What’s the indefinite integral of this? #f(x) = (1-sin^2 x)/(sin^2 x)#

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Answer 1 · 2018-03-10T16:56:28

The answer is #=-cotx-x+C#

We need

#cot^2x=csc^2x-1#

#intcsc^2xdx=-cotx+C#

The integral is

#intf(x)dx=int((1-sin^2x)dx)/(sin^2x)#

#=int(cos^2xdx)/(sin^2x)#

#=intcot^2xdx#

#=int(csc^2x-1)dx#

#=intcsc^2xdx-int1dx#

#=-cotx-x+C#