})

y^{^{''}} + 4 y^{^{'}} + 13 y = 0, y (0) = 3, y^{^{'}} (0) = - 12

x \to 2 lim (x - 5)

\int_{0}^{2} \frac{1}{( 2 x - 1 ) ^{\frac{2}{3}}} d x

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