SB257426
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decompose the integrand
yep thats what i got !!!
Aha ! I get it nowWe need to factorise the denominator:
The integrand can now be decomposed using partial fractions:
also what application did u use to do ur workingWe need to factorise the denominator:
The integrand can now be decomposed using partial fractions:
I typed it in the box for posting replies.also what application did u use to do ur working
haha lolI typed it in the box for posting replies.
Now for a follow up question: hence or otherwise integrate sqrt(tanx)
LaTeXalso what application did u use to do ur working
Brilliant answer btwI typed it in the box for posting replies.
Note that the original solution posted:
does works on some domains  for example, on .
However, for the domain , the integral is
This tells me that there is an issue with signs or in making the assumption that when, in fact and is only when .
Note, for example, that I did not make the substitution as it would follow that ... instead, I substituted and avoided a potential problem. Far too many papers include substitutions that raise problems that are then ignored, yielding correct answers but from technicallyflawed working.
Good answer but there's an easier way than doing partial fraction decomposition, so I thought I might share it:We need to factorise the denominator:
The integrand can now be decomposed using partial fractions:
nice, i was intending for it to be done by sqrt(tanx) = 1/2 (sqrttanx + sqrtcotx + sqrttanx  sqrtcotx) tho
The partial fractions result will now yield both inverse tan and log terms.
Alternatively, focus on
and then subtract the result from the integral found earlier in this thread.