What is the integral of xsin(14x) ?

The integral of xsin(14x) is -1/14 xcos(14x)+1/196 sin(14x)+C

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integral of xsin(14x)

\int x sin (14 x) d x

- \frac{1}{14} x cos (14 x) + \frac{1}{196} sin (14 x) + C

Solution steps

\int x sin (14 x) d x

Apply Integration By Parts

: - \frac{1}{14} x cos (14 x) - \int - \frac{1}{14} cos (14 x) d x

= - \frac{1}{14} x cos (14 x) - \int - \frac{1}{14} cos (14 x) d x

\int - \frac{1}{14} cos (14 x) d x = - \frac{1}{196} sin (14 x)

= - \frac{1}{14} x cos (14 x) - (- \frac{1}{196} sin (14 x))

Simplify

= - \frac{1}{14} x cos (14 x) + \frac{1}{196} sin (14 x)

Add a constant to the solution

= - \frac{1}{14} x cos (14 x) + \frac{1}{196} sin (14 x) + C

x \to - \frac{π}{2} - lim (sec (x))

f (x) = 4 sin (x), (\frac{π}{6}, 2)

\frac{d}{d x} (tanh (x^{2} - 9))

x \to 7 lim (x^{4})

\int (6 x - 5) (3 x^{2} - 5 x)^{3} d x

What is the integral of xsin(14x) ?
The integral of xsin(14x) is -1/14 xcos(14x)+1/196 sin(14x)+C