How Do I Solve This Integral with Completing the Square and Long Division?

  • Thread starter Fiorella
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In summary, the conversation was about solving integrals and trying different methods such as completing the square, long division, and using u-substitution. One person suggested using u-substitution for both integrals, while another suggested rewriting the second integral to make it easier to solve. The conversation ended with gratitude for the help received.
  • #1
Fiorella
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Hello, can someone help me solve this integral? I think I need to complete the square...I've tried many other things but I don't know what else to use :confused:

integral.jpg


and

integral2.jpg


With the last one I did long division and I ended up with: x + x/ (x - 1)...so I can easily solve the first integral of X but now I can't solve the other part... :(
 
Last edited:
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  • #2


Try using latex, it might be a while before we can view your image.
 
  • #3


I posted the image differently :)
 
  • #4


U-sub is the easiest on the first one, u-sub and factor actually...

U-sub the second one too
 
  • #5


Fiorella said:
Hello, can someone help me solve this integral? I think I need to complete the square...I've tried many other things but I don't know what else to use :confused:

integral.jpg


and

integral2.jpg


With the last one I did long division and I ended up with: x + x/ (x - 1)...so I can easily solve the first integral of X but now I can't solve the other part... :(

you could rewrite

[tex]\frac{x}{(x-1)}[/tex]

as

[tex]1+\frac{1}{x-1}[/tex]

if that is any easier for you.
 
Last edited:
  • #6


Fiorella said:
Hello, can someone help me solve this integral? I think I need to complete the square...I've tried many other things but I don't know what else to use :confused:

integral.jpg
Not "complete the square", the denominator is a cube, not a square! The substitution
u= -x3+ 9x+ 1 works nicely.

and

integral2.jpg


With the last one I did long division and I ended up with: x + x/ (x - 1)...so I can easily solve the first integral of X but now I can't solve the other part... :(
You need to review your long division! x2 divided by x- 1 is x+ 1+ 1/(x-1).
 
  • #7


Thank you so much everybody :)
 

1. What is an integral?

An integral is a mathematical concept that represents the area under a curve in a graph. It is a fundamental concept in calculus and is used to calculate the total value of a function over a given range.

2. How do I solve an integral?

To solve an integral, you need to use integration techniques such as substitution, integration by parts, or partial fractions. You also need to know the fundamental properties of integrals, such as the power rule and the constant multiple rule.

3. What are the steps to solve an integral?

The general steps to solve an integral are: 1) Identify the type of integral (definite or indefinite), 2) Simplify the integral if possible, 3) Use integration techniques to solve the integral, 4) Check your answer using differentiation, and 5) Add any necessary constants.

4. Can I use a calculator to solve an integral?

Yes, there are many online and graphing calculators that can solve integrals. However, it is important to understand the concepts behind integration and not rely solely on calculators.

5. Are there any tips for solving integrals?

Some tips for solving integrals include: 1) Familiarize yourself with the basic integration rules, 2) Practice solving different types of integrals, 3) Pay attention to the limits of integration, 4) Simplify the integral before attempting to solve it, and 5) Check your answer by differentiating it.

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