integral x^3 arc tan (x) DC?

Answer 1

following the suggestion , we have ...

u = arctan(x) .............. dv = x³ dx
du = 1/(1 + x²) dx ....... v = ¼ x^4

∫ x³ arctan(x) dx =
¼ x^4 arctan(x) - ¼ ∫ x^4 / (1 + x²) dx =
¼ x^4 arctan(x) - ¼ ∫ [x² - 1 + 1/(1 + x²)] dx =

¼ x^4 arctan(x) - x³/12 + ¼ x - ¼ arctan(x) + C


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Answer 2

take integral by parts

Answer 3

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