Question

Bounded by y=(3x^2+x)/((x^2+1)(x+1)), y=0, x=1

Answer 1

What is to be done?

Answer 2

You may wish to try Partial Fractions!

\(\dfrac{3x^{2} + x}{(x^{2}+1)\cdot (x+1)} = \dfrac{1}{x+1} + \dfrac{2x}{x^{2}+1} + \dfrac{-1}{x^{2}+1}\)

Do you know how to find that expression? There are three separate integration techniques to exercise, there.