Can i find this integral in a simpler way

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In summary, there are two ways of solving the integral ∫x^2/(4x+1)^10 dx - by using partial fractions, and by substituting u=4x+1. Partial integration can also be used to simplify the expressions without solving large systems of equations. Both methods are effective in solving this integral.
  • #1
giokrutoi
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∫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.
 
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  • #2
Partial integration can give you similar terms without solving large systems of equations.
 
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  • #3
mfb said:
Partial integration can give you similar terms without solving large systems of equations.
i got it thank you very much
 
  • #4
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.
I would substitute ##4x+1=u## which makes the entire quotients a lot easier.
 
  • #5
fresh_42 said:
I would substitute ##4x+1=u## which makes the entire quotients a lot easier.
yes that is another good approach thanks very much
 

1. Can I use a substitution to simplify this integral?

Yes, substitutions can often be used to simplify integrals by replacing variables with simpler expressions. This can often make the integral easier to solve or evaluate.

2. Is there a special technique or formula that can make this integral simpler?

Yes, there are various techniques and formulas that can be used to simplify integrals, such as integration by parts, partial fractions, and trigonometric substitutions. These techniques can often make the integral easier to solve or evaluate.

3. Can I use a computer or calculator to find a simpler form of this integral?

Yes, there are many computer programs and calculators that have built-in integration functions or algorithms that can simplify integrals and provide a numerical answer. However, it's important to check the answer and understand the steps taken by the program.

4. Can I manipulate the integrand to make the integral simpler?

Yes, sometimes it is possible to manipulate the integrand, such as using algebraic identities or trigonometric identities, to simplify the integral. However, it's important to make sure that any manipulations done do not change the value of the integral.

5. Can I break up this integral into smaller, simpler integrals?

Yes, sometimes it is possible to break up a complex integral into smaller, simpler integrals using techniques like the substitution method or integration by parts. However, it's important to make sure that the smaller integrals can be evaluated and that they cover the entire range of the original integral.

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