What is the integral of 2xsin(4x) ?

The integral of 2xsin(4x) is 2(-1/4 xcos(4x)+1/16 sin(4x))+C

Popular >

integral of 2xsin(4x)

\int 2 x sin (4 x) d x

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

Solution steps

\int 2 x sin (4 x) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \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

= 2 (- \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)

= 2 (- \frac{1}{4} x cos (4 x) - (- \frac{1}{16} sin (4 x)))

Simplify

= 2 (- \frac{1}{4} x cos (4 x) + \frac{1}{16} sin (4 x))

Add a constant to the solution

= 2 (- \frac{1}{4} x cos (4 x) + \frac{1}{16} sin (4 x)) + C

x \to \infty lim ((x)^{2})

\frac{d}{d x} (\frac{x - 22}{x - 22})

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

\frac{d}{d y} (\frac{x ^{2} y}{x ^{2} + y ^{2}})

\frac{d}{d x} (arcsin (x + lo g_{4} (x)))

What is the integral of 2xsin(4x) ?
The integral of 2xsin(4x) is 2(-1/4 xcos(4x)+1/16 sin(4x))+C