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Maths-

General

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Question

$not stretchy integral subscript blank superscript blank e to the power of x end exponent fraction numerator left parenthesis 1 minus x right parenthesis to the power of 2 end exponent over denominator left parenthesis 1 plus x to the power of 2 end exponent right parenthesis to the power of 2 end exponent end fraction d x equals$

$\frac{e^{x}}{(1 - x)^{2}} + c$
$\frac{e^{x}}{(1 + x)^{2}} + c$
$e^{x} (\frac{1 - x^{2}}{1 + x^{2}}) + c$
$\frac{e^{x}}{(1 + x^{2})^{2}} + c$

The correct answer is: $fraction numerator e to the power of x end exponent over denominator left parenthesis 1 plus x right parenthesis to the power of 2 end exponent end fraction plus c$

$not stretchy integral subscript blank superscript blank e to the power of x end exponent left square bracket fraction numerator 1 plus x to the power of 2 end exponent minus 2 x over denominator left parenthesis 1 plus x to the power of 2 end exponent right parenthesis to the power of 2 end exponent end fraction right square bracket d x$
$not stretchy integral subscript blank superscript blank e to the power of x end exponent left square bracket fraction numerator 1 over denominator 1 plus x to the power of 2 end exponent end fraction minus fraction numerator 2 x over denominator left parenthesis 1 plus x to the power of 2 end exponent right parenthesis to the power of 2 end exponent end fraction right square bracket d x$
And apply the formula
$not stretchy integral subscript blank superscript blank e to the power of x end exponent left square bracket f left parenthesis x right parenthesis plus f to the power of ´ end exponent left parenthesis x right parenthesis right square bracket d x equals e to the power of x end exponent f left parenthesis x right parenthesis plus C$
$e to the power of x end exponent blank left parenthesis fraction numerator 1 over denominator 1 plus x to the power of 2 end exponent end fraction right parenthesis plus c$

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