the integral of 1x^2-5x+14/(x-1)(x^2+9)

Question

the answer i got was ln(x-1)-5/3 tan^-1(x/3) however this is not right..... pleasee help!

Answer 1

If your expression was
(x^2-5x+14)/(x-1)/(x^2+9)
The answer ln(x-1) - (5/3)tan^-1(x/3)is correct.
Read the instructions carefully, sometimes they require a simplified answer, sometime no factoring is permitted, etc.

To avoid confusion, always put sufficient parentheses and / operators.
The posted expression interpreted algebraically is equivalent to:
x^2 - 5x + (14)/(x-1) * (x^2+9)
which is quite different from the expression above.

Answer 2

im sorry the question was

x^2 - 5x + (14)/(x-1) * (x^2+9)

but my answer was not correct for it, what mistake did i make?

Answer 3

For
x^2 - 5x + (14)/(x-1) * (x^2+9)
there is only (x-1) in the denominator, and consequently, you will have a ln(x-1) term together with a number of polynomial terms.

Check carefully the format of the question. If the question shows a division sign, there are implicit parentheses around the numerator and the denominator that you have to insert before posting the expression.

Answer 4

this is how the question is written:

(x^2 - 5x + 14 )/(x-1) * (x^2+9)

for the answer ln(x-1)-5/3 tan^-1(x/3)is it wrong or do i just need to add parenthesis somewhere?

Answer 5

ln(x-1) - (5/3)tan-1(x/3) is correct for (x^2-5x+14)/(x-1)/(x^2+9) only.

You will have to do the integration again for (x^2 - 5x + 14 )/(x-1) * (x^2+9).

However, it will most probably be easier than before.