$\smallint \,\,\frac{{{x^4}\,\, + \,\,{x^2} + \,\,1}}{{{x^2}\,\, - \,\,x\,\, + \,\,1}}\,\,dx$ is equal to

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

\int \,\,\frac{{{x^4}\,\, + \,\,{x^2} + \,\,1}}{{{x^2}\,\, - \,\,x\,\, + \,\,1}}\,\,dx

is equal to

View answer and explanation

Correct option: B

\frac{{{x^3}}}{3}\,\, + \,\,\frac{{{x^2}}}{2}\,\, + \,\,x\,\, + \,\,c

Option B (

\frac{{{x^3}}}{3}\, + \,\,\frac{{{x^2}}}{2}\, + \,x\, + \,c

) is correct because the integral is solved by polynomial long division and then integrating the resulting polynomial.