1/² x (1 - x)² - NCERT Class XII Mathematics Chapter -

NCERT Class XII Mathematics Chapter - - Solutions

Exercise - 7.2
Integrate the functions in Exercises 23 to 59.

Question : 47 of 271

Marks: +1, -0

\frac{1}{\cos^2 x (1 - \tan x)^2}

Solution:

Let

I = \int \frac{1}{\cos^2 x (1 - \tan x)^2} dx

= \int \frac{\sec^2 x}{(1 - \tan x)^2} dx

Put

1 - \tan x = t

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

\therefore I = -\int \frac{dt}{t^2}

= -\frac{t^{-2+1}}{-2+1} + C

= \frac{1}{1 - \tan x} + C

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