integration

Question

integrate ( x^2/(x^2+a^2))dx

will that have a similar answer if a^2 was subtracted?

Answer 1

( x^2/(x^2+a^2))dx

= {(x^2 + a^2 - a^2)/ (x^2 + a^2)}dx

= {integral(x^2 +a^2) / (x^2 + a^2)}dx - a^2 integral 1/(x^2 + a^2)dx

= integral 1 dx -a^2 integral 1/(x^2 + a^2)dx

= x - a*2 * 1/a * tan^-1 (x/a) + c