∫ (sin^3 x)(cos^3 x) dx =?

Question

possible solutions.....


a. (cos^5 x)/5 - (cos^3 x)/3 + C

b. (cos^6 x)/6 - (cos^4 x)/4 + C

c. (cos^7 x)/7 - (cos^5 x)/5 + C

d. (sin^3 x)/3 - (sin^5 x)/5 + C

e. (sin^5 x)/5 - (sin^7 x)/7 + C

or none of these

Answer 1

B.

remember that sin^2(x) + cos^2(x) = 1

Substituting that into the equation, you go through these steps:

sin^3(x)cos^3(x)
sinx(1-cos^2(x)) * cos^3(x)
(sinx - cos^2(x)sin(x)) (cos^3(x)
sinxcos^3(x) - cos^5(x)sinx

Now you have the derivatives to your separate pieces, so integrate the final equation to get (B).

Answer 2

If you put cos x= z
-sinxdx = dz an the integral becomes
-Int(1-z^2)*z^3 dz =- z^4/4+z^6/6 =- 1/4cos^4x+1/6cos^6x +C
(b)

Answer 3

Like whitesox reported, there comes a factor the place you in basic terms can not get a closed style answer. The (3x^2)^(x^2) is quite difficult to combine. yet the place did maximum of those people come from. you haven't got any contacts.

Answer 4

I got sin^4x/4-sin^6x/6+C so I'm pretty sure its none of those.