Integral Calculus> ∫1/x*√(x-1)/(x+1) dx=?_ Sir,p...

∫1/x*√(x-1)/(x+1) dx=?_

Sir,pls tell me the detailed solution of this as soon as possible.thank u in advance...

ajay govind , 9 Years ago

Grade 12th pass

1 Answers

Ajay

Please find the answer, this could be easily solved if you know differentaition of inverse trignometric functions

$\int { \frac { dx }{ x\sqrt { (x-1)(x+1) } } } \\ \\ =\quad \int { \frac { dx }{ x\sqrt { { x }^{ 2 }-1 } } } \\ \quad \\ Put\quad x=sec\theta \quad so\quad that\quad dx\quad =\quad sec\theta tan\theta d\theta \\ \\ =\quad \int { \frac { sec\theta tan\theta d\theta }{ sec\theta \sqrt { { sec\theta }^{ 2 }-1 } } } =\quad \int { \frac { sec\theta tan\theta d\theta }{ sec\theta \sqrt { { { tan }^{ 2 }\theta } } } } \\ \\ \int { d\theta \quad =\quad \theta \quad +\quad C\quad \quad =\quad { sec }^{ -1 }x\quad +\quad C }$