how to integrate` int(cscx)^2/cotxdx` ?

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how to integrate` int(cscx)^2/cotxdx` ?

Postby Integr88 » Tue 05 April, 2011 18:28

what is the integral of ` int(cscx)^2/cotxdx`
please show steps.
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Re: how to integrate` int(cscx)^2/cotxdx` ?

Postby barnamah » Tue 05 April, 2011 18:50

to integrate ` int(cscx)^2/cotxdx` let's write it in a way so it looks simple:
using u substitution we
let `u=cotx`
so `du=-csc^2xdx` (we know this from the integral table either memorize it or formula sheet is provided)

so sub in the above values we have:
`int(-1/u)du`

Move negative sign out side, we have: `-int(1/u)du`. Now it is simple because we know the integral of `1/x` is lnx or `int1/xdx=lnx`. Applying the same rule we have:
`-int(1/u)du=-ln(u)+C` where C is a constant
Now sub in the u which was cotx and we got:`-ln(cotx)+C`

so the final answer is: `-ln(cotx)+C`
Explore and know. That is asked.
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