What is the integral of xsin(7x) ?

The integral of xsin(7x) is -1/7 xcos(7x)+1/49 sin(7x)+C

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integral of xsin(7x)

\int x sin (7 x) d x

- \frac{1}{7} x cos (7 x) + \frac{1}{49} sin (7 x) + C

Solution steps

\int x sin (7 x) d x

Apply Integration By Parts

: - \frac{1}{7} x cos (7 x) - \int - \frac{1}{7} cos (7 x) d x

= - \frac{1}{7} x cos (7 x) - \int - \frac{1}{7} cos (7 x) d x

\int - \frac{1}{7} cos (7 x) d x = - \frac{1}{49} sin (7 x)

= - \frac{1}{7} x cos (7 x) - (- \frac{1}{49} sin (7 x))

Simplify

= - \frac{1}{7} x cos (7 x) + \frac{1}{49} sin (7 x)

Add a constant to the solution

= - \frac{1}{7} x cos (7 x) + \frac{1}{49} sin (7 x) + C

(1 + cos^{3} (x^{7}))^{12}

\frac{\partial}{\partial x} (y^{3} sin (6 x))

f (x) = \frac{2}{3 x + 5}, (- 1, 1)

x \to 0 lim (\frac{x ^{2} + 7 x}{x})

\int (2 t + 3)^{- 3} d t

What is the integral of xsin(7x) ?
The integral of xsin(7x) is -1/7 xcos(7x)+1/49 sin(7x)+C