Question

Integral of 1/(x^2-x+1) ​

Answer 1

`\boxed{\sf \displaystyle{\int}x^ndx=(x^(n+1))/(n+1)}`

`\\ \sf\longmapsto \displaystyle{\int}(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 (x^(-2+1))/(-2+1)-(x^(-1+1))/(-1+1)+1`

`\\ \sf\longmapsto (x^(-1))/(-1)-(x^0)/(0)+1`

`\\ \sf\longmapsto -(1)/(x)-(1)/(0)+1`

`\\ \sf\longmapsto -(1)/(x)-\infty+1`

`\\ \sf\longmapsto \infty`