Determine the antiderivative of y=sin x*cos^n x?

To determine the antiderivative of a function, we'll have
to calculate the indefinite integral of the function (cos
x)^n*sin x.

Int (cos x)^n*sin x
dx

We'll solve the indefinite integral using substitution
technique.

We'll put cos x = t
:

-sin x dx = dt

We'll raise
to n-th power cos x and the variable t:

(cos x)^n  =
t^n

We'll re-write the
integral:

-Int t^n dt = -t^(n+1)/(n+1) +
C

We'll substitute t by cos
x:

Int [(cos x)^n]*sin x dx = -(cos
x)^(n+1)/(n+1) + C