Integrate (sin x)^3: Simplify w/o Parts

[Chadlee88]

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

 

[courtrigrad]

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

Let $$u = \cos x$$

 

[HallsofIvy]

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

 

[FunkyDwarf]

yeh its kind of the crux of calc rly

 

[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)