I tried it using the double angle identity 2 \sin x \

William Collins

William Collins

Answered question

2022-01-03

I tried it using the double angle identity
2sinxcosx
The answer that I got is
cos2x4+c
However Ive

Answer & Explanation

usumbiix

usumbiix

Beginner2022-01-04Added 33 answers

Both answers are correct. You can use double angle identity, as well as u sub for either sinx  or  cosx
The key lies in the +c. All the 3 integrals are a family of functions just separated by a different "+c". In practice, double angle identity is often used as it's more intuitive and simpler in some sense. But the other methods are perfectly acceptable, and not "wrong."
usumbiix

usumbiix

Beginner2022-01-05Added 33 answers

Actually your method is not wrong.
All you need to do is just substitute
c2=0.25+c
and then you get the "correct" answer.
Vasquez

Vasquez

Expert2022-01-08Added 669 answers

12ddxsin2x=sinxcosx
so
sinxcosxdx=12sin2x+constant

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