I tried it using the double angle identity 2sin⁡xcos⁡x The answer that I got is −cos⁡2x4+c However Ive

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I tried it using the double angle identity  2sin⁡xcos⁡x  The answer that I got is  −cos⁡2x4+c  However Ive

usumbiix · Accepted Answer

Both answers are correct. You can use double angle identity, as well as u sub for either sin⁡x  or  cos⁡xThe key lies in the +c. All the 3 integrals are a family of functions just separated by a different &quot;+c&quot;. In practice, double angle identity is often used as it&#039;s more intuitive and simpler in some sense. But the other methods are perfectly acceptable, and not &quot;wrong.&quot;

usumbiix · Accepted Answer

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

Vasquez · Accepted Answer

12ddxsin2⁡x=sin⁡xcos⁡x so ∫sin⁡xcos⁡xdx=12sin2⁡x+constant

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

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