5.4 Indefinite Integrals and the Net Change Theorem/3

$\int \cos ^{3}xdx=\sin {x}-{\frac {1}{3}}\sin ^{3}x+C$

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \begin{align} \frac{d}{dx} {[\sin{x} - \frac{1}{3} \sin^3{x} +C]} &= {\cos{x} - \frac{1}{3}\cdot 3\sin^2{x} \cos{x} +0} \\[2ex] & =\cos{x} - \sin^2{x}\cos{x} \\[2ex] & =\cos{x} - (1-cos^2{x})\cos{x} \\[2ex] & = \cos^3{x} \end{align} }

Note: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 1-\cos^2(x) = \sin^2(x) }