Question

Integral of 1/(x^2-x+1) ​

Answer 1

$\boxed{\sf \displaystyle{\int}x^ndx=\dfrac{x^{n+1}}{n+1}}$

$\\ \sf\longmapsto \displaystyle{\int}\dfrac{1}{x^2-x+1}$

$\\ \sf\longmapsto \displaystyle{\int}x^{-2}-x^{-1}+1$

$\\ \sf\longmapsto \displaystyle{\int}x^{-2}-\displaystyle{\int}x^{-1}+\displaystyle{\int}1$

$\\ \sf\longmapsto \dfrac{x^{-2+1}}{-2+1}-\dfrac{x^{-1+1}}{-1+1}+1$

$\\ \sf\longmapsto \dfrac{x^{-1}}{-1}-\dfrac{x^0}{0}+1$

$\\ \sf\longmapsto -\dfrac{1}{x}-\dfrac{1}{0}+1$

$\\ \sf\longmapsto -\dfrac{1}{x}-\infty+1$

$\\ \sf\longmapsto \infty$