∫−sin(x)*(cos(x))^7dx wrong answer? [SOLVED]

[parisse]

Run ∫−(cos(x))^7*sin(x) (product argument reversed).
The integration algorithm tries to detect a f'(u)*u' form, the first one detected that works is used. Here you could use u=cos(x) or u=sin(x), both work (once you rewrite cos(x)^6 as (1-sin(x)^2)^3). Reverting the arguments will select the other possible u.