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Hello, and welcome to FMH!
I think I would begin by writing:
[MATH]I=\lim_{t\to1}\left(\int_t^2 \frac{x(x+2)^2}{\sqrt{x^2-1}}\,dx\right)[/MATH]
Next, I would consider integration by parts, where:
[MATH]u=(x+2)^2\implies du=2(x+2)\,dx[/MATH]
[MATH]dv=\frac{x}{\sqrt{x^2-1}}\,dx\implies v=\sqrt{x^2-1}[/MATH]
Hence:
[MATH]I=\lim_{t\to 1}\left(\left[(x+2)^2\sqrt{x^2-1}\right]_t^2-2\int_t^2 (x+2)\sqrt{x^2-1}\,dx\right)[/MATH]
Can you continue?
H
Hi, could you perhaps show me how integrate further ?