int 4/[sqrt(x)(x+6)] dx from 0 to infinity
0 and infinity are both problems...solution says to break it up as limits from 0 to 1 and 1 to infinity....why? how is this decided? Is a convenient number just decided upon?
it can be any number as long as and besides is usual and convenient.
we have so in order to get convergence here, these pieces must converge.
the first one does by simple limit comparison test with and for the second one, for each is thus these pieces converge and the original integral does.