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How to integrate cos^4x

How to integrate cos^4x

Indefinite integral integral cos^4(x) dx = 1/32 (12 x + 8 sin(2 x) + sin(4 x)) + constant Expanded form of the integral (3 x)/8 + 1/4 sin(2 x) + 1/32 sin(4 x) + constant Series expansion of the integral at x=0 x – (2 x^3)/3 + x^5/3 + O(x^6) (Taylor series) Definite integral over a half-period integral_0^pi cos^4(x) dx = (3 pi)/8~~1.1781 Definite integral over a period integral_0^(2 pi) cos^4(x) dx = (3 pi)/4~~2.35619 Definite integral mean square integral_0^(2…

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Integral cosx 2

Integral cosx 2

Indefinite integral integral cos(x) 2 dx = 2 sin(x) + constant Alternate form of the integral i e^(-i x) – i e^(i x) + constant Series expansion of the integral at x=0 2 x – x^3/3 + x^5/60 + O(x^6) (Taylor series) Definite integral integral_0^(pi/2) 2 cos(x) dx = 2 Definite integral mean square integral_0^(2 pi) (2 cos^2(x))/pi dx = 2

Cosx^2 integral

Cosx^2 integral

Indefinite integral integral cos^2(x) dx = 1/2 (x + sin(x) cos(x)) + constant Expanded form of the integral x/2 + 1/2 sin(x) cos(x) + constant Series expansion of the integral at x=0 x – x^3/3 + x^5/15 + O(x^6) (Taylor series) Series expansion of the integral at x=∞ 1/4 ((2 x + O((1/x)^13)) + sin(2 x)) Definite integral over a half-period integral_0^(pi/2) cos^2(x) dx = pi/4~~0.785398 Definite integral over a period integral_0^pi cos^2(x) dx = pi/2~~1.5708 Definite integral mean square…

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4/sqrt(2)

4/sqrt(2)

Input 4/sqrt(2) Result 2 sqrt(2) Decimal approximation 2.828427124746190097603377448419396157139343750753896146353… Continued fraction [2; 1, 4^_]