- #1
KLscilevothma
- 322
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I have been doing revision on integration lately, and came across a question that need to resolve (1+u2)/(1+u4) in partial fraction before I can proceed.
1+u4 = (u2-2u+2)(x2+2u+2)
therefore 1+u2 = (Au+B)(x2+2u+2) + (Cu+D)(u2-2u+2)
and I need to find out A, B, C and D
But wait, the next step in my textbook contains something like (1+sqrt(2)u+u2) and (1-sqrt(2)+u2) in denominators, so what is the problem and where does sqrt(2) come from ?
PS
original question:
[inte]dx/[(1+x2)(sqrt(1-x2))]
and the substitution used is :
u=sqrt[(1-x)/(1+x)]
1+u4 = (u2-2u+2)(x2+2u+2)
therefore 1+u2 = (Au+B)(x2+2u+2) + (Cu+D)(u2-2u+2)
and I need to find out A, B, C and D
But wait, the next step in my textbook contains something like (1+sqrt(2)u+u2) and (1-sqrt(2)+u2) in denominators, so what is the problem and where does sqrt(2) come from ?
PS
original question:
[inte]dx/[(1+x2)(sqrt(1-x2))]
and the substitution used is :
u=sqrt[(1-x)/(1+x)]