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anonymous
 one year ago
Using one computer algebra system, it was found that ∫dx/ (1+sin x ) = (sin x  1)/ cos x and using another computer system, this integral is equal to
2 sin (x/2) / cos(x/2) + sin(x/2)... How do I reconcile these two answers?
anonymous
 one year ago
Using one computer algebra system, it was found that ∫dx/ (1+sin x ) = (sin x  1)/ cos x and using another computer system, this integral is equal to 2 sin (x/2) / cos(x/2) + sin(x/2)... How do I reconcile these two answers?

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Loser66
 one year ago
Best ResponseYou've already chosen the best response.0You meant: \(\dfrac {sinx 1}{cosx} \) vs \(\dfrac{sin(x/2)}{cos(x/2)+sin(x/2)}\) right?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\(\color{slate}{\displaystyle \int \frac{1}{\sin(x)+1}dx}\) \(\color{slate}{\displaystyle \int \frac{1(\sin x  1)}{(\sin x+1)(\sin x  1)}dx}\) \(\color{slate}{\displaystyle \int \frac{\sin x  1}{\sin^2x1}dx}\) \(\color{slate}{\displaystyle \int \frac{\sin x  1}{\cos^2x}dx}\) \(\color{slate}{\displaystyle \int \left(\frac{\sin x }{\cos^2x}\frac{\ 1}{\cos^2x}\right)dx}\) \(\color{slate}{\displaystyle \int \left(\tan x \sec x \sec^2x\right)dx}\) \(\color{slate}{\displaystyle \int \left(\sec^2x\tan x \sec x \right)dx}\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I hope this is a helpful approach.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yeah, sec^2x = tan^2x+1 i forget what derivative is what, but whether you need sec^2x or tan^2x, you got it.
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