Solve this integral step by step.?

Question

the indefinite integral of cos^2(x) * sin(x)

Answer 1

this is a very simple integral.
the answer is - (cos x) ^3 / 3 + C. You can arrive at that answer by taking u to be cos x, hence du = - sin x dx. And you change the integral to the integral of a monomial in u. Once you integrate in u, switch back to x.

Answer 2

It's a substitutionl

Let U=cos(x)
dU=-sin(x)

then

Int(-U^2)du = -U^3/3=-cos(x)^3/3

Answer 3

integral cos^2(x)(sin(x)) dx
make u=cos (x) and du= -sinx(x) dx
therefore it becomes integral -u^2 du
take the integral and you get -u^3/3 +C
substitute back in you get -(cos^3(x)/3) + C

Answer 4

You need to use a u-substitution. Let u = cos(x), then
du = -sin(x) dx. Thus you get:
int(cos^2(x)*sin(x) dx)
= - int(cos^2(x)*(-sin(x)) dx)
= - int(u^2 du)
= - u^3/3 + c
= - cos^3(x)/3 + c
Hope this helps.

Answer 5

I = ∫ cos ² x.sinx.dx
let u = cos x
du = - sin x.dx
I = - ∫ u ² du
I = - u ³ / 3 + C
I = (- cos ³ x) / 3 + C