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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- algebra 1
- Need any type help
- Integration issue
- Integration problem
- Differential Equation: Application of D.E: Population Growth
- Differential Equation: Application of D.E: Exponential Decay
- Differential Equation: Application of D.E: Mixing and Flow
- Differential Equation: Application of D.E: Newton's Law of Motion
- Centroid of Composite Area: Rectangle and Two Triangles
- Integral Calculus: Integral of csc^3 cos^3 x dx

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

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

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

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

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

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

You can take it from here.