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

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If \(f(x)=\int \frac{5 x^8+7 x^6}{\left(x^2+1+2 x^7\right)^2} d x(x \geq 0)\) and \(f(0)=0\), then the value of \(f(1)\)…