could someone help me
(x+5)dx/(x^2+x+1)
and this
(1/sqrt(2)*x+1)dx/(x^2-x*sqrt(2) +1)
By completing the square: . That cannot be factored in terms of real numbers and so you cannot use "partial fractions". Make the substitution u= x+ 1/2 instead.
Here, completing the square gives .and this
(1/sqrt(2)*x+1)dx/(x^2-x*sqrt(2) +1)
Again, you can't use partial fractions. Make the substitution instead.
Here is the technique of resolving into partial fractions .
( * the term " 1 + x " exists only for n is odd )
Then , " log " both sides
After that , differentiate both sides ( we call this " Logarithmic Differentiaion ! )
Replace with
Divide both sides by
ps : you should know what a ,b , c , d ... are . for this case ,
let