- #1
Nano-Passion
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Homework Statement
If the power of the secand is even and positive..
[tex]\int sec^{2k} x tan^{n} x dx = \int (sec^2 x)^{k-1} tan ^n x sec^2 x dx [/tex]
The Attempt at a Solution
The way I see it,
[tex] sec^{2k} x = sec^2 x dx * sec^k x dx[/tex]
the next step seems to be to break down sec^k, but on closer introspection, the break down goes something like this
[tex]sec^k x dx = (sec^2 x dx)^{k-1} = sec^{2k-2}x dx[/tex]
I'm having trouble intuitively accepting that something like 2k-2 = k. It doesn't seem to add up, there seems to be something a bit more complex into it that is left out of detail.
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