If ∫cosecxdx=fx+constant, then fx=
tanx2
logtanx2
logsinx
logcosx
Explanation for the correct option:
Find the function fx.
It is known that the ∫cosecxdx=-logcotx2+constant.
So the function fx is -logcotx2 and it can be written as:
fx=-logcotx2=logcotx2-1=logtanx21cotx=tanx
Thus the function fx is logtanx2.
Hence, the correct option is B.
Use the factor theorem to determine whether g(x) is a factor of f(x)
f(x)=22x2+5x+2;g(x)=x+2