pi-2-pi-2-sin-log-x-x-2-1-dx-

Question Number 34446 by dilanho last updated on 06/May/18

\underset{- π / 2}{\int^{π / 2}} \sin {\log (x + \sqrt{x^{2} + 1})} d x =

Commented by math khazana by abdo last updated on 06/May/18

l e t p u t I = \int_{- \frac{π}{2}}^{\frac{π}{2}} s i n {l n (x + \sqrt{x^{2} + 1})} d x

I = \int_{- \frac{π}{2}}^{\frac{π}{2}} s i n (a r g s h x) d x l e t p u t a r g s h x = t \Leftrightarrow

x = s h (t) \Rightarrow I = \int_{- a r g s h (\frac{π}{2})}^{a r g s h (\frac{π}{2})} s i n t c h t d t

I = 0 b e c a u s e t h e f u n c t i o n t \to s i n t c h t i s o d d .