Given y'=e^(arctan x)/(x^2+1), what is the function y?

To determine the primitive function, we'll have to
calculate the indefinite integral of y'.

We'll apply
substitution technique, replacing arctan x by t.

arctan x =
t

We'll differentiate both sides and we'll
get:

dx/(1 + x^2) = dt

We'll
re-write the integral in the new variable:

Int e^(arctan x)
dx/(1 + x^2) =Int e^t*dt

Int e^t*dt = e^t +
C

Int e^(arctan x) dx/(1 + x^2) = e^(arctan x) +
C

The primitive function is: y = e^(arctan x)
+ C