How do I solve this integral? As stated the title, I get to a point which I can't do anything, and

Layla Velazquez

Layla Velazquez

Answered question

2022-06-22

How do I solve this integral?
As stated the title, I get to a point which I can't do anything, and I'm sure I've made a mistake some where, here is my full working out:
e i x cos ( x ) d x u = e i x  |  u = i e i e v = sin ( x )  |  v = cos ( x ) e i x sin ( x ) i e i x sin ( x ) d x + C e i x sin ( x ) i e i x sin ( x ) d x + C u = e i x  |  u = i e i e v = cos ( x )  |  v = sin ( x ) e i x sin ( x ) i ( e i x cos ( x ) + i e i x c o s ( x ) d x ) + C L e t e i x cos ( x ) d x = I I = e i x ( sin ( x ) + i cos ( x ) ) i 2 I + C
But ( i 2 = 1) so the equation should become:
I = e i x ( sin ( x ) + i cos ( x ) ) + I + C
And this is where I'm stuck, I can't simply take I away from both sides, that would make
e i x ( sin ( x ) + i cos ( x ) ) = 0
What have a messed up in the process? And just to make it clear someone in a previous question didn't under understand what v was, it's the same as d v d x , thank you in advance.

Answer & Explanation

stigliy0

stigliy0

Beginner2022-06-23Added 21 answers

e i x cos x d x = e i x e i x + e i x 2 d x = 1 2 ( e 2 i x + 1 ) d x = 1 4 i e 2 i x + x 2

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