{² x}{{² x + 4}} - NCERT Class XII Mathematics Chapter -

NCERT Class XII Mathematics Chapter - - Solutions

Exercise - 7.4
Integrate the functions in Exercises 86 to 108.

Question : 94 of 271

Marks: +1, -0

\frac{\sec^2 x}{\sqrt{\tan^2 x + 4}}

Solution:

Let

I = \int \frac{\sec^2 x}{\sqrt{\tan^2 x + 4}} \, dx

Put tan

x = t \Rightarrow \sec^2 x \, dx = dt

\therefore I = \int \frac{dt}{\sqrt{t^2 + 2^2}} = \log \left| t + \sqrt{t^2 + 4} \right| + C

= \log \left| \tan x + \sqrt{\tan^2 x + 4} \right| + C

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