$\mathop \smallint \nolimits_{ - 1}^1 \,\,\frac{{17\,{x^5}\,\, - \,\,{x^4}\,\, + \,\,29\,{x^3} - \,\,31\,x\,\, + \,\,1}}{{{x^2} + \,\,1}}\,\,dx\,\,\;{\rm{is}}$

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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\int \nolimits_{ - 1}^1 \,\,\frac{{17\,{x^5}\,\, - \,\,{x^4}\,\, + \,\,29\,{x^3} - \,\,31\,x\,\, + \,\,1}}{{{x^2} + \,\,1}}\,\,dx\,\,\;\mathrm{is}

View answer and explanation

Correct option: C

\frac{4}{3}

Option C (

\frac{4}{3}

) is correct because the integral of the odd part is zero, and the integral of the even part is calculated to be

\frac{4}{3}