If f(x) = ∫ 5 x ^ 8 + 7 x ^ 6 ( x ^ 2 + 1 + 2 x ^ 7 ) ^ 2 dx, (x ≥...

f\left(x\right) = ∫ \dfrac{\left(5{x}^{8} + 7{x}^{6}\right)dx}{{x}^{14}{\left({x}^{- 5} + {x}^{- 7} + 2\right)}^{2}}$</p><p>Let${x}^{- 5} + {x}^{- 7} + 2 = t$</p><p>\left(- 5{x}^{- 6} - 7{x}^{- 8}\right)dx = dt$

$⇒ f\left(x\right) = ∫ - \dfrac{dt}{{t}^{2}} = \dfrac{1}{t} + c$

$f\left(x\right) = \dfrac{{x}^{7}}{{x}^{2} + 1 + 2{x}^{7}}$

$f\left(1\right) = \dfrac{1}{4}$