This question is not easy because you need to take a guess for the expression of y.

$latex {Let\ y=\ln (1-2{{x}^{2}})}$

Differentiate y with respect to x.

$latex {\frac{{dy}}{{dx}}=\frac{1}{{1-2{{x}^{2}}}}\times -4x}$

$latex {\frac{{dy}}{{dx}}=\frac{{-4x}}{{1-2{{x}^{2}}}}}$

Integrate both sides of the equation

$latex {y=-4\int{{\frac{x}{{1-2{{x}^{2}}}}}}\ dx}$

$latex {\ln (1-2{{x}^{2}})=-4\int{{\frac{x}{{1-2{{x}^{2}}}}}}\ dx}$

$latex {\int{{\frac{x}{{1-2{{x}^{2}}}}}}\ dx=-\frac{1}{4}\ln (1-2{{x}^{2}})}$

You need to differentiate the y to get an expression for dy/dx, followed by integrating both sides of the expression.

There is no quotient rule for integration, unlike differentiation,so you need to go through the long about way by first differentiating, followed by integrating.

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