Question

Which of these integrals requires the method of integration by parts?

Thank you in advance!

Answer 1

∫ xe³ˣ dx

Explanation:

The first integral can be solved with u substitution (u = ln x).

The third integral can be solved with a Pythagorean identity (cot²x = csc²x − 1).

The fourth integral can be solved with a power reduction formula (cos²x = ½ + ½ cos(2x)).

Only the second integral requires integration by parts.