I'm have a bit of trouble with this integral
I'm pretty sure I have to use parts on it but it's been awhile, any help would be appreciated.
PFD (Partial Fractions Decomposition)
Multiplying through by the LCD we get
Now if we let
we get
So now since the other expression has no real roots we must expand
Equating coefficients we get
and
This gives us
Which implies that
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Just out of curiosity how were you planning to use parts
?
I hate to bring this thread back from the dead, but after I had this question answered I went on to try and find out if the integral was convergent or divergent from -1 to 6. My answer seemed to be way smaller then it should of been, perhaps I'm doing this wrong.
I know that in the original equation that X = -1 was a vertical asymptote so I'd should set
then
Subtract
should equal what the area under the curve is.
any help would be appreciated.
Ln(0) doesn't exist, the limit as x-> 0 of ln(x) is negative infinity. Hence in the latter portion you would be subtracting this value which would cancel out the negative and make it positive infinity. Hence the improper integral diverges and the area is infinite.
Other than not pointing that out, you're right.