Mathematics

Solve $$\displaystyle\int\dfrac {\sqrt {\tan x}}{\sin x \cos x}dx$$


SOLUTION
$$\displaystyle\int\dfrac {\sqrt {\tan x}}{\sin x \cos x}dx$$
Put, $$ \tan x  = t $$

$$\implies \sec^2 x dx = dt$$

Now, $$\displaystyle\int \dfrac{\sqrt{\tan x}}{\sin x \cos x} dx = \int \dfrac{\sqrt{\tan x}}{\tan x \cos^2 x} dx$$

$$ = \displaystyle\int \dfrac{\sec^2 x}{\sqrt{\tan x}} dx = \int \dfrac{1}{\sqrt{t}} dt$$

$$ = 2\sqrt{t} + c$$

$$ = 2\sqrt{\tan x} + c$$

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Subjective Medium Published on 17th 09, 2020
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