How to integrate &#x222B;<!-- ∫ --> 1 sin 4 </ms

veneciasp

veneciasp

Answered question

2022-07-10

How to integrate 1 sin 4 x cos 4 x d x?

Answer & Explanation

Elianna Wilkinson

Elianna Wilkinson

Beginner2022-07-11Added 11 answers

By using the substitution x = arctan t we have d x = d t 1 + t 2 and sin 2 ( x ) = t 2 1 + t 2 , cos 2 ( x ) = 1 1 + t 2 , hence
d x sin 4 ( x ) cos 4 ( x ) = ( 1 + t 2 ) 3 t 4 d t
and the last integral is straightforward to compute through the binomial formula. It equals:
C 1 3 t 3 3 t + 3 t + t 3 3 .

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?