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Numerade Educator

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Problem 59 Hard Difficulty

Find the derivative of the function.

$ g(x) = \displaystyle \int^{3x}_{2x} \frac{u^2 - 1}{u^2 + 1} \, du $

$ \displaystyle \Biggl[ Hint: \int^{3x}_{2x} f(u) \, du = \int^0_{2x} f(u) \, du + \int^{3x}_0 f(u) \, du \Biggr] $

Answer

$2\frac{7 x^{2}-3}{9 x^{2}+1}-\frac{8 x^{2}-2}{4 x^{2}+1}$

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Video Transcript

Okay. Use the chain rule to find the driver of which is our goal. So what we end up with his G Prime of axe is equivalent to 27 X squared, minus three over nine X squared plus one minus eight X squared, minus two over four X squared, plus born.