`g(x) = int_(2x)^(3x)((u^2 - 1)/(u^2 + 1))du` Find the derivative of the function.

Textbook Question

Chapter 5, 5.3 - Problem 55 - Calculus: Early Transcendentals (7th Edition, James Stewart).
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gsarora17 | (Level 2) Associate Educator

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`g(x)=int_(2x)^(3x)(u^2-1)/(u^2+1)du`

`g(x)=int_(2x)^0(u^2-1)/(u^2+1)du+int_0^(3x)(u^2-1)/(u^2+1)du`

`g(x)=-int_0^(2x)(u^2-1)/(u^2+1)du+int_0^(3x)(u^2-1)/(u^2+1)du`

`g'(x)=-((2x)^2-1)/((2x)^2+1)d/dx(2x)+((3x)^2-1)/((3x)^2+1)d/dx(3x)`

`g'(x)=-2((4x^2-1)/(4x^2+1))+3((9x^2-1)/(9x^2+1))`

 

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