∫a+xu=x+a−xa+xdx is equal to

∫a+xa−x+a−xa+xdx=∫2aa2−x2dx=2asin−1⁡xa+c

∫a+xu=x+a−xa+xdx is equal to

∫a+xa−x+a−xa+xdx=∫2aa2−x2dx=2asin−1⁡xa+c

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

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(1) $2 \sin^{- 1} (x l a) + c$

(2) $2 a \sin^{- 1} (x / a) + c$

(3) $2 c o s^{- 1} (x / a) + c$

(4) $2 a c o s^{- 1} (x / a) + c$

answer is B.

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Detailed Solution

$\begin{aligned} \int (\sqrt{\frac{a + x}{a - x}} + \sqrt{\frac{a - x}{a + x}}) d x = \int \frac{2 a}{\sqrt{a^{2} - x^{2}}} d x \\ = 2 a \sin^{- 1} (\frac{x}{a}) + c \end{aligned}$

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