please help. integrate 5sinx^2cosxdx?

Answer 1

I = 5 ∫ (sin ² x) (cos x) dx
Let u = sin x
du = cos x dx
I = 5 ∫ u ² du
I = 5 (u ³ / 3) + C
I = (5 / 3) sin ³ x + C

Answer 2

∫5sin²x cosx dx =
5∫ sin²x (cos x dx)

Make a u substitution
u = sin x
du = cos x dx
The integral becomes:
5∫ u² du =
(5/3)u³ + C
Remember that u = sin x
(5/3)sin³x + C

Answer 3

remember cosxdx = d(sinx)

now substitute

Int5(sinx)^2d(sinx) = 5 Int (sinx)^2 d (sin x) = (5/3)(sinx)^3

Answer 4

int(5sin^2(x)cos(x))dx
= int(5sin^2(x))d(sin(x))
= 5sin^3(x) / 3 + c