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Find the integral of \(8x^3+1\).(a) 2x^4+x+C(b) 2x^6-5x+C(c) 2x^4-x+C(d) 2x^4+x^2 CThis question was posed to me during an interview for a job.This interesting question is from Integration as an Inverse Process of Differentiation topic in chapter Integrals of Mathematics – Class 12

Answer»

Right option is (a) 2x^4+x+C

Explanation: \(\int \,8X^{3+1} \,dx\)

USING \(\int \,x^n \,dx=\frac{x^{n+1}}{n+1}\), we GET

\(\int \,8x^{3+1} \,dx=\int 8x^3 \,dx+\int \,1 \,dx\)

=\(\frac{8x^{3+1}}{3+1}+x\)

=\(\frac{8x^4}{4}+x\)

=2x^4+x+C.


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