Answer
$\ln5$
Work Step by Step
$$16\int_{0}^{1}\frac{x}{8x^{2}+2}dx=8\int_{0}^{1}\frac{d(x^{2})}{8x^{2}+2}$$
$$=\int_{0}^{1}\frac{d(8x^{2}+2)}{8x^{2}+2}$$
$$=\left | \ln(8x^{2}+2) \right |_{0}^{1}$$
$$=\ln10-\ln2$$
$$=\ln5$$
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