Find the indefinite integral of ysin5 xcos xSolutionWell hav

Find the indefinite integral of y=sin^5 x*cos x?

Solution

We\'ll have to evaluate the indefinite integral of the function (sin x)^5*cos x.

Int (sin x)^5*cos x dx

We\'ll solve the indefinite integral using substitution technique.

We\'ll put sin x = t => cos x dx = dt

We\'ll raise to 5th power sin x:

(sin x)^5 = t^5

We\'ll re-write the integral:

Int t^5 dt = t^6/6 + C

We\'ll replace t by sin x:

Int (sin x)^5*cos x dx = (sin x)^6/6 + C