Mathematics

Problem

Let

J=\int \frac{x^{3}}{x^{2}+1}\,dx.

(a) Rewrite

J

as the sum of two simpler integrals that can each be evaluated directly. (b) Hence evaluate

J

, writing your final answer in its simplest form. a. (a) Decompose

\displaystyle J=\int \frac{x^{3}}{x^{2}+1}\,dx

into two simpler integrals. b. (b) Evaluate

J

in simplest form.