int (dx/(1-cosx) ) dx

**Boo** · January 26th 2013, 07:38 AM

Dear All!
please, coudl you help me with:

$\int \frac{1}{1-cosx}dx=-\frac{cosx+1}{sinx}$
is that ok?
Many thanks!

**ibdutt** · January 26th 2013, 08:15 AM

Use the expressions ∫▒cot⁡〖x dx=log⁡|sinx|+C 〗 and ∫▒〖cosec x dx=log⁡〖| cosec x-cotx |+C〗〗

**hollywood** · January 26th 2013, 09:45 AM

Multiply numerator and denominator by $(1+\cos{x})$ .

$\int \frac{1+\cos{x}}{(1-\cos{x})(1+\cos{x})}\,dx =$

$\int \frac{1+\cos{x}}{1-\cos^2{x}}\,dx =$

$\int \frac{1+\cos{x}}{\sin^2{x}}\,dx =$

$\int \csc^2{x}\,dx+\int\csc{x}\cot{x}\,dx =$

$-\cot{x}-\csc{x}+C$

- Hollywood

**Boo** · January 27th 2013, 02:25 AM

Many thanks, Hollywood!!!

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