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evaluate ∫ tan x / sec x + tan x dx

evaluate
∫  tan x / sec x + tan x dx

Grade:12

1 Answers

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

I = \int \frac{tanx}{secx+tanx}dx
I = \int \frac{tanx(secx-tanx)}{(secx+tanx)(secx-tanx)}dx
I = \int \frac{secxtanx-tan^2x}{sec^2x-tan^2x}dx
I = \int \frac{secxtanx-tan^2x}{1}dx
I = \int secxtanxdx-\int tan^2xdx
I = \int secxtanxdx-\int (sec^2x-1)dx
I = \int secxtanxdx-\int sec^2xdx+\int dx
I =secx-tanx+x+c

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