∫(dx/(sin2x−sec(x)))


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Question Number 68116 by aliesam last updated on 05/Sep/19

$\int \frac{d x}{s i n 2 x - s e c (x)}$
Commented by MJS last updated on 06/Sep/19

$look at question 68141$
	Answered by MJS last updated on 05/Sep/19

	$\int \frac{d x}{\sin 2 x - \sec x} =$ $[t = \sin x \to d t = \frac{d t}{\cos x}]$ $= - \frac{1}{2} \int \frac{d t}{t^{3} - t + \frac{1}{2}} = - \frac{1}{2} \int \frac{d t}{(t - α) (t - β) (t + γ)}$ $now decompose and integrate$ $at the end solve t^{3} - t + \frac{1}{2} = 0 to get the$ $constant factors$
	Commented by mind is power last updated on 05/Sep/19

	$c a r d a n$
	Commented by MJS last updated on 05/Sep/19

	$what does ‘ ‘ {cardan}^{″} mean ?$
	Commented by mind is power last updated on 05/Sep/19

	$c a r d a n i s o n e w a y t o s o l v e a l g e b r i c e q u a t i o n o f d e g r e 3 s o r r y f i r m y e n g l i s h$
	Commented by MJS last updated on 06/Sep/19

	$of course! you mean {Cardano}^{'} s method, you$ $are right . I read ‘ ‘ {cardan}^{″} and the only thing$ $that came to my mind was the ‘ ‘ cardan shaft$ ${drive}^{″} . . . haha, blame it on me . . .$
	Commented by mind is power last updated on 05/Sep/19

	$y e a h s o r r y i m f r e n c h m y e n g l i s h i s n o t v e r r y g o o d$
	Commented by MJS last updated on 06/Sep/19
	no problem, I'm from Austria... I had 4 years of French in school but that had been 30 years ago... Je peux encore comprendre partiellement le français écrit, mais je ne comprends plus la langue parlée ...
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