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Kyle Sutton

Kyle Sutton

Answered question

2022-07-07

Investigate to relationship 2 cos x d x ( 1 sin x ) 2 shares with ( 1 + sin x 1 sin x )I have used integration by recognition to go about it showing that,
d d x ( 1 + sin x 1 sin x ) = 2 cos x ( 1 sin x ) 2
However, when I tried integrating 2 c o s x ( 1 s i n x ) 2 I don't arrive back at 1 + s i n x 1 s i n x
So, how do you integrate 2 cos x ( 1 sin x ) 2 ?

Answer & Explanation

Janiyah Patton

Janiyah Patton

Beginner2022-07-08Added 12 answers

hint:Still go thru the traditional steps: u = 1 sin x is the first step. Can you take it from here?
malalawak44

malalawak44

Beginner2022-07-09Added 4 answers

Let
I = 2 cos x ( 1 sin x ) 2 d x ,
Now Let ( 1 sin x ) = t ,, Then cos d x = d t
So Integral
I = 2 1 t 2 d t = 2 t + C = 2 ( 1 sin x ) + C = ( 1 + sin x ) + ( 1 sin x ) ( 1 sin x ) + C
So we get
I = 1 + sin x 1 sin x + 1 + C = 1 + sin x 1 sin x + C , ,
Where C = 1 + C

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