Integral xsin(x)

Integral xsin(x)

Indefinite integral
integral x sin(x) dx = sin(x) – x cos(x) + constant
Alternate form of the integral
-1/2 e^(-i x) x – 1/2 e^(i x) x + 1/2 i e^(-i x) – 1/2 i e^(i x) + constant
Series expansion of the integral at x=0
x^3/3 – x^5/30 + x^7/840 + O(x^8)
(Taylor series)
Definite integral
integral_0^pi x sin(x) dx = pi~~3.14159

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