# Partial Fractions

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?

HallsofIvy
Homework Helper
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?

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

ahhh

so it =

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

:D

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

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
This should be in the Calculus section.

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

This should be in the Calculus section.

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

Yep that's the one

Yep that's the one
Substitutions ...

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

$$dt=\frac 1 x dx$$

You will need to do parts afterwards.