2cos^2x

2cos^2x

Input
2 cos^2(x)
Roots
x = pi n – pi/2, n element Z
Series expansion at x=0
2 – 2 x^2 + (2 x^4)/3 + O(x^5)
(Taylor series)
Derivative
d/dx(2 cos^2(x)) = -4 sin(x) cos(x)
Indefinite integral
integral 2 cos^2(x) dx = x + sin(x) cos(x) + constant
Definite integral over a half-period
integral_0^(pi/2) 2 cos^2(x) dx = pi/2~~1.5708
Definite integral over a period
integral_0^pi 2 cos^2(x) dx = pi~~3.14159
Definite integral mean square
integral_0^pi (4 cos^4(x))/pi dx = 3/2 = 1.5

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