Question

Find the indefinite integral using integration by parts of x cos 3x dx.

Answer 1

To find the indefinite integral of x cos 3x dx using integration by parts, we will apply the integration by parts formula. Let u = x and dv = cos 3x dx. Taking the derivatives and integrals of u and dv, we can substitute these values into the integration by parts formula.

Step-by-step explanation:

To find the indefinite integral of x cos 3x dx using integration by parts, we will apply the integration by parts formula:

∫ u dv = uv - ∫ v du

Let:

• u = x
• dv = cos 3x dx

Taking the derivatives and integrals of u and dv, we get:

• du = dx
• v = ∫ cos 3x dx

Now, we can substitute these values into the integration by parts formula:

∫ x cos 3x dx = x ∫ cos 3x dx - ∫ ∫ cos 3x dx

The first integral on the right side of the equation will require further evaluation using integration techniques.