I have this kind of problem. I have to find a recurrent formula for
I(n)=integrate (tan(x))^n)dx from n=0 to a, and then I need to fine I(0) and I(1).
I wrote it like this
I(n)=int ((tan(x))^(n-1)*(tan(x)))dx and then tried to integrate it partially.
u=(tan(x))^(n-1)
du=(n-1)*((tan(x))^(n-2))/(cos(x))^2
v=int (tan(x)dx)=-log|cos(x)|
But, when I put it back...
I(n)=-tan(x)*log|cos(x)|-(n-1)*int((tan(x))^(n-2)* (log|cos(x)|/(cos(x))^2)
I have this, and I don't know what to do with this new int.