Hello,

How would I find the integral of an even powered tangent function multiplied by an odd powered secant function?

integral(tan^(2m)(x)*sec^(2k+1)(x),x)

For instance, how would we find

integral(tan^2(x)*sec(x),x)?

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?

Thanks,