Question

Evaluate the following integrals:

∫ sin x log (cos x)dx

Answer 1

Let cos x = t

- sin x dx = dt

Now the integral we have is

∫ sin x log (cos x)dx = - ∫ log tdt

- ∫1.log tdt

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 t is first function and 1 as the second function.