The discussion focuses on the integration of the function sec3(2x) * tan(2x) dx. The initial approach involved separating the secant and tangent functions, leading to a substitution with u = cos(2x) and du = -sin(2x)dx. However, the correct substitution should involve u = 2x, resulting in the integral becoming (1/2) ∫ sec3(u) tan(u) du. A more efficient method suggested involves letting v = sec(u) and splitting the integrand into sec2(u) * (sec(u) tan(u)), simplifying the integration process.
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Aerosion said:Homework Statement
(integrate)sec^3(2x)*tan(2x)dx
Homework Equations
The Attempt at a Solution
Okay, so first I tried to separate secant and tangent, to get (integrate)1/cos^3(2x) * sin(2x)/cos(2x)dx. The u would be cos(2x), the du would be -du=sin(2x)dx.
I subsitute these in the aforementioned equation, whcih leaves (integrate)1/u^3 x 1/u. The problem is, I don't think this is right.