Integral Calculus: $\displaystyle \int \csc^3 x \, \cos^3 x dx$ Submitted by Terri Berri OnShop on Sat, 03/04/2017 - 16:53 Integral of csc^3 cos^3 xdx Tags Integration Log in to post comments $\displaystyle \int \csc^3 x Jhun Vert Sun, 03/05/2017 - 17:31 $\displaystyle \int \csc^3 x \cos^3 x \, dx$ $= \displaystyle \int \dfrac{1}{\sin^3 x} \cdot \cos^2 x \cdot \cos x \, dx$ $= \displaystyle \int (\sin x)^{-3} \cdot (1 - \sin^2 x) \cdot \cos x \, dx$ $= \displaystyle \int (\sin x)^{-3} (\cos x \, dx) - \int (\sin x)^{-1}(\cos x \, dx)$ $= \displaystyle \int (\sin x)^{-3} (\cos x \, dx) - \int \dfrac{\cos x \, dx}{\sin x}$ $= \displaystyle \int (\sin x)^{-3} (\cos x \, dx) - \int \cot x \, dx$ You can take it from here. Log in to post comments
$\displaystyle \int \csc^3 x Jhun Vert Sun, 03/05/2017 - 17:31 $\displaystyle \int \csc^3 x \cos^3 x \, dx$ $= \displaystyle \int \dfrac{1}{\sin^3 x} \cdot \cos^2 x \cdot \cos x \, dx$ $= \displaystyle \int (\sin x)^{-3} \cdot (1 - \sin^2 x) \cdot \cos x \, dx$ $= \displaystyle \int (\sin x)^{-3} (\cos x \, dx) - \int (\sin x)^{-1}(\cos x \, dx)$ $= \displaystyle \int (\sin x)^{-3} (\cos x \, dx) - \int \dfrac{\cos x \, dx}{\sin x}$ $= \displaystyle \int (\sin x)^{-3} (\cos x \, dx) - \int \cot x \, dx$ You can take it from here. Log in to post comments
$\displaystyle \int \csc^3 x
$\displaystyle \int \csc^3 x \cos^3 x \, dx$
$= \displaystyle \int \dfrac{1}{\sin^3 x} \cdot \cos^2 x \cdot \cos x \, dx$
$= \displaystyle \int (\sin x)^{-3} \cdot (1 - \sin^2 x) \cdot \cos x \, dx$
$= \displaystyle \int (\sin x)^{-3} (\cos x \, dx) - \int (\sin x)^{-1}(\cos x \, dx)$
$= \displaystyle \int (\sin x)^{-3} (\cos x \, dx) - \int \dfrac{\cos x \, dx}{\sin x}$
$= \displaystyle \int (\sin x)^{-3} (\cos x \, dx) - \int \cot x \, dx$
You can take it from here.