Question

Evaluate the following integrals:

∫ sin x log (cos x) dx

Answer 1

Using BY PART METHOD. Using the superiority list as ILATE (Inverse Logarithm Algebra Trigonometric Exponential). Taking the first function to the one which comes first in the list.

Here log(cos x) is the first function and sin x as the second function.

∫ sin x log (cos x) dx = log (cos x)