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integral fraction numerator e to the power of x end exponent left parenthesis x minus 1 right parenthesis left parenthesis x minus l n invisible function application x right parenthesis over denominator x to the power of 2 end exponent end fractiondx is equal to

  1. e to the power of x end exponent open parentheses fraction numerator x minus l n invisible function application x over denominator x end fraction close parentheses plus c    
  2. e to the power of x end exponent open parentheses fraction numerator x minus l n invisible function application x plus 1 over denominator x end fraction close parentheses plus c    
  3. e to the power of x end exponent open parentheses fraction numerator x minus l n invisible function application x over denominator x to the power of 2 end exponent end fraction close parentheses plus c    
  4. e to the power of x end exponent open parentheses fraction numerator x minus l n invisible function application x minus 1 over denominator x end fraction close parentheses plus c    

The correct answer is: e to the power of x end exponent open parentheses fraction numerator x minus l n invisible function application x minus 1 over denominator x end fraction close parentheses plus c


    integral fraction numerator e to the power of x end exponent left parenthesis x minus 1 right parenthesis left parenthesis x minus l n invisible function application x right parenthesis over denominator x to the power of 2 end exponent end fraction d x equals integral e to the power of x end exponent open parentheses fraction numerator 1 over denominator x end fraction minus fraction numerator 1 over denominator x to the power of 2 end exponent end fraction close parentheses open parentheses ln invisible function application fraction numerator e to the power of x end exponent over denominator x end fraction close parentheses d x
    table row cell equals integral l n invisible function application fraction numerator e to the power of x end exponent over denominator x end fraction d open parentheses fraction numerator e to the power of x end exponent over denominator x end fraction close parentheses end cell row cell equals l n invisible function application open parentheses fraction numerator e to the power of x end exponent over denominator x end fraction close parentheses fraction numerator e to the power of x end exponent over denominator x end fraction minus fraction numerator e to the power of x end exponent over denominator x end fraction plus c end cell end table
    equals fraction numerator e to the power of x end exponent over denominator x end fraction left parenthesis x minus l n invisible function application x minus 1 right parenthesis plus c

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    integral x to the power of 3 end exponent square root of fraction numerator 1 plus x to the power of 2 end exponent over denominator 1 minus x to the power of 2 end exponent end fraction end root d x equals A square root of 1 minus x to the power of 4 end exponent end root minus B x to the power of 2 end exponent square root of 1 minus x to the power of 4 end exponent end root plus C s i n to the power of negative 1 end exponent invisible function application x to the power of 2 end exponent plus D comma text end textthen A+B+C is equal to

    integral x to the power of 3 end exponent square root of fraction numerator 1 plus x to the power of 2 end exponent over denominator 1 minus x to the power of 2 end exponent end fraction end root d x equals A square root of 1 minus x to the power of 4 end exponent end root minus B x to the power of 2 end exponent square root of 1 minus x to the power of 4 end exponent end root plus C s i n to the power of negative 1 end exponent invisible function application x to the power of 2 end exponent plus D comma text end textthen A+B+C is equal to

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