Question

Интеграла x * sin 4xdx,как решить?

Answer 1

По частям
решение смотри во вложении

Answer 2

Solving the Integral ∫x * sin(4x) dx

To solve the integral ∫x * sin(4x) dx, we can use integration by parts. The formula for integration by parts is:

∫u dv = uv - ∫v du

Where u and v are differentiable functions of x.

First, we need to choose u and dv. In this case, we can choose:

u = x dv = sin(4x) dx

Now, we can find du and v:

du = dx v = -1/4 * cos(4x)

Now, we can apply the integration by parts formula:

∫x * sin(4x) dx = -1/4 * x * cos(4x) - ∫(-1/4 * cos(4x)) dx

Solving the integral on the right-hand side will give us the final result.

Let's proceed with solving the integral.