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integrate the following integral ∫ 1/cos^2(x)(1 – tan x)^2 dx

 
integrate the following integral
∫ 1/cos^2(x)(1 – tan x)^2 dx

Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
9 years ago
Ans:
Hello Student,
Please find answer to your question below

I = \int \frac{1}{cos^{2}x(1-tanx)^2}dx
I = \int \frac{1}{cos^{2}x(tanx-1)^2}dx
I = \int \frac{sec^{2}x}{(tanx-1)^2}dx
tanx-1 = t
sec^{2}xdx = dt
I = \int \frac{1}{t^2}dt
I = \frac{-1}{t}+c
I = \frac{-1}{tanx-1}+c
I = \frac{1}{1-tanx}+c

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