# Integration Problem

1. Nov 13, 2006

Could someone plz help me integrate (sin x)^3. Can i use any simpler method asides from integration by parts.??

2. Nov 13, 2006

$$\int \sin^{3} x \; dx = \int (1-\cos^{2}x)\sin x \; dx$$.

Let $$u = \cos x$$

3. Nov 13, 2006

### HallsofIvy

Staff Emeritus
Why do we have so many people who think differentiation and integeration are pre-calculus?

4. Nov 13, 2006

### FunkyDwarf

yeh its kind of the crux of calc rly

5. Nov 14, 2006

### VietDao29

Generally, when the power of the sine function is odd, we use the substitution u = cos(x), and change all sine functions to cosine functions by using the Pythagorean Identity : sin2x + cos2x = 1.
When the power of the cosine function is odd, we use the substitution u = sin(x), and change all cosine functions to sine functions by using the Pythagorean Identity : sin2x + cos2x = 1.
When both powers are even, we use the Power-Reduction Formulae. :)
And in your problem, the power of sine is odd, hence, we use the substitution: u = cos(x)