Integration: What Method to Use?

In summary, the conversation is about finding the integration of x / ((x+1)^4) and what method to use. The suggestion is to try substitution instead, with the substitution u=x+1. The conversation also mentions that you don't need to get du=xdx and that substitution should work. It is also suggested to try partial integration if substitution does not work. The conversation then mentions that the same trick can be applied to x^2 / ((x+1)^4). The conclusion is that substitution is the recommended method for finding the integration in this case.
  • #1
naspek
181
0
integration of x / ((x+1)^4)
i can't use integration by subs..
partial fraction will consume time to answer this question..
which integration method should i use?
 
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  • #2
Try substitution instead, u=x+1
 
  • #3
rock.freak667 said:
Try substitution instead, u=x+1

ok.. when u = x + 1 ; du = 1 dx

i should get du = x dx first..
but subs method didnt work..
 
  • #4
Have faith, because it should work. If it still doesn't for you, post your work here.
 
  • #5
You don't need to get du=xdx. rockfreak's suggestion works fine, just try it. Alternatively you could do a partial integration.
 
  • #6
got it!
(-1/2)(x+1)^-2 + (1/3)(x+1)^-3 + C.

what if i got x^2 / ((x+1)^4)
 
  • #7
The same trick works. You should try it.
 
  • #8
got it! thanks guys! =)
 

Related to Integration: What Method to Use?

1. What is integration and why is it important?

Integration is a mathematical process of finding the area under a curve. It is important because it allows us to calculate quantities such as distance, volume, and mass, which are essential in many scientific fields.

2. What are the different methods of integration?

There are several methods of integration, including the fundamental theorem of calculus, substitution, integration by parts, partial fractions, and numerical methods such as the trapezoidal rule and Simpson's rule.

3. How do I know which method of integration to use?

The method of integration to use depends on the form of the function being integrated. For example, substitution is useful for integrals involving trigonometric functions, while integration by parts is useful for products of functions.

4. Can I use a calculator or computer program for integration?

Yes, there are many calculators and computer programs that can perform integration. However, it is important to understand the principles behind integration and be able to use different methods by hand.

5. What are some real-world applications of integration?

Integration has numerous applications in fields such as physics, engineering, and economics. For example, it can be used to calculate the work done by a force, the volume of an irregularly shaped object, or the net profit of a business over a given time period.

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