Hi I have a proof i'm doing(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

\int \frac{1}{1+\sin(x)}dx

[/tex]

I know that the answer i'm looking for is

[tex]

\frac{\sin(x) - 1}{\cos(x)}

[/tex]

and then

[tex]

\tan(x) - \sec(x)

[/tex]

I have tried integration by parts making

[tex]

u = (1+\sin(x))^{-1}[/tex] and [tex]dv = dx

[/tex]

Eventually I get an answer that contains an ln and an unsolvable integral. I have been at this for 2 hours, can anyone give me a hint or a push in the right direction?

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# Homework Help: Reciprocal of Trig - Integral

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