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evaluate the following integral ∫ {1 + tan x tan(x +theta)} dx

evaluate the following integral
∫ {1 + tan x tan(x +theta)} 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 (1+tanx.tan(x+\theta ))dx
I = \int (1+tanx.\frac{tanx+tan\theta }{1-tanxtan\theta })dx
I = \int (\frac{1-tanxtan\theta+ tan^2x+tanxtan\theta }{1-tanxtan\theta })dx
I = \int (\frac{1+tan^2x }{1-tanxtan\theta })dx
I = \int (\frac{sec^2x }{1-tanxtan\theta })dx
1-tanxtan\theta = t
-sec^{2}x.tan\theta dx = dt
I = \frac{-1}{tan\theta }\int \frac{dt}{t}
I = \frac{-1}{tan\theta }log(t)+c
I = \frac{-1}{tan\theta }log(1-tanx.tan\theta )+c

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