solve the integral (14x+1)/(4x^2-13x-12) .. please help guys .. no one is answering me lately =[ and tomorrow i have a test !!!!

Question

amistre64 · Answer

is the top the derivative of the bottom?

anonymous · Answer

nope ... because you have 13x downstairs and on top 1

amistre64 · Answer

good, then most likely we have to do a decomp 

whats the fators of the bottom?

amistre64 · Answer

factors even

anonymous · Answer

i didin't manage to find real roots from the quadratic equation ...

amistre64 · Answer

let me chk that then

4x^2-13x-12

13^2-4(4)(-12) = 196+ some value

it doesnt go complex

anonymous · Answer

oh yes you are right !!!! i did a mistake with the minus sign !!! any way can you just tell me how to factor when you find the roots ? =]

turingtest · Answer

$$\frac{14x+1}{4x^2-13x-12}=\frac A{4x+3}+\frac B{x-4}$$

amistre64 · Answer

16 and 3

(x-16/4)(x+3/4)

(x-4)(4x+3)

amistre64 · Answer

youhave a test, how is just telling you going to give you the means to solve it?  that comes from experience .... hands on stuff

amistre64 · Answer

turing gave the split up; now we have to solve for A and B

amistre64 · Answer

we do that by trying to recombine the fractions using the unknowns and comparing it with the known numberator

anonymous · Answer

yes ... i see ... thank you very much !!

amistre64 · Answer

14x + 1 = A(x-4) + B(4x+3)

the simple means here is to zero one of the terms out; when x=4 we get A(0) sooo

14(4) + 1 = B(4(4)+3)

B = 57/19  if i see that right :)

amistre64 · Answer

B cancels out when x = -4/3

anonymous · Answer

yes !! thank you i can go on from here peacfully =] .. i will be happy for help with my other questions from the last 2 hours that no one replied yet ;]

amistre64 · Answer

if you repost it we will be able to find it easier, with any luck :)