find-dx-x-2-1-1-x-2-

Question Number 42791 by maxmathsup by imad last updated on 02/Sep/18

f i n d \int \frac{d x}{(x^{2} + 1) \sqrt{1 + x^{2}}}

Answered by MJS last updated on 02/Sep/18

I know this because of the hyperbola formuls

y = \sqrt{x^{2} + 1}

y^{'} = \frac{x}{\sqrt{x^{2} + 1}}

y^{″} = \frac{1}{{(x^{2} + 1)}^{\frac{3}{2}}}

\Rightarrow \int \frac{d x}{(x^{2} + 1) \sqrt{x^{2} + 1}} = \int \frac{d x}{{(x^{2} + 1)}^{\frac{3}{2}}} = \frac{x}{\sqrt{x^{2} + 1}} + C

Commented by math khazana by abdo last updated on 03/Sep/18

t h a n k y o u s i r .

Answered by tanmay.chaudhury50@gmail.com last updated on 04/Sep/18

x = t a n α d x = {s e c}^{2} α d α

\int \frac{{s e c}^{2} α d α}{{({s e c}^{2} α)}^{\frac{3}{2}}}

\int c o s α d α

s i n α + c

= \frac{x}{\sqrt{1 + x^{2}}} + c