Mathematics

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

$I=2\sqrt{\tan x}+C$

##### SOLUTION

Consider the given integral.

$I=\int{\dfrac{\sqrt{\tan x}}{\sin x\cos x}dx}$

$I=\int{\dfrac{\sqrt{\tan x}}{\tan x{{\cos }^{2}}x}dx}$

$I=\int{\dfrac{{{\sec }^{2}}x}{\sqrt{\tan x}}dx}$

Let $t=\tan x$

$dt={{\sec }^{2}}xdx$

Therefore,

$I=\int{\dfrac{dt}{\sqrt{t}}}$

$I=2\sqrt{t}+C$

On putting the value of $t$, we get

$I=2\sqrt{\tan x}+C$

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Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86

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