If $f\left( x \right) = \int {{{5{x^8} + 7{x^6}} \over {{{\left( {{x^2} + 1 + 2{x^7}} \right)}^2}}}} \,dx,\,\left( {x \ge 0} \right),$ $f\left( 0 \right) = 0,$ then the value of $f(1)$ is :

Question

If $f\left( x \right) = \int {{{5{x^8} + 7{x^6}} \over {{{\left( {{x^2} + 1 + 2{x^7}} \right)}^2}}}} \,dx,\,\left( {x \ge 0} \right),$

$f\left( 0 \right) = 0,$ then the value of $f(1)$ is :

$ - $ ${1 \over 2}$

$ - $ ${1 \over 4}$

${1 \over 2}$

${1 \over 4}$

Solution

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