Question about simplification after integration

[asilvester635]

I was going through my notes and I came upon this. I'm confused as how the ln and 5/4 disappeared (highlighted in yellow). Also why did the power of 2 turn into -1? (highlighted in light blue). I'm not sure but I might have copied it incorrectly from the board during class.

 

[Deleted member 4993]

I was going through my notes and I came upon this. I'm confused as how the ln and 5/4 disappeared (highlighted in yellow). Also why did the power of 2 turn into -1? (highlighted in light blue). I'm not sure but I might have copied it incorrectly from the board during class.

The second line should have been:

(7/4)*ln(x+1) + (3/2) * (x+1)^(-1) + (5/4)*ln(x-1) + C

There is no further useful simplification - hence no need for the third line (which is incorrect as posted).

 

[lookagain]

asilvester635,
your first line should have been:

\(\displaystyle \displaystyle\int \dfrac{\frac{7}{4}dx}{x + 1} \ - \ \displaystyle\int \dfrac{\frac{3}{2}dx}{(x + 1)^2} \ - \ \displaystyle\int \dfrac{\frac{5}{4}dx}{x - 1} \)



The next line could have been:

\(\displaystyle \dfrac{7}{4}\displaystyle\int \dfrac{dx}{x + 1} \ - \ \dfrac{3}{2}\int (x + 1)^{-2}dx \ - \ \dfrac{5}{4}\displaystyle\int \dfrac{dx}{x - 1} \)



The last line could have been:

\(\displaystyle \dfrac{7}{4}\ln|x + 1| \ + \ \dfrac{3}{2(x + 1)} \ - \ \dfrac{5}{4}\ln|x - 1| \ + \ C\)



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Your top line was missing the "dx" notation, and my last line shows the required absolute
value bars that were missing. The middle fraction in my answer is written in the style of
its corresponding part in the integrand.