The discussion revolves around finding alternative methods to solve the integral ∫x²/(4x+1)¹⁰ dx. Participants explore various techniques, including partial fractions and substitutions, while seeking simpler approaches.
Participants generally agree that multiple methods exist for solving the integral, including partial fractions and substitution. However, no consensus is reached on which method is definitively simpler or preferable.
Some methods discussed may depend on the participants' familiarity with specific techniques, and the effectiveness of each method could vary based on individual preferences or problem contexts.
i got it thank you very muchmfb said:Partial integration can give you similar terms without solving large systems of equations.
I would substitute ##4x+1=u## which makes the entire quotients a lot easier.giokrutoi said:∫x^2/(4x+1)^10 dx
i know that solving this is possible by partial fractions like A/4x+1 + (Bx+C)/(4x+1)^2 + (Dx+E)/(4x+1)^3
and so on but i would like to know if there is another way of solving this.
yes that is another good approach thanks very muchfresh_42 said:I would substitute ##4x+1=u## which makes the entire quotients a lot easier.