Question

compute the intrgral cos^2(x) * sin2x

Answer 1

Is it
\[\int\limits \cos^2(x) *\sin2(x)\]

Answer 2

yes!

Answer 3

\[Let \ u=\cos^2(x) \tag1 \]\[du=-2\cos(x)\sin(x) dx\tag2 \]
\[\int\limits\limits \cos^2(x)\sin(2x) \ dx= \int\limits\limits \cos^2(x)*2\sin(x) \cos(x) \ dx \]\[Since : \ Sin(2x)=2Sin(x)Cos(x)\]
\[\text{Now substituting (1) & (2) }\]
\[- \int\limits\limits u \ du\]\[= \frac{-u^2}{2}= \frac{-(\cos^2(x))^2}{2}= \frac{-\cos^4(x)}{2} \]

Answer 4

Thank you very much!! This answer was extremly helpfull

Answer 5

You're Welcome =)