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)