integral S (-sin(t))* exp(cos^3(t)) dt

[ori]

integral
S (-sin(t))* exp(cos^3(t)) dt
t from 0 to 2pi
how do i solve it?
10x

[Tide]

Study the SIGNS of the functions very carefully over the full period! :-)

[ori]

I know that
S sin(t) dt
t from 0 to 2pi
is 0
but why also
S (-sin(t))* exp(cos^3(t)) dt
t from 0 to 2pi
?