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Grade 12Integral Calculus

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

taniska

11 Years agoGrade 12

1 Answer

Jitender Singh

11 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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