How would I find the integral of an even powered tangent function multiplied by an odd powered secant function?
For instance, how would we find
I was informed the method would be integration by parts.
Using int(udv) = uv - int(vdu)
if i choose dv to be sec(x), v is not fun to have for the next integral.
if i choose dv to be tan(x)sec(x), i have to integrate sec^3(x).
if i choose dv to be tan(x), the next integral is not fun.
So it seems that i could solve this if would learn how to integrate sec^n(x).
Are there any better methods then what I have outlined above?