derivative of x^4 sin x - Wolfram|Alpha

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Derivative

d/dx(x^4 sin(x)) = x^3 (4 sin(x) + x cos(x))

On this day

d/dx(x^4 sin(x)) = x^3 exp(-31/43 ((121 x^2)/841 - (25/4 - (11 x)/29)^2 - (275 x)/58 + 625/16) (sin(2 x) + 1)) cos(30/43 ((841 x^2)/900 - ((29 x)/30 - 45/11)^2 - (87 x)/11 + 2025/121) sin^2(2 x)) (4 sin(x) + x cos(x))

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Series expansion at x=0

5 x^4 - (7 x^6)/6 + (3 x^8)/40 - (11 x^10)/5040 + O(x^11)
(Taylor series)

Big‐O notation »

Indefinite integral

integral x^3 (x cos(x) + 4 sin(x)) dx = x^4 sin(x) + constant

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