Question

determine the following integral

equation in next post

Answer 1

\[\int\limits_{}^{}\frac{ x-3 }{ x+2 }\]Iv been told to use partial fractions on this one.

Answer 2

is this then the same as previous with the du/u?

Answer 3

nopes.

Answer 4

u know about partial fractions ?

Answer 5

yup, but it looks to me that i have to do these ones backwards?

Answer 6

partial fractions cannot be applied here....i think
there is only 1 factor in denominator...

Answer 7

hmm well my notes say that i need to use them.

Answer 8

u can write x-3 = x+2 - 5
and separate the denominator...

Answer 9

You can rewrite x-3 as (x+2)-5, so that
\[ \int{\frac{x-3}{x+2}dx}=\int{\frac{(x+2)-5}{x+2}dx}=\int{\left(1-\frac{5}{x+2}\right)dx}\]
Then do the substitution u=x+2 for the second term.

Answer 10

hmmmm ok?

Answer 11

-5ln(|x+2|)+x+c

Answer 12

yup.

Answer 13

Yeah, that's right!

Answer 14

sweet just to clarify du =1-5/u?

Answer 15

Not for the substitution I mentioned, for u=x+2, du=dx.

Answer 16

so in the answer do i need to have the |x+2| or can it just be x+2?

Answer 17

You need |x+2|, if you can't be sure that x≥-2.

Answer 18

owk kwl.