# Thread: partial fraction - integration

1. ## partial fraction - integration

can someone explain the underlined steps?

-how does the top line reduce to u-1 in the numerator. isnt (u+1) - 1 = u

-bottom line - is it just a "u" substitution?

thanks

2. here the problem..sorry!

3. Originally Posted by calculus0
can someone explain the underlined steps?

-how does the top line reduce to u-1 in the numerator. isnt (u+1) - 1 = u

-bottom line - is it just a "u" substitution?

thanks
Hi calculus0,

what you have in the numerator is

$\frac{1}{2}(u+1)-1=\frac{1}{2}(u+1)-\frac{1}{2}(2)=\frac{1}{2}(u+1-2)$

4. Originally Posted by Archie Meade
Hi calculus0,

what you have in the numerator is

$\frac{1}{2}(u+1)-1=\frac{1}{2}(u+1)-\frac{1}{2}(2)=\frac{1}{2}(u+1-2)$

where did the 2 come from? where it is -1/2(2)

thank you

5. Originally Posted by calculus0
where did the 2 come from? where it is -1/2(2)

thank you
the -1 is brought inside the brackets using $-1=-\frac{2}{2}$

then we have 0.5 multiplied by 2 seperate terms
so they can be brought inside with 0.5 as common factor

$\frac{1}{2}(u+1)-1=\frac{1}{2}(u+1)-\frac{2}{2}=\frac{1}{2}(u+1)+\frac{1}{2}(-2)$

and now $\frac{1}{2}$ is a common factor

so the -2 can be brought inside the brackets.

6. Thanks!!