Question

\[Evaluate \int\limits \frac{x ^{2}}{x ^{2}+1}\]

Answer 1

Try to solve the numerator as:

\(x^2 + 1 - 1\)

So,

It will become:

\[\int\limits_{}^{}\frac{x^2 + 1-1}{x^2 + 1}dx = \int\limits_{}^{}\frac{x^2 + 1}{x^2 +1}dx - \int\limits \frac{1}{x^2 + 1}dx \implies \int\limits dx - \int\limits \frac{1}{x^2 + 1}dx\]

Answer 2

Try to solve this..

Answer 3

ok thanks. :)