Integrating sin^4(2x): An Alternative Method | No Reduction Formulas Required

[ookt2c]

Homework Statement

How do you integrate sin^4(2x) without the reduction formulas. seems impossible

Homework Equations

i think you have to use integration by parts?

The Attempt at a Solution

 

[Mystic998]

I don't think you can. At least, not without essentially deriving the reduction formulas in the process (assuming you're referring to reduction formulas of Ssin^m(x) cos^j(x))

 

[sutupidmath]

expressing sin^4(2x)=(sin^2(2x))^2=(1-cos^2(4x))/2, and then do the same for cos^2(4x)=(1+cos(8x))/2
i do not see why this would be impossible?

 

[HallsofIvy]

expressing sin^4(2x)=(sin^2(2x))^2=(1-cos^2(4x))/2, and then do the same for cos^2(4x)=(1+cos(8x))/2
i do not see why this would be impossible?

The original post said "without the reduction formulas". I doubt there is any and don't really see why one would care.

 

[sutupidmath]

The original post said "without the reduction formulas". I doubt there is any and don't really see why one would care.

Oh, sorry, i did not know that these are called "reduction formulas", my bad!