Integral of csc^3 cos^3 xdx

March 4, 2017 - 4:53pm

#1
Integral Calculus: Integral of csc^3 cos^3 x dx

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- Transfer Formula for Moment of Inertia Using Variance in STAT Mode
- If tan (3x) = 5 tan (x), what is the value of sin (x)?
- Round off 314.587321 into four significant figures
- Minimum amount of money that must be spent before three gumballs of the same color are dispense
- Calculate 0.5 + 0.5^2 + 0.5^3 + ... + 0.5^20
- In tossing a coin, what is the probability of getting three consecutive heads or tails
- Solve for x: 1/x + 1/(x + 2) = 1
- Angle of Elevation
- Maximum possible volume, given1200cm^2 of material, square base and open top
- What number x is greater than x^n?

$\displaystyle \int \csc^3 x \cos^3 x \, dx$

$= \displaystyle \int \dfrac{1}{\sin^3 x} \cdot \cos^2 x \cdot \cos x \, dx$

$= \displaystyle \int (\sin x)^{-3} \cdot (1 - \sin^2 x) \cdot \cos x \, dx$

$= \displaystyle \int (\sin x)^{-3} (\cos x \, dx) - \int (\sin x)^{-1}(\cos x \, dx)$

$= \displaystyle \int (\sin x)^{-3} (\cos x \, dx) - \int \dfrac{\cos x \, dx}{\sin x}$

$= \displaystyle \int (\sin x)^{-3} (\cos x \, dx) - \int \cot x \, dx$

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