What is the integral of 2xcos(-4x) ?

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

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integral of 2xcos(-4x)

\int 2 x cos (- 4 x) d x

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

Solution steps

\int 2 x cos (- 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 cos (- 4 x) d x

Apply Integration By Parts

: \frac{1}{4} x sin (4 x) - \int \frac{1}{4} sin (4 x) d x

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

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

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

Simplify

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

Add a constant to the solution

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

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\frac{\partial}{\partial x} (3 x^{2} y^{3} - 3 x^{2})

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