Solving Integral Trouble: How to Fit 1/(x^2(2x-3)) into Tables

  • Thread starter Jbreezy
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In summary: In this case, the derivative of x^2 is -1/x. Partial fractions can be found in any math textbook or online.
  • #1
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Homework Statement



Hi I have a broad quesiton. I'm trying to make something fit the form of something in one of the tables in my book I can't seem to quite make it.
integral (1/2x^3 - 3x^2) dx


Homework Equations





The Attempt at a Solution



I just messed with the denomator.
1/(x^2(2x-3))

I can't find something in the tables that fits this. Does anyone have any ideas?
 
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  • #2
Jbreezy said:

Homework Statement



Hi I have a broad quesiton. I'm trying to make something fit the form of something in one of the tables in my book I can't seem to quite make it.
integral (1/2x^3 - 3x^2) dx


Homework Equations





The Attempt at a Solution



I just messed with the denomator.
1/(x^2(2x-3))

I can't find something in the tables that fits this. Does anyone have any ideas?

You can write the given integral as:
$$\int \cfrac{dx}{x^2\cdot x\left(2-\cfrac{3}{x}\right)}$$
A substitution would make it very easy. It is easy to spot.
 
  • #3
I'm sorry I still don't see it. Sub for u = x^2?
 
  • #4
Jbreezy said:
I'm sorry I still don't see it. Sub for u = x^2?

You have x^2 in the denominator i.e 1/x^2. This is the derivative of something very familiar. :rolleyes:
 
  • #5
Jbreezy said:

Homework Statement



Hi I have a broad quesiton. I'm trying to make something fit the form of something in one of the tables in my book I can't seem to quite make it.
integral (1/2x^3 - 3x^2) dx
What you wrote is this:
$$ \int \frac 1 2 x^3 - 3x^2 dx$$

To indicate that 2x3 - 3x2 is in the denominator, put parentheses around the denominator, not the whole fraction, like this 1/(2x3 - 3x2).
 
  • #6
Jbreezy said:

Homework Statement



Hi I have a broad quesiton. I'm trying to make something fit the form of something in one of the tables in my book I can't seem to quite make it.
integral (1/2x^3 - 3x^2) dx


Homework Equations





The Attempt at a Solution



I just messed with the denomator.
1/(x^2(2x-3))

I can't find something in the tables that fits this. Does anyone have any ideas?

Partial fractions.
 
  • #7
Pranav-Arora said:
You have x^2 in the denominator i.e 1/x^2. This is the derivative of something very familiar. :rolleyes:

No sure. This would be -1/x whose derivavite is is 1/x^2 are you thinking ln of something? Ray says partial fractions but this is the section where you have to look them up in tables.
 
  • #8
Jbreezy said:
No sure. This would be -1/x whose derivavite is is 1/x^2 are you thinking ln of something? Ray says partial fractions but this is the section where you have to look them up in tables.

Yes, use the substitution 1/x=t.

Partial fractions can also be used.
 

What is an integral?

An integral is a mathematical concept that represents the accumulation of a quantity over a given interval. It is the inverse operation of differentiation, and is used to find the original function when its derivative is known.

Why is fitting 1/(x^2(2x-3)) into tables considered a "trouble"?

This specific function is considered troublesome because it cannot be easily integrated using standard techniques. It requires advanced methods, such as partial fractions, to be solved.

How can I solve this integral without using tables?

There are several techniques that can be used to solve this integral, such as substitution, integration by parts, and trigonometric substitution. It is important to have a strong understanding of these techniques and how to apply them to different types of integrals.

What are the benefits of using tables to solve integrals?

Tables provide a quick and efficient way to solve integrals without having to use complex techniques. They are especially useful for solving integrals that cannot be easily solved using standard methods.

Are there any limitations when using tables to solve integrals?

Yes, tables are limited to a certain number of functions and may not be able to solve all types of integrals. They also do not provide step-by-step solutions, so it is important to have a good understanding of the underlying concepts and techniques.

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