calculus

find indefinite integral of

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

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  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

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  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

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    👨‍🏫
    bobpursley
  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

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