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Question Number 122967 by bemath last updated on 21/Nov/20

\int \frac{x}{\sqrt{1 - x^{4}}} d x

Answered by bobhans last updated on 21/Nov/20

l e t x^{2} = \sin t \Rightarrow 2 x d x = \cos t d t

\emptyset (x) = \frac{1}{2} \int \frac{\cos t d t}{\sqrt{1 - \sin^{2} t}} = \frac{1}{2} \int d t

\emptyset (x) = \frac{1}{2} t + c = \frac{1}{2} \arcsin (x^{2}) + c .

Answered by TANMAY PANACEA last updated on 21/Nov/20

t = x^{2} \to d t = 2 x d x

\frac{1}{2} \int \frac{d t}{\sqrt{1 - t^{2}}} = \frac{1}{2} {s i n}^{- 1} (t) + C

\frac{1}{2} {s i n}^{- 1} (x^{2}) + C