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evaluate the following integral ∫ 1 + tan x / 1 – tan x dx

evaluate the following integral
∫ 1 + tan x / 1 – tan x dx

Grade:12

1 Answers

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

I = \int \frac{1+tanx}{1-tanx}dx
I = \int \frac{1+\frac{sinx}{cosx}}{1-\frac{sinx}{cosx}}dx
I = \int \frac{cosx+sinx}{cosx-sinx}dx
cosx - sinx = t
(-sinx - cosx)dx = dt
I = \int \frac{-1}{t}dt
I = -log(t) + c
I = -log(cosx-sinx) + c

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