reduction formulae for tan^n[x]

so i have to integrate

Unparseable latex formula:

tan^n(x)\dx

and this is what i have done so far

\displaystyle\int tan^{n-2}(x) \times (sec^2(x) - 1) = \displaystyle\int tan^{n-2}(x) \times sec^2(x) - \displaystyle\int tan^{n-2}(x)[br]

I_n = \displaystyle\int tan^{n-2}(x) \times sec^2(x) - I_{n-2}

how do i work with

\displaystyle\int tan^{n-2}(x) \times sec^2(x)

Make a substitution, remembering that

\frac{d}{dx}\tan x = \sec^2x

Can you not integrate by parts here? :s-smilie:

Well played.

Mathematician!

Can you not integrate by parts here? :s-smilie:

i tried that first but it just made it more complicated, anyway i got the answer with this

\displaystyle\int [f(x)]^m . f'(x) dx = \frac{[f(x)]^{(m+1)}}{ (m + 1)}

would like to know how to do by parts if possible

rg2005

i tried that first but it just made it more complicated, anyway i got the answer with this

\displaystyle\int [f(x)]^m . f'(x) dx = \frac{[f(x)]^{(m+1)}}{ (m + 1)}

would like to know how to do by parts if possible

Not sure, the recognition method is far better.

look in the K.A stroud book , mathematics for engineers 6th edition, shows it

Change sec^2x to 1 + tan^2x, you should get another I_n and a I_{n-2}

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