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integral left parenthesis square root of c o t invisible function application x end root plus square root of t a n invisible function application x end root right parenthesis d x equals f left parenthesis x right parenthesis plus c text  thenf  end text left parenthesis x right parenthesis equals

  1. square root of 2 s i n to the power of negative 1 end exponent invisible function application left parenthesis s i n invisible function application x minus c o s invisible function application x right parenthesis    
  2. square root of 2 c o s to the power of negative 1 end exponent invisible function application square root of s i n invisible function application 2 x end root    
  3. square root of 2 t a n to the power of negative 1 end exponent invisible function application fraction numerator s i n invisible function application x minus c o s invisible function application x over denominator square root of s i n invisible function application 2 x end root end fraction    
  4. square root of 2 c o s to the power of negative 1 end exponent invisible function application square root of 1 minus s i n invisible function application 2 x end root    

The correct answer is: square root of 2 c o s to the power of negative 1 end exponent invisible function application square root of s i n invisible function application 2 x end root


    I equals integral left parenthesis square root of c o t invisible function application x end root plus square root of t a n invisible function application x end root right parenthesis d x equals integral fraction numerator c o s invisible function application x plus s i n invisible function application x over denominator square root of c o s invisible function application x s i n invisible function application x end root end fraction d x
    text put  end text left parenthesis s i n invisible function application x minus c o s invisible function application x right parenthesis text  they  end text I equals integral fraction numerator square root of 2 over denominator square root of 1 minus t to the power of 2 end exponent end root end fraction d t
    equals square root of 2 s i n to the power of negative 1 end exponent invisible function application left parenthesis s i n invisible function application x minus c o s invisible function application x right parenthesis

    equals square root of 2 t a n to the power of negative 1 end exponent invisible function application fraction numerator left parenthesis s i n invisible function application x minus c o s invisible function application x right parenthesis over denominator square root of s i n invisible function application 2 x end root end fraction

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