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

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

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integral of xsin(2x)

\int x \cdot sin (2 \cdot 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

450 (1 + \frac{3 t}{29 + t ^{2}}), 4

x \to 0 lim (\frac{( x + 4 )}{2})

y = 2 x e^{- x}

x \to \infty lim (2.5)

\int_{0}^{4} e^{- 2 x} + 4 d x

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