What is the integral of x*sin(2x) ?

The integral of x*sin(2x) is -1/2 xcos(2x)+1/4 sin(2x)+C

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integral of x*sin(2x)

\int x \cdot sin (2 x) d x

- \frac{1}{2} x cos (2 x) + \frac{1}{4} sin (2 x) + C

Solution steps

\int x sin (2 x) d x

Apply Integration By Parts

: - \frac{1}{2} x cos (2 x) - \int - \frac{1}{2} cos (2 x) d x

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

\int - \frac{1}{2} cos (2 x) d x = - \frac{1}{4} sin (2 x)

= - \frac{1}{2} x cos (2 x) - (- \frac{1}{4} sin (2 x))

Simplify

= - \frac{1}{2} x cos (2 x) + \frac{1}{4} sin (2 x)

Add a constant to the solution

= - \frac{1}{2} x cos (2 x) + \frac{1}{4} sin (2 x) + C

\int 4 3 x + 3 6 x^{5} d x

1 - x^{2} y^{^{'}} - 1 - y^{2} = 0

\frac{\partial}{\partial x} (7)

f (x) = ln (x^{2} + 9)

\frac{1}{x} + tan (x)

What is the integral of x*sin(2x) ?
The integral of x*sin(2x) is -1/2 xcos(2x)+1/4 sin(2x)+C