# Integrate then differentiate?

Calculus Level 4

Given that $$a$$ is a variable independent of the variable $$x,$$ we define $$I$$ as follows:

$\large I = \int_0^{\pi /2} \ln \left( \dfrac{1+a \sin x}{1 - a \sin x} \right) \dfrac {dx}{\sin x}.$

For $$|a| < 1$$, find the value of $$\dfrac{dI}{da}$$ in terms of $$a$$.

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