# Calc 121

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How do you integrate using substitution: the integral from 1 to 3 of: ((3x^2)+(2))/((x^3)+(2x))

There is a trick to this one that grealy simplifies the integral.
Let u = x^3 + 2x. Then
du = (3x^2 + 2)dx
The integral then bemoces just the integral of du/u, which is
ln u = ln (x^3 + 2x)
The limits of integration are from 1 to 3, so the answer is
ln (27 + 6) - ln (1+2) = ln 33/3 = ln 11

THANK YOU SOOOOOOOOOOOO MUCH!!! I actually understand that. Thanks!

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