# Partial Fractions

1. Feb 20, 2008

### Firepanda

Integrate using partial fractions:

(int) (x^3)/(x^2 -1) dx

I have put into the form (int) (x^3)/((x-1)(x+1)) dx

I thought partial fractions had this property:

'Partial fractions can only be done if the degree of the numerator is strictly less than the degree of the denominator.'

And this obviously doesn't, so how do you do it?

2. Feb 20, 2008

### HallsofIvy

Divide! What is x3 divided by x2- 1? What are the quotient and remainder?

3. Feb 20, 2008

### Firepanda

ahhh

so it =

x + 1/(x-1) - 1/(x+1)(x-1)

:D

4. Feb 20, 2008

### Firepanda

While im here I have another question:

(int) 1 to e (ln(x))/x^2 dx

THe question says, use a suitable substitution to evaluate the definite integral, I can do it by parts but I don't want to lose marks for it.

Can any1 suggest the substitution to get me started?
Thx

5. Feb 20, 2008

### rocomath

This should be in the Calculus section.

$$\int_1^e\frac{\ln x}{x^2}dx$$

6. Feb 20, 2008

### Firepanda

Yep that's the one

7. Feb 20, 2008

### rocomath

Substitutions ...

$$t=\ln x \rightarrow e^t=x$$

$$dt=\frac 1 x dx$$

You will need to do parts afterwards.