intleft(sqrt{frac{a+x}{a-x}}+sqrt{frac{a-x}{a | vedclass

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(B) Let $I = \int \left( \sqrt{\frac{a+x}{a-x}} + \sqrt{\frac{a-x}{a+x}} \right) dx$. Simplify the integrand: $\sqrt{\frac{a+x}{a-x}} + \sqrt{\frac{a-

Vedclass · Accepted Answer

$2 a \sin ^{-1}\left(\frac{x}{a}\right)+C$

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(B) Let $I = \int \left( \sqrt{\frac{a+x}{a-x}} + \sqrt{\frac{a-x}{a+x}} \right) dx$. Simplify the integrand: $\sqrt{\frac{a+x}{a-x}} + \sqrt{\frac{a-x}{a+x}} = \frac{a+x + a-x}{\sqrt{(a-x)(a+x)}} = \frac{2a}{\sqrt{a^2-x^2}}$. Now, the integral becomes: $I = \int \frac{2a}{\sqrt{a^2-x^2}} dx$. Using the standard integral formula $\int \frac{1}{\sqrt{a^2-x^2}} dx = \sin^{-1}\left(\frac{x}{a}\right) + C$: $I = 2a \int \frac{1}{\sqrt{a^2-x^2}} dx = 2a \sin^{-1}\left(\frac{x}{a}\right) + C$.

$\int\left(\sqrt{\frac{a+x}{a-x}}+\sqrt{\frac{a-x}{a+x}}\right) d x$ is equal to

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