Question

find the function f such that f'(x)=1/x^2+1 and f(0)=2

Answer 1

F = -1/x+x+C
I integrated the function And then I plugged in f(0)=2:
-1/(0)+(0)+C=2
C=2
F=x-(1/x)+2

Answer 2

i thought the derivative of 1/x^2+1 is arctan

Answer 3

yup that is an identity ugghhhh

Answer 4

wait let me redo it

Answer 5

sure.

Answer 6

so when that function is integrated you get arctan(x)+c
So we tehn plug in f(0)=2:
tan^-1(0)+C=2
0+C=2
C=2
F=tan^-1(x)+2

Answer 7

thank u