- 220

- 20

- Problem Statement
- Evaluate $$\int{\sqrt{\frac{cosx - cos^3x} {1-cos^3x}}}\,dx$$

- Relevant Equations
- All the basic Integration formulae

Let

Substitute ##cosx = t##

Therefore, ##sinx\,dx = -dt##

So,

I'm stuck here...

**= ##\int{\sqrt{\frac{cosx - cos^3x} {1-cos^3x}}}\,dx##***I***= ##\int{\sqrt{\frac{cosx(1 - cos^2x)} {1 - cos^3x}}}\,dx##***I***= ##\int{\sqrt{\frac {cosx} {1 - cos^3x }}}sinx\,dx##***I*Substitute ##cosx = t##

Therefore, ##sinx\,dx = -dt##

So,

**= ##\int{-\sqrt{\frac {t} {1 - t^3}}}\,dt##***I*I'm stuck here...