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evaluate ∫ sin^-1(2 tan x / 1 + tan^2(x)) dx

evaluate
∫  sin^-1(2 tan x / 1 + tan^2(x)) 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 sin^{-1}(\frac{2tanx}{1+tan^{2}x})dx
I = \int sin^{-1}(\frac{2tanx}{sec^{2}x})dx
I = \int sin^{-1}(\frac{2sinx}{cosx.sec^{2}x})dx
I = \int sin^{-1}({2sinxcosx})dx
I = \int sin^{-1}({sin2x})dx
I = \int 2xdx
I = x^2 + c

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