Question

Evaluate the integral: ∫ z eˣ cos(x) dx

Answer 1

To evaluate the integral ∫zeˣcos(x)dx, we can use integration by parts. Assign u = z and dv = eˣcos(x)dx, and then find du and v using differentiation and integration. Apply the integration by parts formula and simplify to evaluate the integral.

Step-by-step explanation:

To evaluate the integral ∫zeˣcos(x)dx, we can use integration by parts. Let's assign u = z and dv = eˣcos(x)dx. Then, we can find du and v using differentiation and integration, respectively.

u = z, du = dz

dv = eˣcos(x)dx, v = ∫eˣcos(x)dx

By applying the integration by parts formula: ∫u dv = uv - ∫v du. We can plug in the values for u, du, v, and dv and simplify the formula to evaluate the integral.