Monday, March 23, 2020

Indefinite_Integral_A0001_solutions

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 Indefinite_Integral_A0001_solutions
Indefinite_Integral_A0001 part_A

 integral x^2 sin^3(x) dx = 1/108 (-81 (x^2 - 2) cos(x) + (9 x^2 - 2) cos(3 x) - 6 x (sin(3 x) - 27 sin(x))) + constant


Indefinite_Integral_A0001 part_B
The graph

An integral may have more than one solution. Check out

Here is an alternative solution:
1/12 x^2 cos^3(x) - 3/4 x^2 cos(x) - 1/4 x^2 sin^2(x) cos(x) + 1/18 x sin^3(x) + 3/2 x sin(x) - (cos^3(x))/54 + (3 cos(x))/2 - 1/6 x sin(x) cos^2(x) + 1/18 sin^2(x) cos(x) + constant

Here is another:

-3/8 e^(-i x) x^2 - 3/8 e^(i x) x^2 + 1/24 e^(-3 i x) x^2 + 1/24 e^(3 i x) x^2 + 3/4 i e^(-i x) x - 3/4 i e^(i x) x - 1/36 i e^(-3 i x) x + 1/36 i e^(3 i x) x + (3 e^(-i x))/4 + (3 e^(i x))/4 - 1/108 e^(-3 i x) - 1/108 e^(3 i x) + constant

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