integrate 4xcos4x dx

Answer 1

We can use integration by parts for this problem:

Let u = 4x and dv = cos(4x) dx, then du/dx = 4 and v = (1/4)sin(4x)

Using the formula for integration by parts, we have:

∫4xcos(4x) dx = (4x)(1/4)sin(4x) - ∫(1/4)sin(4x)(4)dx

Simplifying, we get:

∫4xcos(4x) dx = x sin(4x) - (1/4)∫sin(4x) dx

Integrating the sine term, we have:

∫4xcos(4x) dx = x sin(4x) + (1/16)cos(4x) + C

Therefore, the solution is:

∫4xcos(4x) dx = x sin(4x) + (1/16)cos(4x) + C