(pi^2-4*x^2)/(pi^2+x^2)-cos(x) - Wolfram|Alpha

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Input

(π^2 - 4 x^2)/(π^2 + x^2) - cos(x)

Series expansion at x=0

(1/2 - 5/π^2) x^2 + (5/π^4 - 1/24) x^4 + (1/720 - 5/π^6) x^6 + O(x^7)
(Taylor series)

Big‐O notation »

Series expansion at x=∞

(-4 + (5 π^2)/x^2 - (5 π^4)/x^4 + O((1/x)^6)) - cos(x)

Big‐O notation »

Derivative

d/dx((π^2 - 4 x^2)/(π^2 + x^2) - cos(x)) = ((π^2 + x^2)^2 sin(x) - 10 π^2 x)/(π^2 + x^2)^2

Indefinite integral

integral((π^2 - 4 x^2)/(π^2 + x^2) - cos(x)) dx = -4 x - sin(x) + 5 π tan^(-1)(x/π) + constant

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