by 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.