integrate-x-2-1-x-2-dx-

Question Number 21810 by j.masanja06@gmail.com last updated on 04/Oct/17

i n t e g r a t e

\int \frac{x^{2}}{\sqrt{1 - x^{2}}} d x

Answered by sma3l2996 last updated on 04/Oct/17

x = s i n t \Rightarrow d x = c o s t d t = \sqrt{1 - {s i n}^{2} t} d t

d x = \sqrt{1 - x^{2}} d t \Leftrightarrow d t = \frac{d x}{\sqrt{1 - x^{2}}}

\int \frac{x^{2}}{\sqrt{1 - x^{2}}} d x = \int {s i n}^{2} (t) d t = \int \frac{1 - c o s (2 t)}{2} d t

= \frac{1}{2} (t - \frac{1}{2} s i n (2 t)) + C = \frac{1}{2} (t - s i n (t) c o s (t)) + C

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