 I tried it using the double angle identity 2 \sin x \ William Collins 2022-01-03 Answered
I tried it using the double angle identity
$$\displaystyle{2}{\sin{{x}}}{\cos{{x}}}$$
The answer that I got is
$$\displaystyle{\frac{{-{\cos{{2}}}{x}}}{{{4}}}}+{c}$$
However I've also tried it using u-subsitution.
I let $$\displaystyle{u}={\sin{{x}}}$$. Thus obtaining $$\displaystyle{\cos{{x}}}$$ when differentiating. And cutting the $$\displaystyle{\cos{{x}}}\ \text{ in }\ {2}{\sin{{x}}}{\cos{{x}}}$$ out with the $$\displaystyle{\cos{{x}}}$$ in the denominator below du.
However the answer that I am then getting is : $$\displaystyle{0.25}-{0.25}{\cos{{2}}}{x}+{c}$$

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it usumbiix
Both answers are correct. You can use double angle identity, as well as u sub for either $$\displaystyle{\sin{{x}}}\ \text{ or }\ {\cos{{x}}}$$
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."
Not exactly what you’re looking for? usumbiix
Actually your method is not wrong.
All you need to do is just substitute
$$\displaystyle{c}_{{2}}={0.25}+{c}$$
and then you get the "correct" answer. Vasquez

$$\frac12 \frac{d}{dx} \sin^2 x=\sin x \cos x$$
so
$$\int \sin x \cos x dx=\frac12 \sin^2 x+\text{constant}$$