Posted by **Anonymous ** on Tuesday, December 4, 2012 at 4:00am.

integral (4x^2-3x+2)/(4x^2-4x+3) dx

- Calculus -
**Steve**, Tuesday, December 4, 2012 at 5:00am
long division shows that we have

∫ 1 + (x-1)/(4x^2-4x+3)

= ∫ 1 + (x-1)/[(2x-1)^2 + 2] dx

let (2x-1)^2 = 2tan^2θ, so

(2x-1)^2 + 2 = 2tan^2θ+2 = 2sec^2θ

2x-1 = √2 tanθ

x = (√2 tanθ+1)/2

x-1 = (√2 tanθ-1)/2

dx = 1/2 √2 sec^2θ

∫ 1 + (x-1)/[(2x-1)^2 + 2] dx

= ∫ (1 + (√2 tanθ-1)/(4sec^2θ)) 1/√2 sec^2θ dθ

. . .

= 1/8(x + 1/8 log(4x^2-4x+3) - 1/(4√22) arctan (2x-1)/√2

## Answer This Question

## Related Questions

- Calculus - If f(x) and g(x) are continuous on [a, b], which one of the following...
- Math/Calculus - How would I solve the following integral with the substitution ...
- Calculus - Find the volume of the solid whose base is the region in the xy-plane...
- Calculus II - Integrate using integration by parts (integral) (5-x) e^3x u = 5-x...
- Calculus II/III - A. Find the integral of the following function. Integral of (x...
- calculus (please with steps and explanations) - consider the function f that is ...
- Calculus - integral -oo, oo [(2x)/(x^2+1)^2] dx (a) state why the integral is ...
- Calculus - Use the symmetry of the graphs of the sine and cosine functions as an...
- Calculus (urgent help) - consider the function f that is continuous on the ...
- calculus - 8). Part 1 of 2: In the solid the base is a circle x^2+y^2=16 and the...

More Related Questions