How solve it ? PLEASE use Integration by Change of Variable U Substitution

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1 Answer
Jim H
Jun 7, 2017

Let u = x^3-3x+16 (the argument of the radical).

Explanation:

Then du = (3x^2-3)dx = 3(x^2-1)dx

int (x^2-1)/root(3)(x^3-3x+16) dx = 1/3 int (x^3-3x+16)^(-1/3) * 3(x^2-1)dx

= 1/3 int u^(-1/3) du = 1/3(3/2 u^(2/3))+C

=1/2 root(3)((x^3-3x+16)^2) + C

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