∫(√((cosx−cos^3 x)/((1−cos^3 x))))dx


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Question Number 124334 by Ar Brandon last updated on 02/Dec/20

$\int \sqrt{\frac{\cos x - \cos^{3} x}{(1 - \cos^{3} x)}} d x$
	Answered by MJS_new last updated on 02/Dec/20

	$= \int \frac{\sin x \sqrt{\cos x}}{\sqrt{1 - \cos^{3} x}} d x =$ $[t = \cos x \to d x = - \frac{d t}{\sin x}]$ $= - \int \frac{\sqrt{t}}{\sqrt{1 - t^{3}}} d t =$ $[u = \arcsin t^{3 / 2} \to d t = \frac{2 \sqrt{1 - t^{3}}}{3 \sqrt{t}} d u]$ $= - \frac{2}{3} \int d u = - \frac{2 u}{3} = - \frac{2}{3} \arcsin t^{3 / 2} =$ $= - \frac{2}{3} \arcsin \cos^{3 / 2} x + C$
	Commented by mr W last updated on 02/Dec/20

	$T o M a m m a d l i s i r :$ $y o u s h o u l d h a v e s e e n t h a t a l l o f$ $y o u r p o s t s a r e r e d f l a g g e d . i t m e a n s,$ $p e o p l e {d o n}^{'} t l i k e a l l o f y o u r p o s t s .$ $w h y ? b e c a u s e y o u p o s t e d y o u r q u e s t i o n s$ $i n t h e t h r e a d s o f o t h e r {p e o p l e}^{'} s$ $q u e s t i o n s . t h i s d i s t u r b s a n d i s a l s o$ $n o t r e s p e c t f u l t o o t h e r p e o p l e .$ $i t h i n k o t h e r p e o p l e h a v e t o l d y o u$ $t h i s f o r m a n y t i m e s, b u t y o u j u s t$ $i g n o r e d a l l . i t h i n k o t h e r p e o p l e$ $h a v e a l s o t o l d y o u h o w t o o p e n a n e w$ $t h r e a d f o r y o u r o w n q u e s t i o n, y o u$ $i g n o r e d a l s o t h i s . W H A T I S Y O U R$ $P R O B L E M ? {d o n}^{'} t y o u u n d e r s t a n d$ $E n g l i s h ? w h i c h l a n g u a g e d o y o u$ $u n d e r s t a n d t h e n ?$
	Commented by Mammadli last updated on 02/Dec/20
	Dear ser, I am asking questions that I do not know and I would like you to help
	Commented by Mammadli last updated on 02/Dec/20
	I do not share correctly or how dear ser
	Commented by mr W last updated on 02/Dec/20

	$t h a n k s f o r t h i s c l e a r a n s w e r!$ $y o u s h o u l d n o t p o s t y o u r q u e s t i o n$ $a s c o m m e n t t o a q u e s t i o n o f o t h e r$ $p e o p l e . y o u s h o u l d o p e n a n e w p o s t$ $f o r y o u r q u e s t i o n i n f o l l o w i n g w a y :$ $t o t y p e y o u r q u e s t i o n i n t e x t o r$ $f o r m u l a j u s t u s e c o m m a n d (1) .$ $t o p o s t y o u r q u e s t i o n a s i m a g e$ $j u s t u s e c o m m a n d (2) .$
	Commented by mr W last updated on 02/Dec/20

	Commented by Mammadli last updated on 02/Dec/20
	Thank you very much dear Ser..
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