<img src="https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B%20%5Csec%281%20-%20%20%5Csin%28x%29%20%29%20%7D%20dx" id="TexFormula1" ti

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1 year ago

tle=" \frac{1}{ \sec(1 - \sin(x) ) } dx" alt=" \frac{1}{ \sec(1 - \sin(x) ) } dx" align="absmiddle" class="latex-formula">
Any help with this?

Mathematics

1 answer:

Gnoma [55]1 year ago

4 0

$\displaystyle\dfrac{1}{\sec x(1-\sin x)}=\dfrac{\cos x}{1-\sin x}\\\\\\\int \dfrac{dx}{\sec x(1-\sin x)}=\int\dfrac{\cos x\, dx}{1-\sin x}\\\\\\u=1-\sin x\\du=-\cos x\, dx\\\\\int \dfrac{\cos x\, dx}{1-\sin x}=\int \dfrac{-du }{u}=-\int \dfrac{du}{u}=-\ln |u|+C=-\ln|1-\sin x|+C$

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