dx-x-x-4-1-

Question Number 18650 by thukada last updated on 26/Jul/17

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

Answered by sma3l2996 last updated on 26/Jul/17

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

l e t t = \sqrt{x^{4} - 1} \Rightarrow d t = \frac{2 x^{3}}{\sqrt{x^{4} - 1}} d x

\frac{d x}{\sqrt{x^{4} - 1}} = \frac{d t}{2 x^{3}} \Leftrightarrow \frac{d x}{x \sqrt{x^{4} - 1}} = \frac{d t}{2 x^{4}} = \frac{d t}{2 (t^{2} + 1)}

A = \frac{1}{2} \int \frac{d t}{t^{2} + 1} = \frac{1}{2} {t a n}^{- 1} (t) + C

A = \frac{1}{2} {t a n}^{- 1} (\sqrt{x^{4} - 1}) + C