Find the integration of log(cosx) from 0 to ?/4.

Take log(cosx) as first function and 1 as second function….

Use integration by parts formula that is ∫f(x).g(x) = f(x).g'(x) – ∫f'(x).[∫g(x)dx]dx…

The 1st and 2nd function are taken considering the ILATE rule.

  • I = inverse trigonometric function
  • L = logarithmic function
  • A = algebraic function
  • T = trigonometric function
  • E = exponential function.

The answer is: \(frac{1}{4} (2 C-pi log (2))\).

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