Question

integral of (x+1)/(x^2-5x+6)dx

Answer 1

OK So What problem are you Facing in this integral ?....

Answer 2

I don't know how to approach it.

Answer 3

how do I begin solving it?

Answer 4

In this Integral...

Try to write the above Numerator eq into Denominator eq ...

Answer 5

x + 1 is Linear.... but x^2 - 5x +6 is Quadratic ! So What if some Kinda of Diiferentiation might work ? Think about it ... Answer lies in Proper Substitution

Answer 6

yeah, i've thought about this for over an hour now. I really don't know.

Answer 7

Ok,


d( quadratic) A + B = Linear
--
dx

Here A and B are Constants

Answer 8

Now Substitute Linear By this Value....

Solve the above Equation to Get A and B

Answer 9

A d
---(x^2 -5x +6 ) + B = x + 1
dx

2Ax - 5A + B = x + 1

Comparing Co-efficient s

2A = 1
A = 1
--
2

5A + B =1

5/2 + B =1


B = -3/2


Now REPLACE the Value In the Integral

Answer 10

I'm Writing the d/dx(quadratic) as D....


A*D + B A*D + B
------- dx = ------- dx -------dx
Quadratic Quad Quad

Now Put Quad = T


d/dx(Quad) =dT/dx
Do the substitution ....
For dx And Solve :)


.... I think this much Help is enough...