If ∫dxx2+2x+2=fx+C, then fx=
tan-1x+1
2tan-1x+1
-tan-1x+1
3tan-1x+1
Explanation for the correct option.
Find the function fx.
The integral ∫dxx2+2x+2 can be solved as:
∫dxx2+2x+2=∫dxx2+2x+1+1=∫dxx+12+1=tan-1x+1+C[ddxtan-1x=11+x2]
As it is given that ∫dxx2+2x+2=fx+C, so the function fx is equal to tan-1x+1.
Hence the correct option is A.
Use the factor theorem to determine whether g(x) is a factor of f(x)
f(x)=22x2+5x+2;g(x)=x+2