The original post said "without the reduction formulas". I doubt there is any and don't really see why one would care.sutupidmath said: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 said:The original post said "without the reduction formulas". I doubt there is any and don't really see why one would care.
Difficult integration refers to the process of finding the antiderivative or integral of a function that cannot be easily solved using basic integration techniques.
Integration can be difficult due to various reasons such as the complexity of the function, the lack of known antiderivatives, or the presence of special functions or constants.
One can approach difficult integration problems by using various techniques such as integration by parts, substitution, partial fractions, or trigonometric identities.
Yes, there are several tools and software available that can help with difficult integration problems such as Wolfram Alpha, Maple, or Mathematica. These tools use advanced algorithms and computational methods to solve difficult integrals.
Yes, it is important for a scientist to have a good understanding of integration techniques and be able to solve difficult integration problems as it is a fundamental concept in many fields such as physics, engineering, and mathematics.