Which of the following integrals can be best evaluated using integration by parts?

A. ∫ xsin (x²) dx

B. ∫ x²sin (x) dx

C. ∫ sin² (x) dx

A) can be done using u-substitution ... Let u = x^2, du = 2x dx

C) can be done using trig identity ... cos (2x) = 1 - 2sin^2

B) can only be done using integration by parts. It is a product of 2 distinct functions and a u-sub does not simplify the integral.