# Evaluate the integral

1. Sep 13, 2007

### Jumpy Lee

1. The problem statement, all variables and given/known data

$$\int sin^3(x)cos^2(x)dx$$

3. The attempt at a solution

$$\int sin^3x(1-sin^2x)dx =$$ $$\int sin^3x- sin^5xdx$$

i get stuck here what do i do next and is this even right

2. Sep 13, 2007

### niceperson

we could use complex numbers (de moivres theorem) here and express sin^5x, sin^3x in terms of sin5x, sin3x

(directly integratable)

3. Sep 13, 2007

### Jumpy Lee

is that from calc 2?

4. Sep 13, 2007

### dextercioby

HINT

$$\int \left(1-\cos^{2}x\right) \cos^{2}x \left(\sin x \ dx\right)$$

Do you know how to use the substitution method ?

5. Sep 13, 2007

### Jumpy Lee

yes i do know how to use substution

6. Sep 13, 2007

### dextercioby

Do you see a possible substitution in what i wrote ?

7. Sep 13, 2007

### Jumpy Lee

u = cos x -du = sin x dx right?

Last edited: Sep 13, 2007
8. Sep 13, 2007

### dextercioby

Okay. Very good. Now use it.

9. Sep 13, 2007

### Jumpy Lee

-$$\int (u^2 - u^4)du =$$ -u^3/3 + u^5/5 +c = -cos^3x/3 + cos^5x/5 + c

10. Sep 13, 2007

Well done.