Question

integration of (x²+x+1)dx/(x²+1)(x+2)​

Answer 1

Answer:

=∫x2(1−x21)dx

=\bf{\int{(x^2 - \frac{x^2}{x^2})}\,dx}=∫(x2−x2x2)dx

=\bf{\int{x^2}\,dx-\int{dx}}=∫x2dx−∫dx

=\bf{\frac{x^{2+1}}{2+1}-x+C}=2+1x2+1−x+C

=\bf{\frac{x^3}{3}-x+C}=3x3−x+C

hence, I = x³/3 - x + C