Question

find indefinite integral of

(e^-x)-(1)/(e^-x+(x)^2 dx

Answer 1

my interpretation:

(e^-x - 1)/(e^-x+x^2) , you have mis-matched brackets

even the usual reliable Wolfram had difficulties with that one
http://integrals.wolfram.com/index.jsp?expr=%28e%5E-x+-+1%29%2F%28e%5E-x%2Bx%5E2%29&random=false

the way you typed it, fixing the missing bracket

e^-x - (1/(e^-x+x^2) )

http://integrals.wolfram.com/index.jsp?expr=e%5E-x+-+%281%2F%28e%5E-x%2Bx%5E2%29+%29&random=false

same result,
that's a tough one

Answer 2

let u= (e^-x+(x))^-2

then du = -2/(e^-x+(x)) * (-e^-x+(1))dx

which changes the integral to
1/2 u du

or u^2

Answer 3

and Bob saw an even third interpretation of your typing

(e^-x - 1)/(e^-x+ x )^2

http://integrals.wolfram.com/index.jsp?expr=%28e%5E-x+-+1%29%2F%28e%5E-x%2B+x+%29%5E2&random=false