Question

Cuál es la constante de integración de:

Int: 2x-5x^2+3x^3 / x^3\dx

Answer 1

2x 
----------------------- 
x^2-2x-3)2x^3-4x^2-x-3 
.........2x^3-4x^2-6x 
---------- ------ ---- 
....... ..... ....5x-3 

2x + (5x-3) / (x^2-2x-3) 
= 2x + (5x-3) /(x-3)(x+1) 

(5x-3)/(x-3)(x+1) = A/(x-3) + B/(x+1) 
multiply both sides by (x-3)(x+1) 
5x-3 = A(x+1) + B(x-3) 
let x=-1 
-8 = -4B 
B = 2 
Let x=3 
12 = 4A 
A=3 

A=3; B= 2 
(5x-3)/(x-3)(x+1) = 3/(x-3) + 2/(x+1) 
2x + (5x-3) / (x^2-2x-3) = 2x + 3/(x-3) + 2/(x+1) 
∫[2x + (5x-3) / (x^2-2x-3)] dx = ∫ 2x dx + 3 ∫ dx/(x-3) + 2 ∫ dx/(x+1) 

= 2 (1/2) x^2 + 3 ln(x-3) + 2 ln(x+1) 
= x^2 + 3 ln(x-3) + 2 ln(x+1) + Ccidyah · 2 years ago