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

[Jbreezy]

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?

 

[Saitama]

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.

 

[Jbreezy]

I'm sorry I still don't see it. Sub for u = x^2?

 

[Saitama]

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.

 

[Mark44]

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).

 

[Ray Vickson]

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.

 

[Jbreezy]

You have x^2 in the denominator i.e 1/x^2. This is the derivative of something very familiar.

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.

 

[Saitama]

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.