Fri 4 Mar, 2016 02:07 pm
We are integrating sin x / (cos x)^3 dx. One person broke it into (sin x /cos x) * ( 1 / (cos x)^2 and then simplified into tan x * (sec x)^2 which when integrated becomes 1/2 (tan x)^2. Another person wrote it as (cos x) ^-3 * sin x which then integrated into 1/2 (cos x) ^ -2 or 1/2 (sec x) ^2. How are these 2 equal?
Remember how when you do indefinite integrals, there is a "+ C" term? The two solutions differ by a constant. (tan x)^2 + 1 = (sec x) ^2
We were hedging that way with our answer but felt it wasn't definitive enough.Thanks!