# An integral

1. Dec 14, 2006

### ddr

1. The problem statement, all variables and given/known data

integral defined in 0 (down) and 1 (up) of:
(16x^4 - 4)/(4x^2+1)

2. Relevant equations

3. The attempt at a solution

maybe the partition mode?
who help me?

2. Dec 14, 2006

### neutrino

Just wondering...by any chance, is the denominator of the integrand 4x2+2?

Last edited: Dec 14, 2006
3. Dec 14, 2006

### arildno

Hint:
Use polynomial division first.

4. Dec 15, 2006

### ddr

i can use the substitution rule, with u=4x^2?

5. Dec 15, 2006

### HallsofIvy

Staff Emeritus
You could but it doesn't really help since du= 8xdx doesn't give you anything easy. The numerator obviously factors into (4x2-2)(4x2+2)- that's why arildno asked if the denominator wasn't actually 4x2+ 2 rather than 4x2+ 1. But the world is never that easy, not even homework problems.

Best thing to do is arildno's suggest. Go ahead and divide 16x4- 4 by 4x2+ 1. The result will be a cubic polynomial plus a linear term, Ax+ B, over 4x2+ 1. To integrate Ax/(4x2+1), let u= 4x2+ 1. To integrate B/(4x2+1), use the arctangent.