Help with U Substitution for integral of cos(pi/x^11) / x^12

  • Thread starter miller8605
  • Start date
In summary, the conversation discusses a problem with finding a suitable U substitution for the given integral. After considering u=pi/x^11 and u=x^12, the individual concludes that the correct substitution is u=pi/x^11. However, there are issues with finding the derivative and incorporating it into the original problem. After some simplification, the final answer is determined to be -1/11pi * sin(pi/x^11) + C.
  • #1
miller8605
17
0
I don't have a way of getting the equation to look nice but it's:

integral of cos(pi/x^11) / x^12




I am having issues even finding what I could use as a U substitution. Any help would be great!
 
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  • #2
Thing causing trouble is cos(pi/x^11) / x^12
 
  • #3
How about u=pi/x^11?
 
  • #4
Dick said:
How about u=pi/x^11?

problem with that is when you take the derivative, you don't have the dx int he problem.

i'm almost certain the U has to equal x^12 as then du would then be 11x^11 and you can divide that by 11 and stick a 1/11 out front. I just don't know how to get du out of that stupid fraction. unless I'm going about it completely wrong and it's not a U substitution and it's a by parts question.
 
  • #5
If u=pi/x^11 then what do you think is du?
 
  • #6
(-11pi*x^10) / x^11

if I used the quotient rule correctly
 
  • #7
You forgot to square the denominator.
 
  • #8
Dick said:
You forgot to square the denominator.

it looks like i did, i forgot the derivate of pi was zero, haha. dumb on my part.

but that doesn't get me anywhere because no where in the original problem is the du. i have to get rid of that 1/x^12 somehow.
 
  • #9
Simplify (-11pi*x^10) / (x^11)^2.
 
  • #10
Dick said:
Simplify (-11pi*x^10) / (x^11)^2.

wow, can't believe i missed that. thanks for all your help, i'll post up my answer here in a couple minutes.
 
  • #11
-1/11pi * sin(pi/x^11) + C
 
  • #12
Looks ok to me.
 

Related to Help with U Substitution for integral of cos(pi/x^11) / x^12

1. What is U Substitution and when is it used?

U Substitution, also known as the change of variables method, is a technique used to simplify integrals by substituting a new variable in place of the original variable. This is typically used when the integrand contains a composition of functions, such as in the case of this integral involving a trigonometric function and a power function.

2. How do I choose the appropriate substitution for this integral?

In order to choose the appropriate substitution, you should look for a function within the integrand that resembles the derivative of another function. In this case, the function x^-11 resembles the derivative of x^-10, so we can let u = x^-10.

3. What steps should I follow in order to perform U Substitution?

The steps for U Substitution are as follows: 1) Identify the u-substitution by looking for a function within the integrand that resembles the derivative of another function. 2) Substitute u into the integral, replacing the original function. 3) Rewrite the integral in terms of u. 4) Evaluate the integral. 5) Substitute the original variable back in for u.

4. Can I use U Substitution for all integrals?

No, U Substitution is not always applicable. It is most commonly used for integrals involving a composition of functions, but there are other techniques that may be more appropriate for certain types of integrals.

5. How can I check my work after performing U Substitution?

You can check your work by differentiating the result of the integral. If the derivative matches the original integrand, then you have successfully performed U Substitution. In this case, the derivative of the result should be equal to cos(pi/x^11) / x^12.

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