Question

Evaluate the integral using integration by parts with the indicated choices of u and dv.

A) u = ln(x), dv = dx
B) u = x, dv = eˣ dx
C) u = eˣ, dv = dx
D) u = x², dv = sin(x) dx

Answer 1

To evaluate the integral using integration by parts, we need to choose u and dv in the given choices. Then, we can apply the integration by parts formula to evaluate each integral.

Step-by-step explanation:

To evaluate the integral using integration by parts, we need to choose u and dv in the given choices. Let's go through each choice:

A) u = ln(x), dv = dx

B) u = x, dv = eˣ dx

C) u = eˣ, dv = dx

D) u = x², dv = sin(x) dx

Based on the integration by parts formula, ∫u dv = uv - ∫v du, we can choose u and dv as:

A) u = ln(x), dv = dx

B) u = x, dv = eˣ dx

C) u = eˣ, dv = dx

D) u = sin(x) dx, dv = x²

Now, you can apply the integration by parts formula to evaluate each integral.