I wanted to find a reduction formula for $\displaystyle \int_0^{\pi/4} tan^n x dx$

And I found this as $\displaystyle I_{n} = \frac{1}{n-1} - I_{n-2}$

I found $\displaystyle I_1$ as $\displaystyle \frac{ln2}{2}$ and the last thing I want to do is find, for example, $\displaystyle I_5$.

My working here is as follows:

$\displaystyle I_5 = \frac{1}{4} \int_0^{\pi/4} tan^3 x dx$

$\displaystyle I_3 = \frac{1}{2} \int_0^{\pi/4} tan x dx$

Which gave me

$\displaystyle I_5 = \frac{ln2}{8} - \frac{1}{8}$

Now I think that's wrong. I know I'm looking for an answer in the form

$\displaystyle a\ln2 - b$ where a and b are fractions, but I know my answer's wrong because it is negative - and I checked on wolfram alpha which gives a different integral. Could you please tell me what I have done wrong? Thanks if you can help me